THE UNIVERSITY OF MICHIGAN COLLEGE OF LITERATURE, SCIENCE, AND THE ARTS Department of Physics Technical Report No. 23 THE POLARIZATION PARAMETER IN ELASTIC PROTON-PROTON SCATTERING FROM.75 TO 2.84 GeV Homer A. Neal, Jr. ORA Project 03106 under contract with. DEPARTMENT OF THE NAVY OFFICE OF NAVAL RESEARCH WASHINGTON, D. C. CONTRACT NO. Nonr-1224(23) NR-022-274 Chairman: Lawrence W. Jones adininistered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR April 1966

This report was also a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan, 1966.

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vii ABSTRACT xi ACKNOWLEDGMENTS xiii Io INTRODUCTION 1 II. THEORY 3 A. Density Matrix Formalism 3 B. Phase Shift Analysis 7 C. Regge Pole Predictions 10 IIII EXPERIMENTAL APPARATUS AND TECHNIQUES 17 Ao General Discussion 17 Bo Beam 20 C. Hydrogen Target 24 D. Detection Apparatus and Logic 26 IVo ANALYSIS AND RESULTS 39 A. Data Corrections 39 B. Errors 57 Co Results 62 V. DISCUSSION 75 APPENDIX I: CALIBRATION EXPERIMENT 81 APPENDIX II: RELATIONSHIP BETWEEN THE OBSERVED AND TRUE ASYMMETRIES 99 BIBLIOGRAPHY 103 iii

LIST OF TABLES Table Page I, Counter Dimensions 27 II. SiSi Counter Dimensions 29 III. Analyzer Parameters 42 IVo Polarization Parameter in Elastic Proton-Proton Scattering 63 Vo Expansion Coefficients for Polarization as a Function of O* and T 72 VI. Counter Dimensions for Calibration Experiment 87 VII. Y, 0 Values at Which Asymmetry Measurements Were Made 87 VIIIo Expansion Coefficients for the Asymmetry 89 v

LIST OF FIGURES Figure Page 1o One-pion exchange diagrams for computation of phase shiftse 9 2. Diagram for scattering process in which a pseudoscalar particle is exchanged, 13 3. The experimental layout. 18 4. The beam layout. 21 5, Polaroid exposures of beam spot at extreme energies. 22 6. The hydrogen target assembly. 25 7. Block diagram of electronics. 31 8, Typical spark chamber photographo 33 9, Photograph of spark chambers and associated fiducials. 34 10o Parameterization of incident beam trajectory relative to axis of analyzer, 40 11. Scatter plot of recoil beam at S2S2' 43 12, Histograms of recoil beam distribution in horizontal displacement and angle at carbon target. 45 130 Histograms of recoil beam distribution in vertical displacement and angle at carbon target. 46 14, Histograms of recoil beam distribution in horizontal and vertical displacement at hydrogen targets 47 159 Histograms for the distribution in horizontal angle and horizontal displacement for the rotating fiducial strips. 48 16a. Effect of instrumental differences in counters S2 and S2o 50 l6bo Effect of misalignment of counters S2-S2o 52 vii

LIST OF FIGURES (Continued) Figure Page 17. Hypothetical distribution in y used in deriving the relationship between the median of the y distribution and the counts in S2-S2, 54 18. Diagram illustrating dependence of final asymmetry on initial beam polarization, 56 19o Polarization parameter in elastic proton-proton scattering as a function of center-of-mass scattering angle at.75 GeV. 65 20. Polarization parameter in elastic proton-proton scattering as a function of center-of-mass scattering angle at lo03 GeV, 66 21o Polarization parameter in elastic proton-proton scattering as a function of center-of-mass scattering angle at 1,32 GeV. 67 22. Polarization parameter in elastic proton-proton scattering as a function of center-of-mass scattering angle at 1.63 GeV. 68 23. Polarization parameter in elastic proton-proton scattering as a function of center-of-mass scattering angle at 2.24 GeV. 69 24. Polarization parameter in elastic proton-proton scattering as a function of center-of-mass scattering angle at 2.84 GeV. 70 25. Maximum polarization versus incident kinetic energy, 74 26. Total cross section in proton-proton scattering. 76 27a. Regge theory prediction (a) for the polarization in elastic proton-proton scattering at t = -,3(GeV/c)2, 78 27bo Regge theory prediction (b) for the polarization in elastic proton-proton scattering at t = -o3(GeV/c)2. 79 28, Layout for calibration experiment. 83 29a. Logic used for differential range curve, 84 29bo Differential range curve used in determining energy of beam in calibration experiment. The horizontal scale represents only the copper in the beam; there was, in addition, a constant amount of graphite, lead and scintillatoro 85 viii

LIST OF FIGURES (Concluded) Figure Page 30. Normalized distribution of the calibration beam in the horizontal coordinate at 300 MeV. 91 31. Normalized distribution of the calibration beam in the vertical coordinate at 300 MeV. 92 32. Normalized distribution of the calibration beam in the horizontal angle at 300 MeV. 93 33. Normalized distribution of the calibration beam in the vertical angle at 300 MeV. 94 34. Asymmetry measured in calibration experiment as a function of y for various values of 0 at 400 MeV. 95 35. Asymmetry measured in calibration experiment as a function of y for various values of 0 at 300 MeV. 96 36. Asymmetry measured in calibration experiment as a function of y for various values of 0 at.200 MeV. 96 37. Asymmetry measured in calibration experiment as a function of y for various values of 0 at 150 MeV. 97 38. Asymmetry measured in calibration experiment as a function of y for various values of 0 at 125 MeV. 97 39. Geometry of telescopes for trajectories not coincident with axis of rotation. 100 ix

ABSTRACT A double-scattering technique-has been employed to measure the polarization parameter in elastic proton-proton scattering at.75, 1l03, 1.32, 1o63, 2o24, and 2084 GeVo An external proton beam from the Brookhaven Cosmotron was focussed on a three inch long liquid hydrogen target and the elastic recoil and scattered protons were detected in coincidence by scintillation counters. The polarization produced in the scattering process was inferred from the azimuthal asymmetry exhibited in the scattering of the recoil beam from a carbon target. This asymmetry was measured by a set of two scintillation counter telescopes which symmetrically viewed the carbon target, The analyzing power of this arrangement was previcusly determined in an independent experiment employing a 40% polarized proton beam at the Carnegie Institute of Technology synchrocyclotrono The range of calibration energies, 103 to 415 MeV, corresponds to the basic range of recoil energies analyzed in the primary experiment. The analyzing power was extended to 1000 MeV by utilizing the antisymmetry of the polarization parameter about 90~ in the center-of-mass system. Checks were frequently made to insure that the external proton beam was unpolarizedo False asymmetries were cancelled to a high order by periodically rotating the analyzer 1800 about the recoil beam lineo Spark chambers were employed to obtain the spatial distribution of the beam as it entered the analyzer. This information allowed an accurate determination of the corrections necessary to compensate for any misalignment of the axis of the analyzer relative to the incident xi

beamo The corrected values of the polarization parameter are exhibited as a function of the center-of-mass scattering angle for each incident beam energy. The prediction of the Regge theory that the polarization parameter in elastic proton-proton scattering is related to the total p-p and p-p cross sections has been found to be consistent with the experimental results o xii

ACKNOWLEDGMENTS I would like to thank Professor Michael J. Longo for his invaluable assistance in all phases of this work. I also wish to express my gratitude to Professor Oliver E. Overseth and Professor Martin L. Perl for their numerous contributions to the success of this experiment. For several discussions regarding theoretical interpretation of the experimental results, I am very grateful to Professor Marc Ho Ross and Professor Gordon Lo Kane. I am indebted to my colleagues David E. Pellett, Smith To Powell III, Stephen W. Kormanyos, and Billy Wo Loo for their valuable help during the data accumulation stage of the experiment I wish to thank Mro Orman Haas for the construction of much of the experimental apparatus. I am also grateful to the members of the Cosmotron staff, particularly Mro Malcom McCrum, for their generous technical assistance during the rigging and performance of the experiment. I wish to express my gratitude to the Detroit Evening News Association and the John Hay Whitney Foundation for fellowships awarded during my graduate studies. xiii

Io INTRODUCTION The nature of the interaction between nucleons is of fundamental importanceo A complete theory of nucleon-nucleon interactions must predict not only the angular distributions in scattering experiments but also correlations between the initial and final nucleon spin states. The first successful experimental investigation of the spin dependence of the nucleonnucleon interaction was reported by Oxley, Cartwright and Rouvina1 in 1954. Relatively large proton-proton polarization effects were observed in their studies near 225 MeV, as had been to some extent suggested by the appreciable non-central terms in the existing models of Christian and Noyes,2 Case and Pais,3 and Jastrow.4 There have since been many proton-proton polarization experiments below 1 GeV. Proton-proton polarization data have also been reported by Bareyre et al.5 at 1.7 GeV, and recently by Chamberlain et al.,6 who employed a polarized target, at 17, 2.85, 3.50, 4.00, 5.05, and 6.15 GeV, and by Kanavets et al.7 at 8.5 GeV. At the present there exists no theory that successfully explains the proton-proton interaction in the region 1 to 3 GeVo This region is of considerable interest since here neither high nor low-energy approximations are expected to be valid. The polarization data in this range is, however, sparse. Comparison of the results from the two previous experiments at 1.7 GeV furthermore reveals the existence of a significant discrepancy. In the present experiment, a definitive study of the polarization parameter in elastic proton-proton scattering from.75 to 2o84 GeV has been 1

made. The experimental results can be interpreted in terms of the Regge theory prediction that, for fixed small four-momentum transfer, the polarization varies as (a(pp)-a(pp))/a(pp) (where c(pp) and a(pp) are the total cross sections for p-p and p-p scattering) if only the Pomeranchuck, secondPomeranchuck, p and w poles are considered and certain assumptions are made 8 regarding the functional behavior of the poles and pole-residues. 2

II. THEORY The density matrix formalism is the basis for practically all contemporary analyses of polarization phenomena. Using this formalism we will outline the derivation of the relationship between polarization, asymmetry, and analyzing power for a scattering process. The possibility of calculating the phase shifts for the proton-proton system in the region 1 to 3 GeV is briefly considered. Finally,. Regge pole predictions for the polarization in proton-proton scattering are examined. A. DENSITY MATRIX FORMALISM The polarization of a beam of particles is defined as the expectation value of the Pauli spin vector, a, averaged over all particles in the beam. In general, the goal of polarization experiments is to determine the scattering characteristics of individual spin states. Experimentally, however, we must deal with a mixture of spin states. In order to study the connection between the scattering properties of the "beam averaged" quantum state and individual quantum states, it is convenient to utilize the Von Neumann density matrix. The density matrix formalism was introduced in the analysis of polarization phenomena by Wolfenstein and Ashkin)9 and Dalitz.lO Our presentation here parallels that given by Stapp.ll Let us consider a complete set of quantum states li>. If one defines the density matrix as p = fiPi, (1) i1

where fi is the fractional number of particles in the ith state, and Pj li> = ij, (2) then the expectation value of any operator,,.is <B> = Tr(p8) = Z fj <jll>. (3) J Consider now a scattering process with initial and final states specified by ai and $f If S is the scattering matrix for the process, i.e., if = S4i, and R = S-1, then the density matrix, ps, describing the scattered wave is related to the initial state density matrix Pi by Ps = R pi + () We are here primarily interested in the expectation value of spin-space operators in a particular momentum state k. Let es be a spin-space operator, then its expectation value in momentum state k is <<8_ )> - Tr(p>?_tI0s) (5) < F < => X Tr(pe(k)) where (() is a projection operator for momentum state k, and Tr(p9(k)~g) = Z <ilP?(k) sli> Z E< IpOs li>i = Tr(p(k)s), (6) where p(k) is the spin-space density matrix for momentum state ko Note that Tr(p( k)) = Tr p(k) and therefore <s> = Tr(p(k)8s)/Tr(p(k)). (7) Consider now the elastic scattering of two (Pauli) protons. If we take for our representation the sixteen base vectors al d (where cm is the mth com

ponent of the Pauli spin vector for particle I = 1 or 2, with ao = 1) it is seen that p(W) = Tr(p()) <o, (8) 4 a since p(k) is certainly expandable as p(k) = 7 a ca and from (7) Tr p(k) <a>k a Tr(a) = a Xv (since Tr(ao co2)=-45kbv6). Thus, knowing the fifteen spin correlation 1 2 parameters <aCa>k is equivalent to knowing the density matrix, and, of course, the converse is also true. It is to be noticed in the development so far that the normalization has remained arbitrary. Here we choose the normalization such that Ps(k) M(k,k')pi(k')M+(k,k'), (9) where M(k,k') is the spin scattering matrix whose elements are the scattering amplitudes between the various initial and final spin states (with k'+k). That only a change in normalization has been made is evident from the fact that M(k,k') = const. <-kIRlJk'> The differential cross section is then da (Q) _ Trp( _ Tr M(;')pi(')M(k k') (10) d(,) Trp(') - Trp ) (') 5

It has been shown in Ref. 9 that the most general form of the spin scattering matrix for the proton-proton system consistent with invariance under time reversal, spatial reflections, rotations, and particle exchange is M(kk') = a + b(a.N+a2N.) + c(.N.N) + d(a.. + K) -l'~2 " -11 - -l2 + e(.cal.P2 Pr.K2 oK) (11) where a, b, c, d, and e are functions of k.k' and k, and where N=kxk'/ kxk', P= (k'+k)/l'+kl, and K= (k-k')/lk-k'I. (The corresponding matrix for the spin 1/2 - spin 0 case is simply M(k,k') = a+ba.N and the representation reduces to that of a single Pauli particle.) By utilizing only the assumed form of the matrix M and constructing the appropriate density matrices (using relations (7) to (19)) one can readily derive the following points which are pertinent to the present experiment: 1. If a beam of polarization R and center-of-Mass momentum k' scatters from an arbitrary target at an angle +~ in the plane whose normal is N, then:(k',) =. NA(k' () where E(k',4) =I(c)-I(-N) I( D+I(-4) and I()) is the differential cross section for scattering at angle 4 in the plane containing f' and k'xNi r(k',+) is commonly called the azimuthal asymmetry. A(k',4) depends only on k', 4 and properties of the target and is commonly referred to as the'nalyzing power" of the interaction. This relationship forms the basis for the techniques employed in this experiment. The asymmetry, e(k',4), is easily obtained experimentally, and consequently, 6

so is A(k',$) when P is known, An independent experiment was performed to measure what is essentially the quantity A(k',+). If one knows this quantity, then measurement of the azimuthal asymmetry exhibited by a beam of known energy determines the polarization of that beam. 2, The direction of the polarization vector produced in scattering an unpolarized beam from an unpolarized target is normal to the scattering plane. This can also be inferred directly from the requirement that the interaction be invariant under spatial reflections and the fact that the only axial vectors that can be formed from the physical vectors.kand kt are -kxkk' The treatment of this topic has been non-relativistic, It should be pointed out that a relativistic treatment, though somewhat more involved, yields exactly the same results. This arises because the required Lorentz rotation is about an axis normal to the scattering plane, and thus parallel with the polarization vector.12'13 B. PHASE SHIFT ANALYSIS The possibility of analyzing data from this experiment in terms of phase shifts is briefly considered in this section. Phase shifts provide the most complete description of a scattering process and a convenient connection between theory and experiment. However, phase shift analyses become quite complicated at energies above 400 MeV, where absorption processes can not be neglected. For example, in order to carry out such an analysis for Lmax = 4, there exists one mixing parameter, 7

three singlet and six triplet complex phase shifts to be determined. At present, only cross section and polarization data are available in the region 1 to 3 GeV and, consequently, one must deal with eleven free parameters (i.e., an expansion of I and IP in Legendre polynomials determines only 8 parameters). With this freedom, a multiplicity of phase shift solutions which satisfactorily reproduce the existing data would be obtained. Future experimental data on the proton-proton spin correlation parameters would, of course, limit the number of possible solutions. It should be remarked that Imax = 4 is somewhat conservative for the energy region of interest, and therefore a proper analysis would lead to even more ambiguities than indicated aboveo Now consider the possibility of theoretically predicting some of the phase shifts and calculating the remainder from the experimental data. In the two existing p-p phase shift analyses above 400 MeV (at 660 and 970 MeV) the resonance model has been employed in this manner.16 It has been assumed that the principal inelastic process is single pion production (Fig, lb) in a (3/2, 3/2) state, with the remaining nucleon in a S or Pstate (at 660 MeV) or S, P, or D- state (at 970 MeV), The imaginary part of each phase shift considered is then related to cross sections of processes allowed by the above assumptions. Low energy phase shift solutions were extrapolated to the energy of interest and used to limit the "search" region of the free parameters. Notwithstanding the additional complications due to a larger 1max' a phase shift analysis of our data could be carried out along these lines if a reasonable model could be constructed to supplant 8

C — A — A —,~ (o) (b) (c) Fig. 1. One-pion exchange diagrams for computation of phase shifts. (a) Onepion exchange diagram for the process N+N + N+N. In the energy region below 400 MeV, higher real phase shifts have been successfully predicted from this model (Ref. 14). (b) Inelastic one-pion exchange diagram for the process N+N + N+N+n. This interaction has been assumed to be the dominant inelastic process in all existing phase shift analyses above 400 MeV. Phillips (Ref. 15) has pointed out that while a process as shown in (c) can give singularities near those from (b), the integrated cross section appears to still be dominated by (b) since the other processes can occur only over restricted energy and angular regions.

the above usage of the resonance model, whose range of applicability is _ 400 to 1000 MeV,16 C. REGGE POLE PREDICTIONS The hypothesis of Regge poles in high energy nucleon-nucleon scattering leads to simple predictions for the proton-proton polarization parameter when certain assumptions are made. We will briefly indicate here how these predictions are derived and in Section V compare the predictions with the experimental results. The details of the derivations are to be found in Refs. 17, 18, and 19. Let the proton-proton scattering process be characterized by a spinspace matrix i, chosen so the differential cross section for the process Pd< + P i X+' is dc where \1X2 and \X.2 represent the helicities of the initial and final state protons, respectively. The matrix $ depends only on the scattering angle, 0, and the total center-of-mass energy, Et, and is related to the Feynman amplitudde for the process by the equation M = (2tEt/m2) <k1X2l 1li2>, (12) where m is the proton mass. Symmetry requirements limit the number of independent matrix elements to five. In order to derive the relations between the various $ matrix elements, it is convenient to utilize the known properties of the helicity amplitudes introduced by Jacob and Wick.20 In terms 10

of these amplitudes, the elements of 4 are <x21 Il12> = () (2J+l) < XilTj(Et) l 2,() (13) J where l TJ(Et)l i2> = lS(1)12>X I 1 x, p is the center-of-mass momentum and dK,, are reduced rotation matrices with X = kl-X2 and X' = XI-X2, and S is the angular momentum (J) submatrix of the S- matrix. The rotation matrices have the property that da() = (-1) a() = da(e) () Conservation of parity and isotopic: spin require that <1x i (Et) 1 12> = <-X - ii(Et)l 1 X2> (15) and <.l2 I TJ (Et) l Xl2> = 1 l ITJ(Et)' I21> In addition, time reversal invariance implies <2! I J(Et) I 1X2> = <A12 I (Et) I ix>. (16) The symmetry relations for the elements <AlX2j4)\l'2> are now easily obtained. Here we desire only to find a complete set of independent amplitudes. A suitable choice is found to be 41 = <++1 1++> 42 - <++1l — > 43 - <+-jll+-> 04 - <+-l 4 +> 45 - <++ 14+-> (17) where the quantity 1/2 in the helicity specification has been suppressed. Each Ij is related to a Feynman amplitude through Eq. (14). Recall now that in a scattering process with pseudoscalar exchange, as shown in 11

Fig. 2, the Feynman amplitude is given by Mac-bd = const. Ub75ua 2_t Ud5Uc (18) where uj is a spinor describing particle j, p is the mass of the exchanged particle, and t is the square of the four-momentum transfer. In the Regge theory, it is assumed that the amplitude for the s channel scattering process can be represented as an expansion of contributions from poles in the complex angular momentum (J) plane in the t channel. The position of each pole in the complex J plane changes with energy and, in the t channel, the trajectory corresponding to each pole is specified in the following by a(t) and the residue of each pole by P(t). The exchange of a particle in the diagram in Fig. 2 is analogous to the exchange of a Regge trajectory. Formally, the Regge amplitude corresponding to the exchange of a trajectory is obtained from Eq. (18) by the substitution 1 t Si(t) l P(t)(C)s et)+Pc(t)(-cos t) (t), where Pi is the ith Legendre polynomial and et is the center-of-mass scattering angle in the t reaction. The relation (12) is still true, where M now represents the Regge amplitude. Thus, each ij may be expressed as an expansion in Regge poles. It should be remarked that, as in Fig. 2 where the exchanged particle must have quantum numbers consistent with the initial and final states, only those trajectories whose associated quantum numbers are appropriate need be considered. In the following, the matrix R will represent the relativistic generalization of the density matrix introduced in Section A(4 corresponds to the spinspace matrix M in that context). The optical theorem for proton-proton 12

a b s-chonnel -— pH k-I*I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\ C^ I t - channel Fig. 2. Diagram for scattering process in which a pseudoscalar particle is exchanged.

scattering in terms of the density matrix, center-of-mass momentum p, and 4 becomes a(pp) = Im(Tr Ri )t = o p where Ri is the density matrix for an unpolarized beam and can be written as Ri = bl%5X2%/4 (see Eq. (8)) The total cross section then reduces to s(pp) = 2 Im(+l+43)t = o From Eq. (7), we note that the polarization parameter can be expressed as P = Tr(4Ri4 S)/Tr(4Ri4 ) where S is the relativistic generalization of (a3) and Ri is again the density matrix corresponding to an incident unpolarized beam. Performing the indicated operation and utilizing the relations between the various 4 matrix elements leads to p = _____Im(( 1+42+43-44))+5}... 2 {11141 121+l2+2412+ 1 14_1 The principle of crossing symmetry relates the scattering amplitudes for the s and t- channel processes. That is, knowledge of the 4j's allows the construction of the js, where for our case 4 describes the process p+p + p+p. We may write the total cross section for pp scattering as a(fpp) = 2 Im(41+43) = o Now if one evaluates the above expression for (P in the limit s + oo and 14

assumes the only contributing Regge poles are the Pomeranchuck P, and its nearest neighbor N, it is found that () a ~- f(t)(s/so)^P(t)- N(t) where f is some function of t, and so is a constant generally taken to be 2m2, where m is the nucleon mass.17 On the other hand, by considering the contributions from the secondPomeranchuck P' P, p, and X poles, Hara has shown that the polarization parameter may be related to the total pp and pp cross sections as (p- a t A(t)(o(pp)-a(pp))/ra(pp) where a(pp) and a(pp) represent the total cross sections for pp and pp scattering, and A(t) is a sum of pole residue terms that is expected to be 18 a slowly varying function of t.8 The J and F trajectories have been shown not to contribute in forward nucleon-nucleon scattering in Ref. 21. Even if these trajectories did contribute to the forward amplitude, the magnitude of the contribution would be expected to decrease relatively fast with increasing energy due to the negative a parameters involved. The principal physical difference in the two predictions lies in the assumptions made about the participating poles, and therefore the relative success of the two predictions is of considerable interest. Our results at t = -.3 (GeV/c) have been independently fitted with the following functional forms: a. P(s) = a sb, a and b constants bo P(s) = c((a(pp)-o(pp))/o'(pp)), c constant The resulting fitting curves are presented and discussed in Section VO 15

IIIo EXPERIMENTAL APPARATUS AND TECHNIQUES A. GENERAL DISCUSSION The polarization parameter in elastic proton-proton scattering has been measured in the energy region,75 to 2.84 GeV by employing a double-scattering technique. An external proton beam from the Cosmotron accelerator was extracted at the desired energy and focused on a 3" long liquid hydrogen targeto The elastic scattered and recoil protons were detected by scintillation counter telescopes S1S1 and So(S2SA) at the appropriate kinematic angles (Fig. 3), The geometry was such that counts from inelastic processes were negligible. The polarization of the recoil beam was determined from the left-right asymmetry exhibited in its scattering from a carbon target. This asymmetry was measured by scintillation counter telescopes TTT2 and UiU2o In order to cancel any instrumental asymmetries, these telescopes were periodically interchanged by rotating the analyzer 180~ about the recoil beam lineo The amount of carbon in the second target depended on the recoil beam energy. Typically.5% to 3% of the protons incident on the carbon target scattered into the telescopes. A beam pulse of 4 x 109 protons incident on the hydrogen target resulted in about 20 analyzed recoil protons. The analyzing power for the geometry used in the second scattering was determined in an independent calibration experiment utilizing a 40% polarized proton beam at the Carnegie Institute of Technology synchrocyclotron (see Appendix I) o The range of calibration energies, 103-415 MeV, corresponds to the principal 17

~ - \/SPARK CHAMBERS So,'LH ~ ~ ~ ~~ A ARBN TARGET~\ 6 \ \ 1'1'- l^ 0LEAD ABSORBER s///~ ^^^^q^ ~'2/ I(I)~~~~~I i'/' - - " ~'. ~~DOOR 0 2 3I4 5 6 FEET KFg. 5. The experimental layout.

range of recoil proton energies analyzed in the primary experiment. The analyzing power was determined also at several energies above 415 MeV by utilizing the antisymmetry of the pp polarization parameter about 900 in the center-of-mass system. For example, at the incident proton beam energy of 1.35 GeV the scattered protons of energy 350 MeV and 1000 MeV have the same polarization in magnitude; we can directly determine the asymmetry exhibited by the 1000 MeV protons and the polarization of the 350 MeV protons (since this energy lies in the calibration range), and can consequently determine the analyzing power at 1000 MeVo The argument, of course, assumes that the incident beam is unpolarized. Frequent checks were made to insure that the incident beam was unpolarized by separately analyzing recoil protons on each side of the incident beam line, In all cases, the incident polarization determined in this manner was consistent with zero. Important accidental rates were constantly monitored and were found to be negligibly small, Also, contamination due to scattering from the hydrogen target assembly was found to be completely negligible. The left-right asymmetry in scattering from the carbon target is quite sensitive to the relative alignment of the average incident beam trajectory and the axis of the analyzer. In order to make corrections for any such misalignment, spark chambers were employed upstream of the analyzer in both the analysis and calibration experiments to obtain the spatial and angular distribution of the incident beam with respect to the analyzero In the calibration experiment, the dependence of the asymmetry on the relative orientation of the analyzer and the average beam trajectory was studied in 19

detail. Results from this study furnished the derivatives necessary in make ing the required corrections in the primary experiment. Bo BEAM The beam layout is shown in Fig. 4. External proton beam III from the Cosmotron was extracted at the energies.75, 1o03, 1,32, 1.63, 2924, and 2.84 GeV and focused on the hydrogen target by means of three bending magnets, M300, M304 and M305, and two pairs of quadrupole magnets, Q302-Q303 and Q306-Q3070 First, the beam is corrected in angle by magnet M500; this is necessary because the virtual beam source in the Cosmotron varies laterally with energy. Quadrupoles Q302-Q303 then focus the beam at F1. This intermediate focus in included in the beam design to optimize transmission and therefore minimize background contamination. Magnets M304 and M305 bend the beam through a total angle of 15~. Finally, quadrupoles Q306-Q307 are used to achieve a second focus at the hydrogen target. The width of the beam spot at the hydrogen target varied from 5 3/16" at 2.84 GeV to l1-1/4" at.75 GeV. The angular spread was typically ~.5~. Polaroid exposures in the beam at.75 and 2.84 GeV. are shown in Fig.o 5 Initial values for the magnet gradients were computed utilizing the 7090 computer program OPTIKo22 The corresponding currents were determined from existing gradient-current graphs. Final operating currents were determined by studying properties of the beam spots at the two foci (by means of television cameras which viewed scintillating screens placed in the beam) 20

P~~~ ~ ~ ~ ~ M~~~~~~~~~~~~~~~~~~~~ 300 HlOX36~~~~~ 4M SrO -)(I 141 8 M -6 /..:- UR6~Tl MK3 H~~~~~~~~~~~~~,~~~~~.,,,,....p tv!EXrp/I RI SCA L E.' FEET Fig. 4. The beam layout.

(a) Polaroid exposure at (b) Polaroid exposure at hyfirst focus at.75 drogen target at.75 GeV. GeV. (c) Polaroid exposure (d) Polaroid exposure at hyat first focus at drogen target at 2.84 2.84 GeV. GeV. Fig. 5. Polaroid exposures at the extreme energies. Beam spot size is generally exaggerated due to overexposure. 22

as.the magnet currents were varied about their initial values. In most cases the final and initial currents differed by less than 1%o Intensities up to 1 x 1011 protons per pulse were obtainable in this beam. However, our requirement that the important accidental rates in the analyzer be less than 2% generally limited the maximum usable intensity to 4 x 109 protons per pulse. The beam spill was approximately 150 ms with an effective duty cycle of 50%. The energy of the incident beam was determined initially by the usual field and frequency methods as described in a Cosmotron internal reporto23 A somewhat more reliable determination results from the analysis of the experimental kinematic parameters. As will be described in a later section, spark chambers were used to sample the recoil beam, By projecting each track in the sample to the hydrogen target and requiring that the conjugate proton scatter, at a point in the hydrogen target along this trajectory, at the average angle allowed by the geometry, one is able to calculate an incident proton energy value for each such event. The average of these values taken over several hundred events at each of many angular settings is expected to provide an accurate determination of the beam energy. This scheme is somewhat insensitive to small lateral and angular changes in the incident beam trajectory, since for these changes the sum of the scattered and recoil proton angles remains practically constant. The values of the energies used throughout this work were obtained in this manner and differ from the field-frequency values by less than 3~5o5 in all caseso 23

The two pairs of scintillation counters R1-La and R2-L2 were placed in the tails of the incident beam, as shown in Fig. 3, to provide constant monitoring of the beam position and angle. Also, a television camera viewed a.005" scintillator which was centered on the beam line at the hydrogen target. Corrections were easily made for any deviation of the beam from the design trajectory by varying the currents in magnets M304 and M505. In order to reduce the halo around the focal spot, a 24" deep lead collimator with a 2" x 2" opening was placed upstream of the hydrogen target. The beam was also collimated in magnet M500 to reduce the beam phase space volume, The width of this collimator was varied with beam energy. Beam vacuum pipes were employed between magnets M300 and M304, and between magnet 1M05 and the hydrogen target. Helium bags were used over that portion of the beam path where beam pipes could not conveniently be used, Since helium has a much lower density than air, it effectively reduces the multiple coulomb scattering of the beam. Co HYDROGEN TARGET The exterior features of the hydrogen target assembly are shown in Fig, 60 Liquid hydrogen is contained in the inner vessel A, which is a 1 5" long,.01" thick, mylar cylinder of radius 1.25", with a.005" thick mylar hemispherical cup attached at each end. The overall length of the target in the median plane is 3"1 The target vessel is located in a vacuum produced by evacuating outer vessel CO To reduce heat transfer further, the hydrogen target was wrapped with o002" of superinsulation (aluminized mylar), The incident beam enters 24

cm, 4"3 iilii......i i~?!?!..?z i;;.....~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~......~..J.......... 0 ii~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!iiiii~ ou. 4..f. 7'... 25~~~~~~~~~~~~~~Q ~-~~~~~~~~~~~~~~~~~~~~~~~h iiiii1~

vessel C through a o005" thick, circular mylar window, and the scattered protons emerge through two.005" mylar wraplaround windows (only the inner window supports the vacuum). The center of the target vessel was marked with a vertical crosshair. The superinsulation described above was wrapped in such a way that the crosshair was externally visible. This crosshair was used to position the target in the designed location and to also provide a reference for aligning the various counters relative to the hydrogen target. The effect of background events due to scattering from the mylar associated with the target assembly was frequently investigated by accumulating data with the target empty. It was found that this effect was completely negligible, Do DETECTION APPARATUS AND LOGIC The deployment of the various counters is shown in Fig, 3. All counters are plastic scintillators viewed by RCA 6810-A photomultipliers through lucite light pipes. Counter dimensions are given in Table Io In order to facilitate the alignment of the axis of the analyzer with the hydrogen target by means of a transit at the downstream end of the analyzer, counters Ao, and S2-S2 were designed with 1" diameter holes through their centers, Counters R1-L1 and R2-L2 are beam position monitoring counters, The high voltages on these counters were adjusted so that R1 and R2 produced the same output at L1 and L29 respectively, when exposed to identical beams, These counters were employed in the tails of the incident beam. The signals from these four counters were displayed on an oscilloscope; a change 26

TABLE I COUNTER DIMENSIONS Counter Width x Height x Thickness S2 1-1/2" x 911 x 1/4"* SA 1-1/2" x 9" x 1/4 1* Ao 9" x 21" x 1/2" (1-1/8" dia. hole through center) Al 10-1/4" x 22" x 1/2" A2 10-1/4" x 22" x 1/2" TA 8" x 18" x 1/2" T2 10-1/4" x 22" x 1/2" U1 8" x 18" x 1/2" U2 10-1/4" x 22" x 1/2" So 3-1/4" x 9-3/8" x 1/8" S1 see Table II Si see Table II *Counters S2 and S2 are identical and are mounted as shown below: T S2 s2 X9" 1l" dia. hole l/ ucite light pipes The dimensions of the S2-S2 counters were changed during the latter part of the experiment, after it was realized that the angular resolution could be appreciably improved without significantly sacrificing analyzing rate. Agreement of the polarization measured in the two situations was good and hence no distinction is made in the presentation of the results~ The new dimensions of S2 and S2 were 1-1/8" x 9" (wxh), with all other parameters as shown above 27

in the relative amplitude of the Ri-L1 signals and/or the R2-L2 signals indicated a shift in the beam positiono In order to prevent the accidental rates in the various counters from becoming prohibitively large when the spill length or intensity of the external beam fluctuated, the output from an auxiliary lucite cerenkov counter (not shown), which was located directly in the external beam, was used to gate off the electronics while the beam intensity was in excess of some preset level. This technique proved effective since most "spikes" in the beam spill had a width of a few milliseconds, while the reaction time of the monitor counter and the associated logic was a few nanoseconds. Scattered protons were detected by the "S1' arm, which consists of two counters, S1 and S1. The dimensions of the counters used as S1 and S1 changed with energy. Design studies showed that the most reasonable compromise between high counting rates and low accidental rates would be obtained by choosing S2-S2 S1 and S1 such that they subtended approximately the same center of mass solid angle. The dimensions of the S2-S2 counters were taken fixed (see Table I) and those of S1 and Si variable. Each S1 and S{ scintillator was mounted on identical threaded fittings that allowed rapid changeover from one pair to another. See Table II for the dimensions of the S1 and S1 counters usedo The recoil protons were detected and analyzed by counters on the'S2" arm in appropriately delayed coincidence with the scattered protons (Sis{). A typical recol proton which is accepted by the geometry produces a count in So and in S2 or S22 either scatters into one of the two telescopes 28

TABLE II Sj-Sj COUNTER DIMENSIONS* Si Si (width x height) (width x height) 1.35" x 1035" 2.34" x 3.12" 1 56" x 2.08" 1.68" x 2.76" v168" X1 2.,76"1 2Q85" x 50 25" 1 90" x 3 50" 2. 21 " x 4. 58"1 3.75" x 9.00" 2.50" x 6.00" *Thickness of all counters: 1/4". U(=U1U2) or T(=T1T2), or passes through anti-counter Ao, Anti-counter Ao served to greatly reduce the accidental rates by negating any chance coincidences that occur when the proton scatters through too small an angle to be accepted by the telescopes. Anti-counters Al and A2 served primarily to reduce the accidental events in which a proton directly enters telescope T or U without passing through S2 or S2. The analyzer consists of the counters S2, S2 T1, T2, U1, U2, Ao and a carbon target, Each of these components is rigidly mounted in a single rotating carriage, for which a rotation of 180~ effectively interchanges the two telescopes T and U. As is shown in Section IV-A, the average of the azimuthal asymmetries measured with the analyzer in the two orientations is essentially independent of any instrumental differences between the two telescopes. Counters S2 and S2 are also effectively interchanged by a 180" rotation of the carriage. When the quantity ((S2-Ss2/(s2+Sg2S-S2)/(S+S2) II) 29

is zero, where the subscripts refer to the carriage orientation, the median of the beam at Sa-S is very nearly centered on the axis of rotation of S2-S2' This fact was utilized in the experiment to guarantee that the separation of the axis of the analyzer and the recoil beam at the analyzer would be small. As a matter of experimental procedure, prior to accumulating data at each point the angular setting of the Si arm was slightly varied until the above expression was less than o02 in magnitude. Spark chambers (see Fig. 3) were employed to determine the relative orientation of the average recoil beam trajectory and the axis of the analyzero Deviation from colinearity was generally small (< O07" at carbon target and <.07~, in horizontal plane). The measured corrections were applied to the data in the manner discussed in Section IV-A. The two spark chambers are identical thin-plate (O001" Al) chambers with four.375" gaps and a width and height of 5" and 12-1/2", respectively The chambers were filled with a mixture of 85% helium and 15% neon gases at a pressure of 1 atmosphere. During the course of the experiment both hydrogen thyratrons and spark gaps were used to "fire" the chambers, The chambers were triggered by every Nth analyzed recoil. proton, where N was typically in the range 10 to 20. The scaler unit initiating the trigger was not reset between beam pulses, and consequently there existed no correlation between the triggering and the beam spill; this insured that the sample of events photographed was unbiased. Typically, one or two events were photographed per frame of film. The film was advanced between beam pulses. A diagram of the electronic logic is shown in Figo 7. Most logic units were commercially available modules 30

SI S So S2 S2 Ao A, A2 T, T2 UI U2 to coincidence circuits S, Sp So S2 om P > if ier C' nti " ~ _C ^ s; s', So SI C 1 I O I I~ -I- I c ^ ^~^ ^ o I CI ^'^"1 Ito spark,~' *chamber M triggering 1i C I Coincidence I,i D' Discriminator l Splitter I0 /0 0 Mixer I(n -' ( I % - 1 n I.__'_ Dela y I 03 (n':: i-' ~ Scaler Fig. 7. Block diagram of electronics.

described in Refo 24, In order to accurately determine the position of the axis of rotation of the analyzer in the spark chamber pictures, fiducial strips which rotated with the analyzer were viewed by the camerao A typical spark chamber photograph is shown in Fig. 8o Fiducials F1 and F2 are fixed and F3 to F6 rotate. Directly underneath F3o F6 are fiducials F3., F6 which appear on the spark chamber film when the analyzer is in the alternate orientation. The axis of rotation is determined, for example, as the average of the line F3F4 (measured with the analyzer in the orientation shown) and the line F3F4 (measured with the analyzer rotated by 180~ from the orientation shown). All fiducials were Sylvania luminescent panels with a mask of the desired dimensions superimposed (see Figo 9). These panels were continuously powered by 70 voaoCo A Beattie- Coleman camera and 35mm Linagraph Shellburst film were employed for the photographyo The nominal angular acceptance of the telescopes T and U is 9~-26~o This range represents a compromise between high analyzing power and high counting rate. Different configurations of the analyzer were used depending on the recoil proton energy; a configuration is specified by the thickness of the carbon target and the amount of lead absorber between T1 and T2 (and U1U2). The absorber served to discriminate against low energy background. These parameters, for each configuration (see Table II), were chosen to optimize the analyzing rate and minimize background contamination over each respective range of energieso The maximum amount of carbon in the target was limited by the requirement that the recoil protons, after scattering 32

~qcds3TSooqcd aqmesBzqo Beds'Od^TI "AL// L 1 / \ *I I /' 0 * U / U / ~ Jr

Binoryfa S-2 Spark chambers B, f ome s:ii:ii~ii~i~iii-:iiigi~i:iil':~ii-i~~i~i:'::ic o u n terii~jii iiii~~~iiii~~~i-ii~~~iiiii —iii-iiii::ii~~~~~~~~~li: -ii:::ii~~~~~~iiii::i~~~~~i'lii~~~iii::ii::iii':i::iisiii~~~~~~~~~~~iiiiiiiii~~~~~ii~~iiiB~~ ~i-iilil~ ~~~iiP:.:sli-;ii~~~~~~~i-ii~~~iiiiii-ii'`iiiiiii'~ X:~i: E~~~~~b~~~~l~~~~~~~~'~~~~WI~~~~~~*~~~~~~~~~~ ~~~~~.~~~~~~al~~~~~~~~~~~~~~~~~daaasesss~~~~~~~~~~~~~~~~~~a~~~~~s~~~~~~~s~~~~~899s~~~~~~~~~~~~..~~~~~~~~~~~ p g l: ~ ~ ~ ~ ~ ~ ~ ~.......,Zealand<~~~~~~~~~~~~~~~~~~~~~~~~~...........~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:~ii S,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.....:':: ii'~~~~~MR MIN~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:,~1 ii:iiiliiii~~''iW ~ - p~~~~~~~ E~~~~ E~~~~~se~~~~~~~~ I~~~~~~~~~l~~~~~i~~~~'l:51~~~~~~~~~~~~~~~~~~~~~~~""""""""""""""""""~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~rl:~~~~~~~~i'''::'iii::::i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i::...... N~~~~~~~~~~i~~~~~~1 ii~~~~~Kg htgrp fsar hmer n sscae fdcas

from the carbon, have sufficient energy to be efficiently detected by the telescopes T and U. The additional carbon at the higher recoil energy points often entirely compensates for the effect of the drop in the differential cross section in the first scatter; the analyzing rates were therefore approximately constant at all angles. The asymmetry is the fractional difference of the events S1S1So(S2 or S2) T1T2AoA1A2 and S1SLSo(S2 or S2) UU2AoA1A2, where bars denote anti-coincidence, and the appropriate sign is chosen (depending on the orientation of the carriage)~ For the case of the incident protons scattering to the right, the recoil protons generally scattered preferentially to the right at the carbon target. The procedure used in making a typical "run" will now be described. First, with the appropriate counters installed for S1 and S1, the "31 arm was surveyed to the desired kinematic angle utilizing a transit mounted directly beneath the center of the hydrogen target. The'S1" arm was mounted on rails so its angular position could be easily changed; in aligning the arm, checks were made to insure that both S1 and S3 were at the appropriate kinematic angle. Each of the counters shown in Figo 3, with the exception of S2-S2 and Ao, had a o015" diameter pin mounted through its exact center. These pins were externally visible and were used in aligning the counters. Next, the "S2" arm was aligned. This arm was mounted on the same rail system as the "S1" arm and its angular position was also easily variedo A vertical crosshair marked the center of the S2-S2 counter pair and the "S2" arm was positioned such that this crosshair appeared at the desired kinematic 35

recoil angle as measured by the transit mentioned above. A transit at the downstream end of the analyzer, and which was centered on the axis of rotation of the analyzer, was used in "pointing" the axis at the center of the hydrogen target. The "pointing" procedure did not change the angular setting of S2-S2 since the analyzer was pivoted directly underneath S2-S2. The spark chambers were easily moved in and out of the beam line for the alignment process. Next, the appropriate amount of carbon was installed in the second target. If required for the particular recoil energy being studied, the lead absorber between T1 and T2 (and U1 and U2) was changed Also, film for the spark chamber photography was changed at this time, Now, with the beam on, all counters were timed and then the angular setting of the "S1" arm was varied slightly (by a remotely controlled motor) until the median of the recoil beam was centered on the axis of rotation of the analyzer at the carbon target, as discussed earlier in this section. At this point accumulation of data was begun. After approximately 10,000 protons had been analyzed, the readings of all scalers were printed out by an online typewriter. The process was then repeated with all parameters the same. Then the analyzer was rotated 1800 about the recoil beam line by a remotely controlled motor and a set of four measurements of the above type were madeo The analyzer was then rotated to its original position and two final measurements were made. This particular sequence of carriage orientations minimizes the amount of time used in rotating the analyzer, while allowing a high degree of cancellation of false asymmetries, even if these asymmetries drift in time, Spark chamber photographs were taken in uniformly 36

spaced intervals throughout the above sequence. Important accidental rates were constantly monitored by scaling coincidences between the pertinent counters with their signals delayed in such a manner that only chance coincidences could occur. 37

IV. ANALYSIS AND RESULTS A, DATA CORRECTIONS The relative alignment of the axis of the analyzer and the mean recoil beam trajectory is quite crucial, as, for example, a misalignment of o1" at the carbon target (or a divergence of o1~) would result in an error of approximately.08 in the polarization parameter. Spark chambers were employed to determine the corrections necessary to refer the measured asymmetries to the asymmetries that would have been observed if there were no misalignment. In this section the manner in which these corrections were applied to the data will be discussed. In the calibration experiment (see Appendix I) the asymmetry produced by scattering a 40% polarized proton beam from carbon target C (Figo 28) was measured at several beam energies, with the same geometry used in the primary experiment, for various orientations of the beam relative to the axis of the analyzer, Analysis of these data yielded an asymmetry function E(y,G,p), where y is the separation of the axis of rotation of the analyzer and the centroid of the recoil beam at the carbon target, e is the angle between the beam and the axis of the analyzer, p is the beam momentum, and E is the asymmetry produced by scattering a 40% polarized proton beam with these parameters (see Figo 10), In the primary experiment the problem is the following: Knowing the asymmetry em observed in scattering an arbitrarily polarized proton beam, 39

Axis of analyzer Left telescope Right telescope Center of carbon target Incident beam Incident beam Fig. 10. Parameterization of incident beam trajectory relative to axis of analyzer. 40

and y, 6, and p, what is the polarization, P, of this beam. In Appendix II it is shown that the asymmetry, Eo, which would have been observed if the centroid of the recoil beam were coincident with the axis of rotation of the analyzer, is related to the measured asymmetry Emn by co = Em -(y,,p) where a(yep) = E(y,e,p) - E(O,O,p). Each experimental point was corrected in this manner by calculating a from the sample of events photographed. The analyzing powers. A, for our geometry and the y and e slopes of a (at y = 0, 8 = 0), together with other parameters of the analyzer are presented in Table IIIo From the true asymmetry, co, the polarization parameter is given by Go/A. A linear function approximates a to the desired accuracy, and therefore a can be evaluated from y and 0 (ie., higher moments are not necessary), Both y and 0 were determined from analysis of the spark chamber photographs. Each accepted event was required to have originated from the hydrogen target (appropriately enlarged to account for multiple coulomb scattering) and to have passed through the counter pair 2S2S. This restriction greatly reduces the effect of any asymmetrical background contributions on the measured average beam trajectory. A scatter plot of the beam distribution at counters S2S2 at a typical data point is exhibited in Fig, llo Due to the plotting routine used in making this plot, each asterisk represents one or more protons and, consequently, the distribution presented is not the true density distribution~ The relative accidental contributions are somewhat exaggerated 41

TABLE III ANALYZER PARAMETERS Thickness Lead Between aC I tion Energy of Graphite T1-T2 (and 6y y=0 = A tion Energy (MeV) r 0 O A (MeV) Target U1-U2) e=O e=0 1 1000 9.0" 1.3 58" 221.104 236 710.221.104 264 650.221.104 263 615.221.104.262 580.221 o104 260 520.221.104 o259 500.221.104 259 45o.221.104.259 425.221.104.259 415.221.104.259 400.243.110.257 375.301.130 o341 350.360.151.425 2 350 7.0" 0.0" 156.078.238 325.179.088.307 300.202.099.378 270.246.118.428 260.261.125.445 3 240 2.5" 0.0".151.082.288 210.184 105.301 200.196.113.310 4 185.75" 00".165.102 335 150.214.127 330 120 o224 o144 230 35 150.25" 0.0".162.122 317 135.159.129.277 125.157.136.238 103.110.151.222 42

Horizontal coordinate ROLL 52 Z b.00 + ~ + + ~.-+-~-*-_*. * +~ +- ~ -* ~~~+ I I I I * I ** I I I I I V I I I I I* 1I I I* I I I S I I * ** I I I I I I I I I I * I * I * I I I I * 4. 44 * I I. ~.~ 4 t I I * ** ** *** ** * * I I * ******~ ~ ** * * * ~ 4 I 3.600 + —- * * ** * 4* ***** *** * * * ** — + I * 4 *** ** *~*~ ** ~~ ** I ~~. _ ~ ~ ~ ~ ~ ~ ~~~~~~ ~ I * **4 **4* * * 4 * 4 * I I * * ****** * ** * 4 * *** * I I * *' * *.. ** **** * I I * ***** * ** * ~** ** * *** I I ~******* **** * * * * ~* ** I 2 1 * * *4**~ 4* *4** ~~ ~ 1.......*.............. a) I * * *** -*** ~* ****** I f I * **** *** ** * * ** I h. rl <I f* *fttf *** * f* *** *t I N I *ft4 ft44 ftf.t I O I 4 ** *44*4* 4 **4 44*4444444* 1 I * * ** *** *** * ** *4 I -1.200 + —- 4* ** ********** ** *** *f —, I * * 4 * 4 *** 4 *******m***** I 0 I ** 44 4*4 * *** * 4 ***'* 4 I I.* *** * ** * ** ** * * * * I I * * **** * *** ***** *44 * I I ** *4** 4 444 4* 4* 4 * I I * * *' * * * *4*'*** * *** * I I **4 * * *** * *** 4 * * I I * *4* *44 4 *444 4*4*4 4 * I -3.600 + —- * *** * * * *4** **,m - - + I ****** * **** * ~ ~ * ** i I ** _ _4 _ __ - * I I 4 * I I * * * I I * 44 1 I * * * I I I I I I *I * I * I I I I -6.000 + -- +.........+ ~t+.....*~. +-+ f + + + + -5.000 -4.CO0 -3.000 -2.Coo00 -1.C00.000 1.COO 2.000 3.000 4.000 o."c$ Y (inches) Fig. 11. Scatter plot or recoil beam at S2S2.

in this method of plotting. It should also be remarked that the coordinates of each event are rounded to the nearest grid intersection before plotting. The solid lines enclose the region occupied by counters S2S2. The profile of the S2S2 counter pair is prominent; the hole in the center of the plot is the image of the 1" circular hole in S2S2 (see Table I). Typical histograms of the recoil beam distribution are shown in Figs. 12-14. As was discussed in Section III-D, the axis of rotation of the analyzer was referred to the fixed fiducial system by fiducial strips which rotated with the analyzer and appeared on the spark chamber film. The distribution in measured horizontal angle and displacement of these strips relative to the fixed fiducial coordinate system, at a data point where the total number of measurements was 1050, is shown in Fig. 15. As a check on the accuracy of the beam centroid determinations from the spark chamber photographs, the median of the recoil beam at S2S2, as calculated from the number of counts in S2S2, was compared with the median of the y distribution obtained from the spark chamber photographs. In most cases the agreement was quite good. The discrepancies found were attributed to accidentals in the spark chamber photographs and corrections were made utilizing the median determined by S2S2. We will explicitly show how the position of the median of the recoil beam at S2S2, relative to the axis of the analyzer, can be found from the knowledge of the number of counts in S2 and S2 in each of the two supplementary carriage orientations. Before dealing with this problem, however, the importance of the relative efficiencies of the counters S2S2 and their alignment with respect to the axis of the analyzer will be investigated. It should be pointed out that this analysis applies not only 44

Horizontal coordinate 0.05 0.04 - z o D 0.03 0.02 0 z 0.01 - 0.00 L -5.0 -4.0 -3.0 -2.0 -I.0 0 1.0 2.0 3.0 4.0 5.0 DISTRIBUTION IN Y AT CARBON TARGET (inches) Horizontal angle 0.10 0.08 z o _ 0.06 () N 3 0.04 Z 0.02 - 0.00 -5.0 -4.0 -3.0 -2.0 -1.0 0 1.0 2.0 3.0 4.0 5.0 DISTRIBUTION IN THETAIY) (degrees) Fig. 12. Histograms of recoil beam distribution in horizontal displacement and angle at carbon target, 45

Vertical coordinate 0.025 - ~~ 0.020 z 0 m C 0.015 (Iw N 0.010 0 z 0.005 0.000 ~ I I ~ I -5 -4.0 -3.0 -2.0 -1.0 0 1.0 2.0 3.0 4.0 5.0 DISTRIBUTION IN Z AT CARBON TARGET (inches) Vertical angle 0.05 0.04 - z 0 0.0rn 0.03 C,) N _ 0.02 z 0.01 o.oo,I I I _ I l -5.0 -4.0 -3.0 -2.0 -1.0 0 1.0 2.0 3.0 4.0 5.0 DISTRIBUTION IN THETAIZI (degrees) Fig. 13. Histograms of recoil beam distribution in vertical displacement and angle at carbon target. 46

Horizontal coordinate 0.05 0.04 - z 0 P CD I I 5 0.03 -I (n Er w N J 0.02 - 0 z 0.01 - 0.00'-5.0 -4.0 -3.0 -2.0 -1.0 0 1.0 2.0 3.0 4.0 5.0 DISTRIBUTION IN Y AT HYDROGEN TARGET (inches) Vertical coordinate 0.10 0.08z 0 E 0.06-n 03' 0.040 z 0.02 -5.0 -4.0 -3.0 -2.0 -1.0 0 1.0 2.0 3.0 4.0 50 DISTRIBUTION IN Z AT HYDROGEN TARGET (inches) Fig. 14. Histograms of recoil beam distribution in horizontal and vertical displacement at hydrogen target. 47

Horizontal angle 0.5 1 1 oooI I I I I I I I I 0.5 0.4 - 0 H 0 - N J 0.2r z 0.1 O.OI o0.o0 _____ -5.0 -4.0 -3.0 -2.0 -1.0 0 1.0 2.0 3.0 4.0 5.0 (degrees) DISTRIBUTION IN THE ANGLE WHICH THE ROTATING FIDUCIAL STRIPS MAKE WITH THE X AXIS Horizontal coordinate 0.5 0.4 - z 0 I — GD E 0.30 0 w N J 0.2 - <M 0 z 0.10.0C I -5.0 -4.0 -4.0 -1.0 0 1.0 2.0 3.0 4.0 5.0 (inches) DISTRIBUTION IN THE Y VALUE AT WHICH THE ROTATING FIDUCIAL STRIPS CROSS THE Y AXIS Fig. 15. Histograms for the distribution in horizontal angle and horizontal displacement for the rotating fiducial strips. 48

to 2S2S but also, with the obvious modifications, to the telescopes T and U. Let L1 and R1 represent the number of counts in S2 and S2, respectively, for the carriage in position I, and L2 and R2 the number of counts in S2 and S2, respectively, for the carriage in position II. We will allow the following possibilities and independently examine their consequences: 1.' the actual number of protons passing through counter S2(S2) differs from the measured number by a constant, A2(A2), times the actual number, and 2. the center of the S2-S2 counter pair does not lie exactly on the axis of rotation. For part 1 assume L1 = L1 + A2L1, where Li is the true number of protons scattered to the left of the axis of rotation in carriage orientation I (see Fig. 16a). Similarly, R1 = RI + At2R L2 = Lo + A L R2 = R2 + A2R2 Define B = 1/2((L1-R1)/(L1+R1) + (L2-R2)/(L2+R2)) (LL2-R1R2)/N1N2 where N1 = L1 + R1 N2 = L2 + R2 Therefore, [ = (LIL2( i+A2Xi+A2)-R R2(i+A2)( +A2)) / ((L (i+ A2) +R(i+A2)) (L( 1+A2) +R( 1+A2))) 3 = o(l+A2+A2) to first order in A2 and A2, where is the "true" value of 1. 49

Axis of rotation Counter S' Counter S2 Carriage Orientation II counts scaled =L2 L2+ L, counts scaled = RR2 +2 R2 where L?2 is the true number where R2 is the true number of events through S2 and A2 of events through S2 and A2 is is the inefficiency factor for the inefficiency factor for counter S2. counter S2. Axis of rotation Carriage Counter S2 Counter S2 /Oientti I \counts scaled t=LI = L +2LI counts scaledo = counts scalIed =Li = IL\ + A2L!I counts scaled = Ri = R+A2RI Fig. 16a. Effect of instrumental differences in counters S2 and S2. 50

As will be shown below 2 Y med where Ymed is the median of the y-distribution. The maximum P value used in the experiment was.05, and the scaler data indicates a reasonable upper limit for A2 and A'2 to be o.1 Therefore, the maximum error in 3 due to instrumental differences between the counters is.010 (Avmed.020")o This error was found to be negligible for practically all cases encounteredo Next, the dependence of P on the misalignment of S2-S2 relative to the axis of rotation is examined (Fig. 16b). The notation is the same as aboveo In addition define 51L(52L1) to be the number of protons between the axis of rotation and the S2-S2 counter boundary when the carriage is in orientation I(II), The quantity (51-52)/(51~+5 is approximately equal in magnitude to the center of gravity of the y sub-distribution in the region yl to Y2, since experimentally L. L For the entire experiment it was true that IY1-Y21 0.o04" Therefore the difference 1I1-21 is at least an order of magnitude smaller than either 51 or 2.o We will take 5 = 5z = 5o Then Li = Ll(l+5) L, = L(1+5) L2 = L2(l-F) R =- R= ~ l- L R2 = + 3L2 and = (LlL2"Rl.R2)/((L(+R1)(L2+R2)) = o + An, where A31 < 262 51

Axis of rotation S2 S2 boundary Ay.. S2 \./ \. 1:\ i. -* i -77~.*; 1 carriage orientation \rV — ~-y2 - - - - _ i, T T count s scaled = L2= L2( - 82), counts scaledR2 = R +82 L where L2 is the number of protons to the left of axis of rotation and 2 L02 protons pass through region A. Axis of rotation countsscaled = L = L ( I + ), counts scaled R = R -8 1, where L~I is the number of protons to the left of the axis of rotation and 8 L protons pass through region B. $2 /B\ S2,L —— I_- -yl- - _ ---— J \carriage orientation S2 S2 boundary Fig. 16b. Effect of misalignment of counters S2-S2. 52

From the spark chamber photographs it is known that the region Y1-Y2 contains less than 2% of the total number of particles in the distribution, Therefore, the maximum error is 3 due to misalignment of S2-S2 is 00032 (or Aymed <.006") and can be neglected. The-relationship between P and Ymed will now be ascertained. Figure 17 shows a hypothetical distribution in y at S2-S2o If H represents the average number of events per inch in the interval (Ym,yr) where Ym is the y-coordinate of the median and Yr is the y- coordinate of the axis of rotation, then the fractional number of particles contained in (ym,Yr) is Hr/N, where N is the total number of events in the distribution and 7 = Ym-yro If we designate the number of particles in the shaded region by L, then the fractional number of particles in (ym,yr) is also seen to be 1/2 - L/N. Equating these two expressions leads to 7 = - _/((2H/N)) since = 2L/N - 1 Therefore 7 = -= /.7 or since the ratio (H/N) is approximately constant at.35 or.25 depending on the set of S2-S2 counters used. Corrections due to the energy loss of the recoil beam between the first and second targets were not necessary since the corresponding energy loss in 55

NUMBER OF EVENTS PER INCH AXIS OF MEDIAN ROTATION I,, ~~~~~...'.... ~~~ ~...': "' ".' -.'~..:.'".: ~~~~~. ~~~ ~ ~~~'~ ~ ~~~~~~~' —" "'"." I ~~~ I ~ ~~ ~~ o ~ ~ ~'Yr Ym F i g. ~ ~ ~ ~ ~ ~ 17 yohtcldsrbto ny sdi eiigterltosi between~~~~ th meino h itiuinadtecut nS-~ 54~

the calibration experiment was very nearly the same. If the external beam were polarized, the polarization parameter would not be equal to the negative of the recoil polarization, as has been tacitly assumed so far, From a study of the mechanisms involved in accelerating and extracting the incident beam, it appears unlikely that an incident polarization would be present. Nevertheless, a systematic search for an incident polarization was made employing techniques which will now be discussed. Suppose the internal beam (of 2N1 protons) is polarized by an amount P1 by a left scattering in the accelerator (Fig. 18)o Let us designate the analyzing powers for the second and third scattering by P2 and P3, where the second scattering occurs at the hydrogen target and the third scattering at the graphite target of the analyzer. Also, it will be assumed that the three scattering planes are parallel. Then the number of incident protons scattering to the left three times (at 01,E2,03) is LLL = Nl(l+Pl)(l+PP2)(l+P3) + N(l-P1)(1-P2)(l-P3) Similarly, LLR = N1(l+P1)(l+P2)(1-P3) + N1(l-P1)(l-P2)(l+P3) LRL = N1(l+P1)(1-Pl)(1+P3) + Nl(l-"P)(l+P2((l-P3) LRR = N1(l+P1)(l-P2)(1-P3) + N1(l-P1)(l+P2)(l+P3) The asymmetry observed when the second scatter is to the left is CL = (LLL-LLR)/( LLL+LLR) = (P2P3+P1P3)/(l+PlP2).L + PP3 where -L is the asymmetry that would have been observed if there existed no 55

GR A PITE TARGET~. ON YROGEN TARGET *' f ~ A GA~~E ARE TARGET C BEINTERN~~~~ ~AL /EAQAAM/ f/ prtfs w~ith spinl upN - POI_ _ prot fls wi spin -oe e No 1i L\ eoi.. illustrating c pend-en Vig, iB*,Da HYDROGENAHIT TARGET ^ /^^ ^>^^ GR^TETARGCT~~~~~~~ ^^^^~~~~~? p^CIO~~~~~~~~~~~~~~~~l~d ~o^^^ TAR~GET ~^>^ ~"=Id~o IAGE (j\Z ^~ INTRNAL BEAM I 3^^ b ^\ nig.^ 18. a'^

initial polarization (PI). The asymmetry observed when the second scatter is to the right is (taking into account the change in sign of the polarization of the second scattered protons) R = -(LRL-LRR)/(LRL+LRR) (P2P3- P1P3)/(1-P P2) e - PiP3 If we define E = 1/2 (eL+)R) then ao = P2P3(1i-)/(i-PlA) Z _p where AT is the contribution to the averaged asymmetry, e, due to the incident beam being polarizedo It is seen that an incident beam polarization can be detected by comparing EL and eR, which are the asymmetries measured with the analyzing system in the orientation shown in Figo 3 and in the orientation with 1- -+ 1 and 02 + -02 Furthermore, all dependence of the average asymmetry C on P1 vanishes to first order, and the necessary correction can be calculated to an even higher order. Experimentally, however, no systematic difference between eL and pR was found and no corrections for an incident polarization were necessary. Bo ERRORS In this section the possible sources of error will be discussed and the magnitude of their effects examined. These errors include the uncertainty due to counting statistics, statistical error in the beam center of gravity, 57

accidentals, misalignment of counters in the analyzing telescopes, a difference in efficiencies between the telescopes, and scanning bias, It is known from the theory of the binomial distribution that if the probability of one of two mutually exclusive results in Pg then the probable error in Lp, the number of pa type successes after N trials, is LLp(i-Lp/N).25 For the moment, assume that the beam has vanishing width so a common probability can be assigned to each particle. The error in the average asymmetry determined in this situation is then since A(L/N) = (1 L) N N and 2L N where L is the number of protons scattered to the left and N is the total number analyzed. The effect of a beam of finite width can now be investigatedo Imagine the incident beam to be divided into n bins with Ni(= Li+Ri) being the total number of protons in the ith bino If we further require that Ni = N/n, the average asymmetry for the entire beam is = ( LiERi )/N = 2Li/N - 1= ZiNi i i i If the Aei are assumed uncorrelated, the probable deviation in E is given by (A2) - 1((Ai)) n i It was shown above that (for a beam of vanishing width) (ACi)2 = (= i)/Ni 58

Therefore, (A')2 = (1 - i) The second term in this expression is always at least two orders of magnitude smaller than the first, and can be neglected. Therefore, in computing the statistical error in the asymmetry the expression AE = N was used. The statistical errors in the beam centroid were calculated from the relations Iy = (yy) / N, Ae = I / N i i where N is the number of events in the reconstructed distribution. Three possible cases for accidental background contamination in the analyzer telescopes will be studied: 1. background proportional to the number of true events, with the proportionality factor being the same for both telescopes, 2.) background additive and the same for both telescopes, and 3.) background additive but different fo.r each telescope. In the following let L and R represent the number of particles that scatter into the left and right telescopes, respectively, and B is a parameter characterizing the accidental contributions; the superscripts M and T represent "measured" and "true." N T Case 1. L = L (1+B) RM = T(1+B) AeM = 0 (i.e., no error in this case) Case 2. LM LT + B RM RT + B AM = -(2B/N)ET Assume B/N =.01 and eT =.04, then As A.001 and is negligible. 59

Case 3 LM LT + B RM = RT + Br AM - (B-Br)/N Assume B-Br =.C1N, then AcM.= Ole It is seen that accidentals of the type in Case 5 potentially pose the most serious problem, At each data point the quantities (B-Br)/(B+Br) and (B+Br)/N were measured. For all cases it was true that (B-Br)/N <, 002 Therefore, even accidentals of type 3 produce no appreciable error in the measured asymmetry. Furthermore, comparison of asymmetry measurements made at high and low beam intensities experimentally established that the effect of accidentals was negligible at the beam intensity normally usedo Examination of the recoil beam distribution reconstructed from spark chamber photographs reveals in some cases a sizable number of accidental spark chamber events, The higher accidental rates in the chambers is to be expected because of the long resolviing time of the chambers compared with scintillation counters, The most significant of these events, as far as their effect on the determination of the beam center of gravilty is concerned, are those that appear at large distances from the axis of the analyzer In order to eliminate events of this type, each accepted spark chamber event was required to originate from the hydrogen target and intersect the counter pair S2-S2o The spark chamber accidentals that remain are thus contained in the region ~l5"' at o2SS, and are not expected to produce a shift in the y center of gravity by more than,i015" (corresponding to an error in the corrected asymmetry of -.,003. assuming no accidental effect on ) ) The effect of an asymmetry in the efficiency of the two analyrzing telescopes, due to differences in scintillator, associated electronics, or 60

alignment, could be quite significant. It has been shown in Section IV-A, however, that their effect on the average of the asymmetries measured by S2-S2 with the carriage in each orientation is negligible. The argument and result is identical for the case of the analyzing telescopeso If the difference between the telescopes is characterized by a parameter q, and the counts in the left and right telescopes specified by L and R (with superscripts representing"'measured" and "true," and subscripts specifying the carriage orientation), where TM = T M T RM T Iand M RT i -= Li(1-i), L L, = R, and then Ae/e A q, where e is the average azimuthal asymmetry. It is experimentally known that l q < 02, and consequently the maximum contribution to the error in E is always less than. 003 All spark chamber film was scanned utilizing a semiautomatic digitizing machine. The basic unit for this machine was 0023" (corresponding to approximately o003" in real space). Reproducibility and linearity checks were periodically made, Approximately 97% of all film was rescanned with the film reversed (i.e., left and right reversed) and the results averaged with the corresponding normally scanned results to minimize scanning bias. The unrescanned data was corrected by the average universal difference in the two scans0 It is believed that no significant scanning bias remains in the averaged data. The individual errors included in calculating the total error in the measured polarization are summarized below (where A = analyzing power}, y 61

and Qe are the derivatives of the asymmetry with respect to y and. 8 at y = 0, 0 = 0, as determined in the calibration experiment):...statistical counting error (typically.020) A e statistical error in average value of y A (typically o015) A~...statistical error in average value of 6 (typically o010) o015 a. error due to accidentals in spark chamber photographs A (typically 01l).005 ooerror due to differences in analyzing telescopes A ((maximum of.003/A) During the course of the experiment many measurements of the polarization parameter were repeated one or more times. In most cases, reproducibility was better than one standard deviation. The above errors are combined in quadrature and presented in Table IV, There exists, in addition, a 5% uncertainty in the polarization due to normalization (see next section), C. RESULTS A summary of the final results is presented in Table IV, and the cor — responding graphs, for each incident beam energy, appear in Figso 19-24. Each entry in Table IV represents the combined data, in most cases, from two or more separate measurements, The polarization parameter is well known at 75 GeV. Results from independent experiments by Betz,26 Cheng,27 and Ducros et alo28 show good 62

TABLE IV POLARIZATION PARAMETER IN ELASTIC PROTON-PROTON SCATTERING Incident Proton Energy ecm p AP (deg.) 43.85.541 0075 47.19 o513.044 675 GeV 53 25 o530 o029 63098 470.067 86.29.097 078 39.88.419 0031 42.47 464 o040 53060 o481 o023 57.81 o417.038 1103 GeV 61.62 325 0033 65 32.258.073 68 52.245 033 71,37.265 037 77.25.095 o029 88.25 -.021 034 32.30.361,036 34 77 0403 0030 39oo6 o343 o045 46.63 o407.025 49 77.339.022 1.32 GeV 5. 13 266.020 61.21.190.025 68.26.034.030 74.76 o062 032 81.81.059.034 88,23 034,029 28087.228 o029 32.80 o352 032 38.55 o335.025 44.07 369 o020 49.67 177 o040 1 63 GeV 56.03 151.053 1063 GeV 61o91 o141.035 67004 o025 o028 73 93.025. 030 80. 57 oOOO.031 63

TABLE IV (Concluded) Incident Proton Energy cm p AP (deg.) 25.32.227.031 27.09.315.026 30.42.252.026 36.08.292.030 38.74.229.052 40.41.205.025 43.45.178.027 2.24 GeV 47.14.182.033 50.65.163.037 52.25.134.036 54.01.147.032 57.04.o48.075 62.22.020.041 69.30.093.050 85.24.006.061 22.18.193.026 23.78.188.054 31.65.237.039 2.8^4 GeV 35.91.199.057 41.37.175.037 47.15.142.071 60.04.115.055 72.72.043.059 64

.65.45 -l. 75GeV.25. THIS EXPERIMENT A DUCROS ET AL CHENG 0 BETZ.05 0 20 40 60 80 ) cm Fig. 19. Polarization parameter in elastic proton-proton scattering as a function of center-of-mass scattering angle at.75 GeV.

1.03 GeV ~ THIS EXPERIMENT A DUCROS ET AL.65 o HOMER ET AL.45.25.05 0 20 40 60 80 cm Fig. 20. Polarization parameter in elastic proton-proton scattering as a function of center-of-mass scattering angle at 1.03 GeV. 66

1.32 GeV * THIS EXPERIMENT.65.45.25.05 I I I I I I t I 0 20 40 60 80 ~ cm Fig. 21. Polarization parameter in. elastic proton-proton scattering as a function of center-of-mass scattering angle at 1.32 GeV. 67

1.63 GeV THIS EXPERIMENT A BAREYRE ET AL.6 5 UCRL 1440.45 P.25.0 5 I I I I I I I I i 0 20 40 60 80 ) cm Fig. 22. Polarization parameter in elastic proton-proton scattering as a function of center-of-mass scattering angle at 1.63 GeV. 68

2.24 GeV THIS EXPERIMENT.6 5.45 P.2 5.05 i 0 20 40 60 80 E cm Fig. 23. Polarization parameter in elastic proton-proton scattering as a function of center-of-mass scattering angle at 2.24 GeV. 69

2.84 GeV THIS EXPERIMENT A UCRL I 1440.65.45 P.25.05 ~ —! I. - I i I I I i'' 0 20 40 60 80 ( cm Fig. 24. Polarization parameter in elastic proton-proton scattering as a function of center-of-mass scattering angle at 2.84 GeV. 70

agreement. Since the polarization parameter at.75 GeV is better known than the polarization of the beam used in the calibration experiment, data from this experiment have been normalized to give good agreement with the existing mean curve at.75 GeV. The corresponding calibration beam polarization is thus predicted to have been 40% + 5% (see Ref. 29). Data from this experiment have been fitted with a two dimensional least squares function of the following form: ~=5,k=4 P(E,q* ) -= A kE-1 sin e*6 2k-l(cos e*) ~=l,k=l where P(E,O*) is the polarization parameter for incident beam energy E and center-of-mass scattering angle e*, and 6(cos e*) are Legendre polynomials. The values of the coefficients Ak' and their associated errors, are given in Table V. In Figs. 20-24 the smooth curve shown is the plot of the function P(E,e*) at the appropriate value of E. At 1.03 GeV (Fig. 20) results from this experiment are consistent with the results of the Birmingham group0~ and the preliminary results of the Saclay group.28 Data at 1.32 GeV are exhibited in Fig. 21. The maximum in the fitting function occurs at approximately 40~ in the center-of-mass system and has the value of approximately.41. Because of the significant discrepancy in the results of the Chamberlain group6 and Bareyre et al.5 at 1.7 GeV, measurements have been made near this energy (Fig. 22). Our results show better agreement with the latter. New polarization data at 2.24 GeV are shown in 71

TABLE V EXPANSION COEFFICIENTS FOR POLARIZATION AS A FUNCTION OF 0* AND T C~k k+ 1 2 3 4 1 4.0790~ ~6429 1.5032+~ 9790 5.9178+1.3195 2.3870~.9549 2 -5.4880+1.1308 -1.628+~1.200 -11.2572~2. 1926 -4.2545+1.4606 3 2.9906+.6046 -.2148~.8827 6.8023+.8o81 2.5720~.1890 4 -.6894~.0366.6532~.4588 -1.5837~.4164 -.6798~+ 3479 5.0555+.0191 -.1521~+ 0592.1158~.0747.0700~ o0491 72

Fig. 23. The trend of smaller polarizations for higher energies continues to be true here. In Fig. 24 results at 2.84 GeV are shown. Agreement with the Chamberlain group6 at this energy is quite good. A plot of the maximum polarization versus energy is given in Fig. 25. 73

.6 m THIS EXPERIMENT I?) Pmax.:.2 0.2.5 1.0 5. E(GEV) Fig. 25. Maximum polarization versus incident kinetic energy. 0 Ref. 6 0 Ref. 31 * Ref. 30 A Ref. 32 A Ref. 5 0 Ref. 29 V Ref. 28 V Ref. 27 * Ref. 33 74

TV DISCUSSION The polarization parameter in elastic proton-proton scattering is seen to vary smoothly with incident beam energy and center-of-mass scattering angleo It is notable that the polarization becomes very small in the angular region 60~70~ at 1.32, lo63, and 2.24 GeVo At present this behavior is not theoretically understood. The peak in the maximum polarization occurs at the incident beam energy of x 700 MeV and is quite prominento It is interesting to note that at approximately this energy the total proton-proton cross section is approaching a relative maximum, presumably due to single pion production (Fig. 26). Results from this experiment have been analyzed in terms of two specific predictions developed in the framework of the Regge theory, as described in Section II-C. The predictions are that, for fixed small four-momentum transfer t, the polarization should vary as a. P(s) = asb b. P(s) = c(c(p )-a(pp))/a(pp) where s is the invariant mass squared, and a. b, and c are constants, and o(pp) and o(pP) are total cross sections for proton-proton and proton-antiproton scattering0 Since, as stated in Section II-C, the t dependence of the polarization is expected to be approximately - tJ7, these predictions appear valid only for Itl < o3(GeV/c)2 (ioe,, only for those values of t at which the polarization is increasing as a function of center-of-mass scattering angle)0 No w, the value of t at which the maximum value of the polariza75

: 200 0 0 0 I 10 (n 0 I I.5 1.0 1.5 T(GeV) Fig. 26. Total cross section in proton-proton scattering.

tion occurs at a given energy is essentially independent of the energy and is equal approximately to -.3(GeV/c) 2 Data on the maximum polarization from this experiment were fitted with the two above formso The values of the parameters used in the fits shown in Fig. 27 are a = 5o915, b = -lo475, and c =.425. Data on the cross sections in b were taken from Refs 34 and 35. It is seen that both predictions a and b. agree remarkably well with the polarization data from.75 to 6 GeV. Fits to the data at other values of t notably different from tl =.3(GeV/c)2 are not given since for It! >.3(GeV/c)2 the assumptions required in making the predictions do not appear to be justified, and almost no data presently exist for Itl <<.3(GeV/c)2. 77

>.6) C *THIS EXPERIMENT (D l 5.915 (s)-1.475 ~ ~0.2.5 1.0 5. E(GEV) Fig. 27a. Regge theory prediction (a) for the polarization in elastic proton-proton scattering at t = -.3(GeV/c)2. 0 Ref. 6 T Ref. 28 * Ref. 30 * Ref. 33 or a.02.5 1.0 5. E(GEV) Fig. 278. Regge theory prediction (a) for the polarization in elastic proton-proton scattering at t = -.3(GeV/c)2. O Ref. 6 V Ref. 28 * Ref. 30 * Ref. 55 A Ref. 5 78

9.6 - ~ Ti *THIS EXPERIMENT To I' ^^(425)(o-(PP)-a-(PP)) <, H I <r' 02 5 1.0 5 E (G EV) Fig. 27b. Regge theory prediction (b) for the polarization in elastic proton-proton scattering at t = -.3(GeV/c)2. 0 Ref. 6 T Ref. 28 N 0.2.5 1.0 5. E(GEV) Fig. 27b. Regge theory prediction (b) for the polarization in elastic proton-proton scattering at t = -.3(GeV/c)2. O Ref. 6 V Ref. 28 * Ref. 30 * Ref. 33 A Ref. 5 79

APPENDIX I In this section the details of the preliminary calibration experiment will be presented, It was shown in Section IIDA that in a scattering process the azimuthal scattering asymmetry, c, is related to the polarization, P, of the incoming beam, and the analyzing power, A, of the interaction by the expression e = PAo For a given analyzer, the quantity A can depend only on the incoming beam energy. In a calibration experiment the quantity e is measured, and, since the beam polarization is known, the analyzing power is determined, The above statements assume, of course, that the incident beam is coincident with the axis of symmetry of the analyzer; experimentally, this is not the case, In order to refer the measured asymmetries to the axis of the analyzer, the relative orientation of the analyzer axis and the average beam trajectory at each energy was determined from spark chamber photographs, and the dependence of the asymmetry on this relative orientation was studied. The range of energies over which the calibration measurements were made correspond to the basic spectrum of recoil protons to be analyzed in the primary experimento The calibration measurements were made utilizing a proton beam at the Carnegie Institute of Technology synchrocyclotrono A 40O% 5% polarized beam was produced by an internal scattering from a carbon target. The polarization of this beam was determined by normalizing our data from the primary experiment to give good agreement with the existing mean curve at.75 GeV, 81

where the polarization parameter is well known, The extracted polarized beam of 105 protons/cm2 sec entered the experimental area through a 1" x 1-7/8" collimator in the shield wall of the synchrocyclotrono The beam then was bent through an angle of 20~ by a magnet, collimated, and subsequently analyzedo The beam layout is shown in Figo 28~ A differential range method, as illustrated in Fig. 29, was employed to determine the beam energy. The quantity C = C1C2C3C4C5/C1C2 was measured as a function of the thickness of copper between counters C3 and C40 For small amounts of copper, essentially all beam protons have sufficient energy to traverse the entire array of counters and thus C is smallO As additional copper is added, C becomes larger since now more protons are stopping before C50 The maximum value of C should occur when the average beam proton stops in C4o If more copper is added, most protons fail to reach C4. and thus C is again smallo Therefore, the value of the copper thickness at which the maximum C value occurs determines the initial range of the beam and thus the initial kinetic energyo36 In calculating the energy, account was taken of all material in the beam upstream of the stopping point, which includes air, scintillator, and a fixed amount of graphite and lead which was added to reduce the beam energy to a level that required a reasonable number of copper sheets for the differential range curveo The incident energy was determined to be 415 ~ 15 MeV. This value agreed with the energy of 415 ~ 10 MeV de29 termined by Kane et al,2 using a similar method in this beam. The analyzer was calibrated for proton energies of 103, 125, 150, 165, 185, 200, 240, 260, 300, 350, 400, and 415 MeVo Variation of the energy was 82

TRANSIT U\\ /T2 LEAD \\ ~\ I ^^~^^ ^ ~ ABSORBER U!\ CARBON TARGET (C) SPARK CHAMBERS SHIELDING \\N%.\\%. \ BENDING MAGNET COLL IMA TOR AND DEGRADER K N RE TA INER' e' \~ \ CYCLOTRON SHIELD WALL \ \\\ Fig. 28. Layout for calration experiment ^~~\ \

COPPER (Variable) /EAD (32.10 gms./cm DEGRADER BENDING C C2 C(32.0gms/cm /MAGNET C4 C5 a 200 i Proton Beam Co C, C2 Coincidence CI C2C3C4C5 Coincidence To Scaler To Scaler Fig. 29a. Logic used for differential range curve.

415 MeV 2.5 DIFFERENTIAL RANGE CURVE 2.0 1.5 O 1.0 \.5 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 THICKNESS OF Cu (gm/cm2) Fig. 29b. Differential range curve used in determining energy of beam in calibration experiment. The horizontal scale represents only the copper in the beam; there was, in addition, a constant amount of graphite, lead and scintillator. 8-)

accomplished by inserting appropriate amounts of graphite in the exit collimator of the synchrocyclotrono The effect of the energy degradation on the incident polarization is assumed negligible 37 The experimental layout is shown in Figo 28 and the counter dimensions in Table VIo A typical event is SIS2 T1T2 A. The analyzer has been previously described in Section IIi.Do With the exception of the "beam proton" selection counters, the electronic logic used in the calibration experiment is the same as used in the primary experiment and described in Section IIl-Do In order to measure the dependence of' the asymmetry on the relative orientation of the axis of the analyzer and the average incident beam trajectory, the analyzer was mounted on a platform that could be translated + 1" and independently rotated ~ 1~ in the horizontal plane. For each energy and corresponding analyzer configuration (see Section III-D), the asymmetry was measured at each of the thirteen nominal (ye) points in Table VII, where y and 0 are as defined in Fig. 10. Each of these (ye) points was corrected by y9 0, the centroid of the beam relative to the analyzer as determined from the analysis of the spark chamber photographs (referral of the beam to the axis of the analyzer was made possible by the utilization of the rotating fiducial strips, as described in Section III-D)o The calibration experiment therefore furnishes the function E(y,0.p), that is, the asymmetry as a function of y, 6, and the momentum po The analyzing power at the momentum p and analyzing configuration j is Ej(O^Op)/Pin, where Pin is the calibration beam polarization. The derivation given in Appendix II shows that this information is sufficient to determine the polarization in an analysis 86

TABLE VICOUNTER DIMENSIONS FOR CALIBRATION EXPERIMENT Counter Width x Height x Thickness S1 1" x 3-1/2" x 1/8" S2 1/2" x 7" x 1/4 Ao 9" x 21" x 1/2" (1-1/8" dia. hole through center) T1 8" x 18" x 1/2" T2 10-1/4" x 22" x 1/2" U1 8" x 18" x 1/2" U2 10-1/4" x 22" x 1/2" TABLE VII Y, 0 VALUES AT WHICH THE ASYMMETRY MEASUREMENTS WERE MADE Y".000.003 o006 -.003 -oo006 500 - 500 1. 000 1.006.994 -1.006 -1.000 -.994 0~.000 463.926 -.463 -.926.o.000.000.926 -. 926 -.926..000.926

experiment if em, the measured asymmetry, y, 0, and p for that experiment are known, provided, of course, that y, 0, and p lie within the calibration range. Least squares fits to the data were made using the functional form Ej(y,(,p) = A(p) + Ai(p)y + Ai(p)e + Aj(p)ye + Aj(p)ye-'-f- A(p)o2 A(p)y2 2 + Akp)^ + A(p)y +- A0p)^ + A p)y^ + A+(p)y + Ao(p)0,3 where j j j j 2 A~(p) = 1 -+ D+ 2P + DX3p o No physical reason is given for expecting this form to be appropriate: its utility is that accurate interpolation between data points is obtained, The values of the D coefficients, for y in inches, 0 in degrees, p in GeV/c, are given in Table VIII, and the analyzing powers determined from these fits in Table III. There exists an uncertainty in the analyzing power due to counting statistics (see Section IV-B) and the statistical error in determining the mean beam trajectoryo In all cases the contribution of this uncertainty to the determination of the polarization parameter is negligibleo Histograms of the beam distribution in the horizontal and vertical spatial coordinates, and the horizontal and vertical angular coordinates, respectively, are shown in Figs~ 30-33 for the incident beam energy of 300 MeVo Graphs of the asymmetry versus y for various values of e are presented in Figso 343~8 for a central energy at each of the five analyzer configurations 88

TABLE VIII EXPANSION COEFFICIENTS FOR THE ASYMMETRY Configuration I (350-415 MeV): 1D I I I 4 DQ 1 D12 D13 0 10.2842 -21.1817 11o0158 1 - 2.7532 7.5758 - 4.6712 2 5.4611 -10.9575 5.6125 3 -.6805 1.2335 -.5550 4,0880 -.2688.1778 5.8846 - 1.9223 o 0378 6.0455 -.2524.2909 7 2.7214 - 5.8532 3 1433 8 - 4.4262 9o5001 - 5.0905 9 9.0864 -19.0560 10.0203 10 - 4.2901 9.2357 - 4.9721 Configuration II (260-350 MeV):;R2~ II II II Di I Di 2 Di 3 0 -.8885 3.1496 - 2.3053 1.7482 -.7772.0925 2 -.1898 1.0309 -,8184 3 - 1.2725 3.0438 - 1.8280 4.8936 - 2.1747 1 3247 5 o6557 - 1,6772 1.0637 6 - 1.4150 302839 - 1.9205 7 -.6969 1.5899 -.9069 8 -.5984 1.5363 -.9775 9 2.0968 - 4,9734 2,9741 10 lo9549 - 4,7240 2,8361 Configuration III (120-240 MeV): Q III III III + D22 D DQ3 0 1.1525 - 2,9180 2.0518 1,5764 - 5245 -.1363 2.3362 -.1579 - 02877 3 o 5184 - lo 6544 1 02892 4. 4352 103427 - 1.0262 5. 04490 lo2585 -.8703 89

TABLE VIII (Concluded) Configuration III (120-240 MeV) (Continued): ~ III III III D1 D~2 D~3 6 1- 1523 303750 - 2o4844 7 o1221 o1845 -.0153 8 o,0603 - 3o0194 2,1398 9.6123 - lo8436 1.4189 10 o0471 - o1443 o1139 Configuration IV (120-185 MeV): IV IV IV Di, D~2 DQ3 0 - 1.5236 506529 - 4,8062 1 - 1.5827 6.6157 - 601350 2 1o3499 - 4.2218 306243 3 - 4092 1.4014 - 1,2158 4 -.0261.1113 -.1278 5 - o1472.4163 -.2720 6 - o6052 2,0908 - 1.8112 7.9259 - 35484 3o3853 8.4673 - o15257 o 1814 9 8791 - 2,8031 2 2387 10 - 1,7074 6,4331 - 6 0385 Configuration V (103-150 MeV): I TV V V DRi Do2 D 3 0.7895 - 3,1312 3o5005 1 - 7.0633 28, 3104 -270 6236 2 - 2,1389 9,2196 - 9.2979 3 -.1387.6968 -.8685 4 - 200387 8o0550 - 7o8621 5.2150 - 9197 1o0014 6 -.9681 3.9775 - 4o0156 7 o 0257 - 4,2290 4o3013 8 - 6278 2.5547 - 2.6069 9 6 2300 -24,8554 24,6071 10 204375 - 9.4953 9 1977 90

.16.14 z.120 N,.06.04 Horizontal coordinate (inches) Fig. 30. Normalized distribution of the calibration beam in the horizontal coordinate at 300 MeV. 91 91

.018.016 -.014.012Cn (/).010 -.008Z.006 -.004.002 0 -3.5 -2.7 -1.9 -1.1 -.3.5 1.3 2.1 2.9 3.7 4.5 Vertical coordinate Z (inches) Fig. 31. Normalized distribution of the calibration beam in the vertical coordinate at 300 MeV. 92

.16.14 - z 0 F-. 120.10w N.08 < c.06 0.04.02 -4.0 -3.2 -2.4 -1.6 -.8 0.8 1.6 2.4 3.2 4.0 HORIZONTAL ANGLE (degrees) Fig. 32. Normalized distribution of the calibration beam in the horizontal angle at 300 MeV. 93

.072 -.064 -.056 - z o.048 - 5.040 - IC(.032 a l N 1 L'.024 ~ _.016.008 - -4.0 -3.2 -2.4 -1.6 -.8 0.8 1.6 2.4 3.2 4.0 VERTICAL ANGLE (degrees) Fig. 33. Normalized distribution of the calibration beam in the vertical angle at 300 MeV. Reference angle is arbitrary. 94

I. I I I.. I.60 - 400 MeV.40.20 - 0'.00 - -.20 -.40.8 5" -.45" -.05.35".75. 15" Y Fig. 34. Asymmetry measured in calibration experiment as a function of y for various values of e at 400 MeV. A_

.60 t 300 MeV.40.20 ~0'.00 0' 5~ -.20 -.40 -.85" -.45" -.05".3 5".75" 1. 15" Y Fig. 35. Asymmetry measured in calibration experiment as a function of y for various values of e at 300 MeV..6 O 200 Mev.40.20 E B'IZ- Z.00 - -.20 -.40 -.85" -.45" -.05".35".75" 1.15" Y Fig. 36. Asymmetry measured in calibration experiment as a function of y for various values of e at 200 MeV. 96

.60 150MeV.40.20 0'.00: ^^: -.20 -.40 -.85" -.45" -.05".35".75" 1.15" Y Fig. 37. Asymmetry measured in calibration experiment as a function of y for various values of 0 at 150 MeV..60 125 MeV.40.20.00 -.20 -.40 - 1' | I'I I I I I I I I, -.85 -.45" -.05".35".75" 1.1 5" Y Fig. 38. Asymmetry measured in calibration experiment as a function of y for various values of e at 125 MeV. 97

APPENDIX II In this section a relationship is derived between the asymmetry measured when a proton beam with centroid specified by y and 4 is incident on the analyzer and the asymmetry that would have been observed if the beam had entered the analyzer with both y and 4 zero-(see Fig. 39), The azimuthal asymmetry, ems measured by the telescopes is Cm = (RM-LM)/(RM+LM) where 2 Rm = nN S (e)(l+E(e))de L'1 Lm = nN,fTL S()+c) ( e) )de and N is the number of incident protons, n is the number of participating target protons, E(e) is the azimuthal asymmetry for scattering at angle e(E~(-) = -(e))), and S(e) is the probability for an unpolarized beam to scatter through an angle eo Let 2R = e2-S2-$, then to first order in 4 and y/v3 2 = y cos e2/v3 Also RK = 61 51 4 L = -e2 -5, 299

Axis of analyzer Left telescope Right telescope / /~/ V4 / - 81 81 / Fig. 39. Geometry of telescopes for trajectories not coincident with axis of rotation. 100

where 1 =C 2 92 since V3 = V4 and cos i0/cose2 = 1lo1 Let B I(A,B) = nN s(e)(i+e(e))de and note that I(A+AAB+AB) = (A,B) + ABS(B)(l+E(B)) Nn- AAS(A)(i++(A)) Nn where AA and AB are small increments in A and B, respectively. If we set 5 = 51+4 then LM = I(-e28,-1-6) = I(-2,-e0) - Nn S(-e0)(li+(-e0)) + 5Nn S(=-2)(l+e( -2)) RM "I(e15,e2-8) - 1(e1,2) - 5Nn s(e2)(1+(e(2)) + 5Nn s(e1)(1+c(e9)) We may neglect the terms containing S(~92) since for our geometry S(01)/S(~+2) 100. The measured asymmetry becomes e -M RM M I(e1,92):-I(-e02 9-e)+ +Nnb S( e) (2) M =.RH+rLM I(e1,e2)+I(-e29-e )+ Nnb S(9e)(2(e ) )' = (Eo-a)/(1+cE(ei)) where a = 2Nn5 S( 1e)/(I(E1, 02)+I(-02 -Ej)) In all cases encountered le(e91) I < 005; therefore we may write cM eo+Cz without introducing any significant error0 101

Thus a may be assumed a function of y, 4, and beam energy only, and is consequently a definite property of the analyzer. Data from the calibration experiment were used to evaluate a(y,jp) in the following manner. In the calibration experiment (Appendix I) the asymmetry em(yg gp) was determined for the range of y, 4, and p anticipated in the primary experiment. The function ca(y,,p) over this range is merely 9(y,,p) = Cm(yYp) - em(O,,p) Knowledge of O(y,,p) allows determination of the true asymmetry Eo(OOp) from the measured asymmetry, EM(y,4p), in an analysis experiment as EO(O,O,p) = EM(y,94P) - U(y9,p) when y, 4 and p are known, 102

BIBLIOGRAPHY 1o C. L. Oxley, Wo F. Cartwright, and J. Rouvina, Phys. Revo 939 806 (1954). 2. R. So Christian and H, P. Noyes, Phys, Rev, 70, 85 (1950). 3o Ko Mo Case and Ao Pais, Phys. Revo 80, 203 (1950)o 4. Ro Jastrow, Phys. Revo 81i 165 (1951) 50 P. Bareyre, J. F. Detoeuf, L. W. Smith, R. D. Tripp, and L. Van Rossum, Nuovo Cimento 20, 1049 (1961), 6. tI Steiner, Fo Betz, 0. Chamberlain, B. Dieterle, P. Grannis, C, Shultz, Go Shapiro, Lo Van Rossum, and D, Weldon, Polarization in Proton-Proton Scattering Using a Polarized Target, Part II, Lawrence Radiation Laboratory Report UCRL-11440, June 1964 (unpublished.) 7o Vo Po Kanavets, I. I. Levintor, B. V. Morozov, M. Do Shafranov, Zh, Eksperim, i. Teor. Fiz, 45 1272 (1963). 8, YO Hara, Phys. Letters 2 246 (1962), 9. L. Wolfenstein and J, Ashkin, Physo Rev 85, 947 (1952) 10. R. H. Dalitz, Proc. Phys. Soc. (London) A65, 175 (1952). 11, M. H. MacGregor, M. Jo Moravcsik, and H. PO Stapp, Ann, Rev, Nucl. Sci, 10_ 291 (1960). 12. H. P. Stapp, The Theory and Interpretation of Polarization Phenomena in Nuclear Scattering (Thesis), Lawrence Radiation Laboratory Report UCRL3098, August 1955 (unpublished) 130 Ho P. Stapp, Phys, Rev, 103, 425 (1956)o Ko-Co Chou and M. I. Shirokov, Soviet Phys. JETP, 7, 851 (1958); G. Breit, Phys. Rev, 106, 314 (1957). A Garren, Phys. Rev 96, 1709 (1954); B. Steck, Zo Physik, 144, 215 (1955)o 14. P. Cziffra, Mo Ho MacGregor, Mo J. Moravcsik and H. P. Stapp, Physo Rev. 114, 880 (1959)o 150 RoJoNo Phillips, Nuclear Physics 30, 148 (1962)o 103

BIBLIOGRAPHY (Continued) 16o N. Hoshizaki and So Machida, Progo Theor. Physo 29, 49 (1963) YO Hama and No Hoshizaki, Prqog Theoro Phys0 31. 609 (1964). 17. I. Jo Muzinich, Phys0 Rev. Letters 9, 475 (1962)0 18. Y0 Hara, Progo Theoro Phys0 28, 1048 (1962) 19o M. Lo Goldberger, Mo To Grisaru, So Wo MacDowell, and Do Y. Wong, Phys, Rev. 12% 2250 (1960) 20. Mo Jacob and G. C. Wick, Ann. Physo 7, 404 (1959). 21. Yo Hara, Progo Theor. Phys. 28, 711 (1962). 22. Thomas Jo Devlin, Optik: An IBM 7090 Computer Program for the Optics of High-Energy Particle Beams, Lawrence Radiation Laboratory Report, UCRL-9727, 1961 (unpublished). 230 Go W. Bennett, Cosmotron Internal Report No, GWB-2. 24o Ro Sugarman9 F0 C, Merritt, and Wo Ao Higginbotham, Nanosecond Counter Circuit Manual, Brookhaven National Laboratory Report BNL711(T-248), 1962 (unpublished) o 25. Po Go Hoel, Introduction to Mathematical Statistics, (John Wiley and Sons, Inco, New York, 1958), second edition, Cho 5, po 67. 26. F. W, Betz, Polarization Parameter in Proton-Proton Scattering from 328 to 736 MeV (Thesis), Lawrence Radiation Laboratory Report UCRL115659 1964 (unpublished) o 27. D. Cheng, Nucleon-Nucleon Polarization at 700, 600, 500, and 400 MeV (Thesis), Lawrence Radiation Laboratory Report UCRL-11926, July 1965 (unpublished). 28. Y. Ducros, Ao de Lesquen, J. Movchet, Jo C. Raoul, Lo Van Rossum, J. Deregel, Jo Mo Fontaine, Ao Boucherie, and J. F. Mougel, Determination of the Asymmetry Parameter in Proton-Proton Scattering up to 1.2 GeV, Oxford International Conference on Elementary Particles, September 1965 (unpublished) o 29. Jo Ao Kane, R. Ao Stallwood, R. Bo Sutton, T. M, Fields,, and Jo Go Fox, Physo Revo, 95., 1694 (1954)30, Ro Jo Homer, Wo Ko MacFarlane, Ao Wo O'Dell, Eo Jo Sacharidis, and Go Ho Eaton, Nuovo Cimento 23, 690 (1962)0 104

BIBLIOGRAPHY (concluded) 31. J. Tinlot and R. E. Warner, Phys. Rev. 124, 890 (1961). 32. 0. Chamberlain, E. Segre, R. D. Tripp, C. Wiegand, and T. Ypsilantis, Phys. Rev. 105, 288 (1957). 33. L. Azhgirey, Yu. Kumekin, M. Mescheryakov, S. Nurushev, V. Solovyanov and G. Stoletov, Physics Letters.l8 203 (1965). 34. R. Wilson, The Nucleon-Nucleon Interaction, Experimental and Phenomenologic Aspects (Interscience Publishers, 1963). 35. W. Galbraith, E. W. Jenkins, T. F. Kycia, B. A. Leontic, R. H. Phillips, A. L. Read, and R. Rubinstein, Total Cross-Sections of Protons, AntiProtons, Pi-and K- Mesons on Hydrogen and Deuterium in the Momentum Range 6-22 GeV/c, Brookhaven National Laboratory Report BNL-8744 (unpublished). 36. D. W. Ritson, Techniques of High Energy Physics (Interscience Publishers, 1961). 37. E. Heiberg, U. E. Kruse, L. Marshall, J. Marshall and F. Solomitz, Phys. Rev. 97, 250 (1955); L. Wolfenstein, Phys. Rev. 75, 1964 (1949). 105

UNCLASSIFIED Security Classification DOCUMENT CONTROL DATA -R&D (Security claasitfcation of title, body of abstract and indexing annotation must be entered when the overall report is clasified) 1. ORIGINATING ACTIVITY (Corporate author) 2a. REPORT SECURITY C LASIFICATION University of Michigan, Department of Physics Unclassified Ann Arbor, Michigan 2b GROUP 3. REPORT TITLE THE POLARIZATION PARAMETER IN ELASTIC PROTON-PROTON SCATTERING FROM.75 TO 2.84 GeV 4. DESCRIPTIVE NOTeS (Type of report and Inclusive dates) Technical Report No. 23 5. AUTHOR(S) (Last name. first name, initial) Neal, Homer A., Jr. 6. REPORT DATE'7. TOTAL NO. OF PAGES 7b. NO. OF REFS April 1966 115 37 8a. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER(S) Nonr-1224 (23) b. PROJECT NO. 03106-23-T NR-022-274 c. sL. OTHSR REPORT NO(S) (Any othernumber that may be assigned ihs. report) d. 10. A v A IL ABILITY/LIMITAtiON NOTICES Distribution of this document is unlimited I1. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Department of the Navy Office of Naval Research Washington, D. C. 13. ABSTRACT A double-scattering technique has been employed to measure the polarization parameter in elastic proton-proton scattering at.75, 1.03, 1.32, 1.63, 2.24, and 2.84 GeV. An external proton beam froi the Brookhaven Cosmotron was focussed on a three inch long liquid hydrogen target and the elastic recoil and scattered protons were detected in coincidence by scintillation counters. The polarization produced in the scattering process was inferred from the azimuthal asymmetry exhibited in the scattering of the recoil beam from a carbon target. This asymmetry was measured by a set of two scintillation counter telescopes which symmetrically viewed the carbon target. The analyzing power of this arrangement was previously determined in an independent experiment employing a 40% polarized proton beam at the Carnegie Institute of Technology synchrocyclotron. The corrected values of the polarization parameter are exhibited as a function of the center-of-mass scattering angle for each incident beam energy. The prediction of the Regge theory that the polarization parameter in elastic proton-proton scattering is related to the total p-p and p-p cross sections has been found to be consistent with the experimental results. DD 1 JAN 64 1473 UNCLASSIFIED Security Classification

UNCLASSIFIED Security Classification 14 LINK A LINK B LINK C _____________KEY WORDO____S [ROLE WT ROLE WT ROLE WT INSTRUCTIONS 1. ORIGINATING ACTIVITY: Enter the name and address imposed by security classification, using standard statements of the contractor, subcontractor, grantee, Department of De- such as: fense activity or other organization (corporate author) issuing (1) "Qualified requesters may obtain copies of this the report. report from DDC." 2a. REPORT SECUIITY CLASSIFICATION: Enter the over-.2a. REPORT SECURI Y CLASSIFICATION: Enter the. over- (2) "Foreign announcement and dissemination of this all security classification of the report. Indicate whether b n ot aut report by DDC is not authorized" "Restricted Data" is included, Marking is to be in accordance with appropriate security regulations. (3) "U. S. Government agencies may obtain copies of this report directly from DDC. Other qualified DDC 2b. GROUP: Automatic downgrading is specified in DoD Di- users shall request through rective 5200.10 and Armed Forces Industrial Manual. Enter the group number. Also, when applicable, show that optional. markings have been used for Group 3 and Group 4 as author- (4) "U. S. military agencies may obtain copies of this ized. report directly from DDC Other qualified users 3. REPORT TITLE: Enter the complete report title in all shall request through capital letters. Titles in all cases should be unclassified.,, If a meaningful title cannot be selected without classification, show title classification in all capitals in parenthesis (5) "All distribution of this report is controlled. Qualimmediately following the title. ified DDC users shall request through 4. DESCRIPTIVE NOTES: If appropriate, enter the type of._____ report, e.g., interim, progress, summary, annual, or final. If the report has been furnished to the Office of Technical Give t I ive i e dates when a specific reporting period is Services, Department of Commerce, for pale to the public, indicovered. cate this fact and enter the price, if known. 5. AUTHOR(S): Enter the name(s) of author(s) as shown on 11. SUPPLEMENTARY NOTES: Use for additional explanaor in the report. Enter last name, first name, middle initial. tory notes. If military, show rank and branch of service. The name of the principal author is an absolute minimum requirement. 12. SPONSORING MILITARY ACTIVITY: Enter the name of the departmental project office or laboratory sponsoring (pay6. REPORT DATE: Enter the date of the report as day, ing for) the research and development. Include address. month, year, or month, year. If more than one date appears on the report, use date of publication, 13. ABSTRACT: Enter an abstract giving a brief and factual 7a. TTF':The total page count summary of the document indicative of the report, even though 7a. TOTAL NUMBER OF PAGES: The total page couint it may also appear elsewhere in the body of the technical reshould follow normal pagination procedures, i.e., enter the port. If additional space is required, a continuation sheet shall number of pages containing information. be attached. 7b. NUMBER OF REFERENCES: Enter the total number of It is highly desirable that the abstract of classified reports references cited in the report. be unclassified. Each paragraph of the abstract shall end with 8a. CONTRACT OR GRANT NUMBER: If appropriate, enter an indication of the military security classification of the inthe applicable number of the contract or grant under which formation in the paragraph, represented as (TS). (S). (C). or (u). the report was written. There is no limitation on the length of the abstract. How8b, 8c, & 8d. PROJECT NUMBER: Enter the appropriate ever, the suggested length is from 150 to 225 words. military department identification, such as project number, 14. KEY WORDS: Key words are technically meaningful terms subprt'u Aer, uystem~numbers, 4asf nuimber etA*14. KEY WORDS: Key words are technically meaningful terms subproject number, system numbers, task number, etc. subpre, or short phrases that characterize a report and may be used as 9a. ORIGINATOR'S REPORT NUMBER(S): Enter the offi- index entries for cataloging the report. Key words must be cial report number by which the document will be identified selected so that no security classification is required. Identiand controlled by the originating activity. This number must fiers, such as equipment model designation, trade name, military be unique to this report. project code name, geographic location, may be used as key 9b. OTHER REPORT NUMBER(S): If the report has been words but will be followed by an indication of technical conassigned any other report numbers (either by the originator text. The assignment of links, rules, and weights is optional. or by the sponsor), also enter this number(s). 10. AVAILABILITY/LIMITATION NOTICES: Enter any limitations on further dissemination of the report, other than those UNCLASSIFIED Security Classification

UNIVERSITY OF MICHIGAN 3 9015 03483 5556