COO- 1112-5 THE UNIVERSITY OF M I C H I G A N COLLEGE OF LITERATURE, SCIENCE, AND THE ARTS Department of Physics Technical Report LAMBDA-PROTON INTERACTIONS Walter L. Gibbs ORA Project 04938 -.:. under contract w:ith U.-' S. ATOMI:C ENERGY COMMISSION CHICAGO OPERATIONS OFFICE CONTRACT.NO. A( 1-1)-1112 ARGONNE, ILLINOIS administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR November 1967

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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, 1967. ii

TABLE OF CONTENTS Page LIST OF FIGURES. iv ABSTRACT viii CHAPTER I. INTRODUCTION 1 1-1. Introductory Remarks 2 1-2. A-P Elastic Scattering 4 1-3. Outline of the Report 7 II. THE DATA AND ITS REDUCTION 10 2-1. Reduction of Data 11 2-2. Scan Biases 16 2-3. The Impulse Approximation and Spectator Protons 20 2-4. The Strange Particles 23 III. MESON FINAL STATE INTERACTIONS 40 3-1. Reduction of Fitted Data 41 3-2. Meson-Baryon and Meson-Meson Resonant Reactions 44 IV. RESULTS AND CONCLUSIONS 52 4-1. The Inadequacy of the Spectator Model 53 4-2. The A-P Interaction 55 4-3. Summing Up 64 APPENDIX I. The Hulthen Theory of the Deuteron 75 APPENDIX II. Cusp Phenomena and Z-A Conversions 81 REFERENCES 94 ACKNOWLEDGEMENTS 97 iii

LIST OF FIGURES Figure Page 1. The low energy A-P elastic scattering data. 9 2. The intermediate and high energy A-P elastic scattering data. 9 3. An example of the event topology type 2 prong and 1 V. 25 4. An example of the event topology type 2 prong and 2 V's. 25 5. An example of the event topology type 4 prong 1 V. 25 6. An example of the event topology type 4 prong and 2 V's. 25 7. The coplanarity angle of the lambda. 26 8. The mass of the lambda. 27 9. The range-momentum curve in deuterium. 28 10. Bubble density vs particle momentum in deuterium. 29 11. The lambda laboratory path length. 30 12. The life time of the lambda, in its rest frame. 31 13. The lambda laboratory momentum spectrum corrected for the indetecability of short traveling events. 32 14. The laboratory proton momentum distribution. 33 15. The orientation of the proton with respect to the 7r+ beam. 34 16. The orientation of the proton with respect to the lambda. 35 17. The orientation of the lamnbda with respect to the beam. 36 iv

LIST OF FIGURES(continued) Figure Page 18. A comparison of the A laboratory momentum spectra from the reactions w D - P A K (nw) and w P - A K (nv). 19. A comparison of the K meson momentum spectra from the reactions w+ D - P A K and. P * A K nv). 38 2 20. The four momentum transfer A2 from the deuteron to the A-P system. 39 21. A comparison of the A K effective mass spectra from the reactions Tr D [pK+ w A (lower fig.) BK w w,+v A and. the reactions P + w 7 Ao (upper fig.) 47 22. A comparison of the A-w effective mass spectra from the reactions + p KO ~+ wo A w D p K+ + _- (lower fig.) w.w- A and. the reactions K ~ 7 ~ A WT P 4 K+ - (upper fig.) 48 Kw A 23. A comparison of the Kw effective mass spectra in the reactions + p KO 7r+ oF A D-[ [+ + - (lower fig.) P K w T A( and + P 4 + (upper fig.) 49 24. A comparison of the K w effective mass spectra in the reactions + P KO v+ A D7{ D~C 0 (lower fig.) K A (

LIST OF FIGURES(continued) Figure Page 25. A comparison of the A-r effective mass spectra from the reactions D P K 7, A (lower fig.) and. + K w- A V P ~4 {K~ r A (upper fig.) 26. The A-P effective mass spectrum. 66 27. The invisible events. 67 28. The percent interaction as a function of MAp. 68 29. The percent interaction is compared with A-P elastic scattering behavior. 69 30. The proton momentum spectra as a function of MAp. 70 31. The scattering angle in the center of mass assumming the proton is initially at rest. 71 32. The scattering angle under the assumption that the proton is initially distributed isotropically with a Hulth4n momentum probability. 72 33. The A-P effective mass spectrum of events with Pp < 225 Mev/c. 73 34. The A-P effective mass spectrum of events with 100 < Pp < 225 Mev/c. 74 35. A schematic representation of the deuteron based on the Hulthen theory. 81 36. The Hulthen momentum spectrum. 82 37. The angle e defined. 83 vi

LIST OF FIGURES(continued) Figure Page 38. The definition of the limiting angle. 84 39. Comparison of the observable spectator distribution with the protons from an earlier experiment. 85 40. The A-P elastic scattering cross section near the EN threshold as predicted by Dullemond and De Swart (1962). go 41. A comparison of the predictions of Dullemond and. De Swart (1962)with our data. 91 42. The Z. A conversion probability of Karplus and Rodberg (1959) for certain values of their parameters. 92 43. A schematic representation of intermediate Z states. 93 vii

ABSTRACT LAMBDA-PROTON INTERACTIONS By Walter L. Gibbs This research was undertaken in order to study the lambda-proton interaction having a center of mass energy ranging between 2050 Mev and 3500 Mev, with particular attention being paid. to the possibility of resonance phenomena. The experiment is part of a study of the interactions of 3.65 Bev/c m mesons in a deuterium filled bubble chamber. The lambdas were created in reactions of the type a+ d 4 p A (Kn), where (Kir)+ is a combination of pions and kaons which have net positive charge, isospin 1/2 or 3/2, and srangeness + 1. Departures in the behavior of protons and. lambdas from the behavior predicted by assurmming no interaction are carefully examined.. The behavior of the proton is examined. in light of the "spectator model", based on the "impulse approximation" and the Hulthen theory of the deuteron. The behavior of the lambda is examined. in light of properties -0 0O of the reaction w- p - A (Ki), where (Ki) is a combination of pions and kaons having strangeness +1, isospin 1/2 or 3/2, and. zero net charge. This reaction is charge symmetric to the reaction i+N, A (K)+ and, assuming charge symmetry, the cross sections are equal. The A-P effective mass spectrum is especially interesting, VL ll

Although this spectrum, when contrasted to a background of non-interacting events, reaveals none of the previously announced. resonances, there is a significant accumulation of events above background in the range 2100-2200 Mev. This enhancement, whose center is at 2125 Mev, and whose width at half maximum is 40 Mev is discussed in terms of A-P elastic scattering and phenomena associated with the Z-N threshold at 2130 Mev. ix

1 CHAPTER 1 INTRODUCT ION

2 1-1. Introductory Remarks Unlike the two nucleon system, most of whose features have been amply studied over the last thirtyfive years, the story of the lambda-nucleon system is just now beginning to unfold. A complete description of the lambda-nucleon system must include a knowledge of the scattering properties, the angular distribution and cross section as a function of energy, as well as a knowledge of the bound and non-bound, or resonance, states of the system. The possibilities of a bound state or a resonance in the lambda-nucleon system are of special interest. At present, the deuteron is the only known bound state between two baryons, and. no baryonbaryon resonance has yet been conclusively established. On the basis of SUx symmetry predictions, nine "particles" may be placed. in a 1T decuplet with the deuteron. All of these particles would. have spin = 1, baryon number = 2, and they would include, besides the S(strangeness)= 0 deuteron, an S = 1 isospin doublet, an S = -2 triplet, and an S = -3 quartet. The S = -1 doublet would presumably be coupled. via the strong interactions to AP and. AN. This experiment was undertaken to study the AP interaction having a center of mass energy ranging between 2050 Mev and 3500 Mev, with particular attention being

paid to the possibility of resonance phenomena. The experiment is part of a study of interactions of 3.65 BeV/C w mesons in a deuterium filled bubble chamber. The lambdas were created. in reactions of the type f+ d p A (Kv)+ where (Kw)+ is a combination of pions and kaons which have net positive charge, isospin 1/2 or 3/2, and strangeness + 1, that is (Kw) K, K+ K o, K+, etc. Only the final states of the lambda and proton are directly observable, so that any properties relating to the initial state must be inferred. It is presumed that the positive pion hits the neutron in the deuteron, creates a lambda, a kaon, and perhaps some additional pions, and then the lambda subsequently interacts with the proton. Certain ambiguities, however, are implicit in such an experiment. First, the initial momentum of the proton in the deuteron is not known, so that it is not always clear whether the lambda and proton have indeed interacted; the proton may act as a mere spectator to the reaction. Moreover, the final state contains a kaon, and, perhaps.pions as well, which may have interacted strongly with the proton, the lambda, or both, and there is, in general, no way-to determine that the

sequence of reactions is as described above. A more straightforward way to study the AN interaction is to observe scattering events directly. This can be accomplished by creating lambdas of known momentum in collisions of the type w - p A K~ and. then looking for scattering events involving the A, such as AP - AP A number of experiments of this kind have been performed., the results of which will be discussed below. The chief advantage of a deuterium experiment over the direct approach is that the lambda is created in the immediate vicinity of the proton, and thus has ample opportunity to interact. This produces many more events than one could expect from a comparable experiment using the direct approach, because of the short A lifetime, so that resonance phenomena are possibly more readily examined. 1-2. A-P Elastic Scattering. The first examples of A-P elastic scattering were observed in 1959 by Crawford et al.(1959) A sample of 650 A's from associated. production: - P A K~ with momenta ranging from 500 to 1000 Mev/c yielded 4

5 elastic scattering events, from which an average cross section of 40 + 20 mb was calculated. Since then, a number of similar experiments have been performed, and in lieu of describing them chronologically we will summarize their results grouped according to momentum range. Low momentum: P < 400 Mev. The experiments of Alexander et al (1965), SechiZorn et al (1964) and. Pieckenbrock et al (1964) yielded a total of 314 elastic scattering events with A momentum ranging from 120 Mev/c to 400 Mev/c. The results, shown in Figure 1, are seen to be not entirely in agreement with one another. It is clear from this figure, however, that the cross section rises rapidly as momentum decreases, typical of many other elastic scattering cross sections. This rapid rise at low,momentum seems to be adequately described by the effective range approximation: 35 _ 22 2 k + [l/at 1/2 rt k ] + 22 k + [l/as 1/2 rs k ] where k is the lambda wave number and at, rt, as and rs are. adjustable parameters of the theory. Alexander et al (1965) found values of as = -2.46 f at =-2.07 f r = 3.87 f rt = 4.5 f

whereas Sechi-Zorn et al (1964) found a = -3.6 f r = 2 f S S at = -5.3 f rt = 5 f Other forms beside the effective range formula above also describe the rapid rise of the cross section at low momentum shown in Figure 1. Ali et al (1956) has fit cross sections calculated from simple potential models (in the Born approximation) and found that the low energy data was best described (in a least squares sense) by a Yukawa potential V = -U (23/4-) exp(-pr)/ r with. = 1.024 f1 U = 454 MeV f3 A complete study of the angular distribution is difficult to perform in the low energy region due to the fact that small angle scatters yield. a proton which does not go far enough in the bubble chamber to be detected. Alexander et al (1965) finds that the angular distribution of visible events is roughly isotropic. Sechi-Zorn (1965), however, finds a forward peaking in the angular distribution above P = 260 Mev/c as does Piekenbrock. Intermediate momentum: 400 < P < 1500 Mev/c. Roughly 200 ALP elastic scattering events have been observed in the region 400 < P < 1500 Mev/c by a number

7 of researchers: Alexander et al (1961), Arbuzov et al (1962), Groves (1963), Beilliere (1964) and Cline et al (1967). The results are plotted in Figure 2, and are consistent with a constant cross section in this momentum region. Taken in toto, the angular distribution in this region is consistent with isotropy, although Arbuzov (1962) sees an angular distribution peaked in the backward. direction, and Groves (1963) sees a distribution peaked slightly forward. High momentum: P > 1000 Mev/c Seventy high momentum events have been recorded by Vishnevskii et al (1966) and Bassano et al (1967). The cross sections are plotted in Figure 2. As Bassano et al (1967) points out, the slow decrease of the AP cross section at high energy is similar to the well known behavior of the PP elastic cross section and moreover, the two total cross sections are virtually identical in magnitude at high energy. The angular distribution is strongly peaked in the forward direction at high energy just as is the PP angular distribution. In toto, the elastic scattering data is too meager to reveal a resonance in the A-P system unless its width is extremely broad. 1-3. Outline of the report The scheme of this report is as follows. In

Chapter 2 we discuss the genesis of the events studied and. the reduction of the data relevant to the experiment. Chapter 3 deals with the presence of the two body meson-baryon and meson-meson resonances in our data and how they are detected, and Chapter 24 examines our findings with respect to the AP interaction and. presents our conclusions.

0 Sechi-Zorn et al (1964) 0 Alexander et al (1966) 300- A Piekenbrock et el (1964) V Groves (1963) 200 100. 0 ~ 200 300 400 500 P. (Mev/C) Fig 1. The low energy A-P elastic scattering data. 40 A BeilliEre et al (1964) 0 Alexander et al (1961) 0 Groves (1963) Q Arbuzov et al (1962) V Vishnevskii et al (1966) 30 0 Cline et al (1967) O Bassano et al (1967) E 20 I0 0 I 2 3 i4 5 s (Mev/C) Fig 2. The intermediate and high energy A-P elastic scattering data.

GHAFTrER 2 THE DATA AND ITS REDUCTION

11 2-1. Reduction of Data The film analyzed. in this experiment was exposed. in the Brookhaven 20-inch deuterium chamber in 1963-64. The total exposure produced 256,500 frames, of roughly 15 beam tracks per picture. The pictures were then scanned and measured at Randall Laboratory, using the four scanning machines and three measuring machines available. A description of these machines may be found in Moebs (1965). Both scanning and measuring machines project the film onto a green translucent screen and. magnify the image. The scanning machines magnify the image to 1.3 times life-size on three machines and 1.1 times life-size on the other. All the events were measured at a magnification of 2.6 times life-size. The events studied in this report were distinguished by having a lambda coming from an interaction vertex with a slow proton. Acceptable events may have one V, such as in the reaction w+ D - K+ P A or two V's, as in the reaction w+ D -, + P A K~ Moreover, the interaction vertex may have additional w+ w- pairs, so that four or even six prong events with one or two V's were found.. Examples of the major types of topologies found are shown in Figures 3 - 6. The scanning procedure used to locate events with a possible lambda-proton final state interaction

12 was as follows. Each frame was first scanned for V's. Once a V was found, the positive prong was checked. with a template relating curvature and bubble density for protons and w+ts. If this simple check showed. the positive prong was consistent with being a proton, and. hence the V was consistent with being a lambda, a vertex was looked for which satisfied the criterion that the line joining the vertex and the tip of the V split the prongs of the V. Next, each positive prong of the vertex was examined to see if it was consistent with being a proton. Positive tracks which stopped without decaying yielded the best proton candidates. In the case where no such stopping track was available, each non-decaying positive prong of the vertex was examined with the curvature - bubble density template. If it was possible to associate more than one vertex with a proton candidate with a particular lambda, an expecially constructed template was used to help resolve the ambiguity. This template compared the angle the proton from the lambda decay makes with the flight path of the lambda, and. the bubble density of that proton predictded by a Lorentz transformation from the rest frame of the lambda, where the proton has a momentu:m consistent with

13 +7T P P +M + + M - M M = 37 Mev That is, the magnitude of the proton momentum in the lambda rest frame is determined uniquely; it must be equal to 100 Mev/c: |P*I = 100 Mev/c Since the component of the momentum transverse to the direction of the Lorentz transformation is unchanged by that transformation, i.e., V fLI sin =83 P* sin e* the laboratory momentum of the proton must obey the inequality: I f|< P*/sin GL This relationship places a lower bound on the bubble density of a proton making an angle less than a specified angle with the flicht path, since the bubble density is related to the laboratory momentum as follows: bubble density.fl + (M/PL) where M is the mass of the particle. If an ambiguity still remained as to which vertex was to be associated with a particular V, both vertices were measured, and one vertex subsequently eliminated by a coplanarity test to be described below.

14 If a vertex was found to have a positive prong consistent with being a proton, the following information was recorded by the scanners: The frame number of the event the bubble density of the vertex proton (or, in the case of a stopping proton, its length), the bubble density or the length of the lambda proton, the number and nature of the other prongs of the vertex, and finally, whether another V particle was present. A single scan of the film produced 2,579 events recorded in this manner. Part of the film was scanned independently, yielding an estimated scan efficiency of 70%. The coordinates of the tracks in both the vertex and the V were recorded on one of the Michigan digitizers * and the results were run through the computer programs CHECK, which makes sure the measurement confomns to the proper format, and TFRED, which fits a second order curve to the measured points, and thus reconstructs- the track in three-dimensional space, TRED then computes the components of the momentum, the momentum errors, and the bubble density of each track for five different mass hypotheses (electron, w, K, proton, deuteron). The coordinates of the vertex and the * For a description of these machines, see Moebs (1965).

15 tip of the V are also available in TRED, so that the flight path of the lambda is readily calculable from TRED output. TRED was not always successful in reconstructing tracks in three-dimensional space, however, due to faultily measured points or awkward camera perspectives. Three-hundred and one events failed TRED twice and we eliminated them from the sample. The 2,278 events which had successfully passed through TRED were then run through a single program which calculated the effective mass of the lambda and the coplanarity angle, i.e., the angle between the flight path of the lambda and the normal to its decay plane. Only those 1,141 events whose lambda effective mass lay within the interval 1100 < MA < 1130, and.-whose cosine of the coplanarity angle lay within the interval -.08 < cos O <.08 were selected for further study. Figures 7 and 8 show a plot of the coplanarity angle and lambda mass for the events which passed TRED. The width at half maximum of the coplanarity plot is about 20, and the plot is consistent with symmetry about a coplararity angle of 900. The width at half maximum in the lambda mass plot is about 6 Mev. The plot centers at the lambda mass of 1115 as expected,

16 and. has a width consistent with being due entirely to our measurement errors. Bubble density predictions of TRED were then compared with the observed bubble density to determine whether the protons in both V and the vertex were indeed protons. 540 events were eliminated in this manner, so that there were 601 events remaining which had a definite lambda associated with a vertex in which a proton resided. 2-2. Scan Biases Both protons and lambdas are subject to consistent scan biases. The most serious bias is against slow protons which may stop before leaving a recognizable track in the chamber. No protons were observed with momenta less than 50 MIev/c, although on the basis of the impulse approximation, to be discussed below, a momentlum of about 45 Mev/c'should predominate. As shown in Figure 9, a proton with momenta less than 50 Mev/c travels a distance of less than.06 cm in the chamber, which, even under a magnification of 1.3 is too short to be observed. Protons with momenta in the range 50 to 100 Mev/c, traveling a distance of.06 to.6 cm in the chamber can be observed, but not consistently so. It was fouind, however, that those with momentum above 100 Mev/c, i.e., traveling a dis

17 tance greater than.6 cm, were consistently found, and were consistent with the spectator model described below, in the region 100 Mev/c to 200 14ev/c. The bias against slow protons is not believed to be crucial for the study of A-P final state interactions since slow protons are deemed the least likely to have undergone interactions. This point will be discussed more fully subsequently. Figure 10 shows the approximate dependence of bubble density on momentum for m's, Kts and protons. it can be seen that fast protons are indistinguishable from w and K meson by means of bubble density analysis. The highest momentum at which a reasonably reliable distinction can be made is, 1700 Mev/c, thus no proton with momentum greater than 1700 Mev/c was accepted, introducing a bias against fast protons. Although fast protons are believed. to be among thos which have vigorously participated in interactions, relatively few protons have momenta greater than 1700 Mev/c. A more serious form of bias results from lambdas

18 which decay so close to the vertex that they are indistinguishable from ordinary four or six prbng events. Figure 11 shows the distribution of lambda laboratory path lengths. Although path lengths as short as.15 cm were observed, those lambdas with path lengths shorter than.2 cm were not found consistently. We may estimate the number of events lost in this manner by computing the distribution of the lifetimes in the rest frame of the A, and comparing the distribution with the theoretical distribution e- / T, where r is the mean lifetime of the A. This is done in Figure 12, where the lifetime of the A in its rest frame has been calculated from the formula T A MD / PC where M is the mass of the A, and P and D its laboratory momentum and path length. The mean life used in -10 Figure 12 is 2.61 10 sec., which is the average of several published values.* The straight line fitted to the data on a semilog scale determines a A lifetime of 2 +.4 10-10 sec. for this experiment, well within the range of the previously published values. * The published values are found in Rosenfeld (1967).

19 Figure 12 shows that, although the curve remains exponential down to t/T -.1, there are about 60 events missing in the range G < t/T <.1. These stem from lambdas which decay close to the interaction vertex and are confused with the prongs of the vertex. In an effort to determine if these missing events introduce a serious bias into our lambda momentum spectrum we have calculated a corrected momentum spectrum as follows. We assumne the probability of observing a lambda which has travelled a distance D in the laboratory is Pr e/ where D =.2 cm By the above relation for the lifetime we may write this probability as a function of momentum: -D MA Pr = e PC PA and thus obtain a relation between the number of observed events in a momentum interval No (P) and the actual number of events in that momentum interval N (P): N (P) = N0 (P) / Pr

20 Figure 13 shows such a corrected lambda momentum spectrma with the number of events found. by the above formula rounded off to the nearest integer. Although the weighting favors slower ATs, since there were few slow Ats observed experimentally, the missing events are more or less evenly distributed over she momentum range. 2-3 The Impulse Approximation and Spectator Protons A'spectator proton' we define as one which has not participated in any collision with another particle. The behavior ofla spectator proton is predicted by the impulse approximation model.* In its simplest fornm,this model makes a two-fold prediction: In collisions between particles and deuterons, only one of the deuteron constituents is struck, and the nucleon which is not struck preserves the motion which it had at the moment of the collision. The impulse approximation is based on three assumptions: 1. The projectile "sees" only one of the constituents of the deuteron. * A description of this modal in the context of the S matrix formalism may be found in G. F. Chew (1952).

21 The validity of this assumption depends on the energy of the projectile. Low energy projectiles are capable of discerning only the coarsest structure of the target since the de Broglie wavelength of the projectile,'/p, is large. The Hulthen deuteron, as seen by a pion of 3.65 Bev/c, is depicted schematically in Figure35 of appendix I. This picture shows an average distance between the nucleon centers of 3 fermis, while the individual nucleons have a radius of 1 fermi. This is an effective radius, taking the spatial extent of the pion at 3.65 Bev/c momentum into account. At our momentum, this assumption is justified to the extent that one can believe phenomenological theories of the deuteron.* 2. The collision is "sudden" in the sense that the collision time is small compared with the period of the deuteron. It R is the range of the force involved, and V the velocity of the projectile, the collision time is R/v. For pions at our momentum, this is roughly to 5 x 10 sec. As shown in appendix I, the period of the deuteron is -22 roughly 3.10 sec. so * For a complete discussion of the deuteron see L. Hulthen (1957).

22 td / r deuteron 5/3 10 << 1 3. The deuteron is weakly bound in the sense that the binding energy is small compared with the collision energy. Since the pion nucleon center of mass energy is roughly 2800 Mev and the binding energy is 2.226 Mev, this criterion is amply fulfilled. Thus, the assumptions of the impulse model are satisfied, and we might expect the proton momentum spectrum and angular distribution to be identical with those distributions prior to the collision. Since the deuteron is primarily, S wave, (see Hulthe'n (1957)) and. also unpolarized, there is no preferred. direction in the lab. and. the angular distribution should. be isotropic. The momentum spectrum of the proton, as predicted by the Hulthen theory is given in Appendix I, Figure 36. In Figures 14 and. 15 we examine the proton d.istributions in light of the impulse model. Figure 14 shows the proton momentum distribution superimposed upon which is a Hulthen distribution normalized so that the areas under the two curves between 100 and 150 Mev/b agree. We see that discrepancies between the two curves start arising at 225 Mev/b and the faster protons are not described at all by the impulse model. Figure 1 shows the angular distribution of the protons made with respect

23 to the beam. The distribution in no way resembles the isotropic distribution predicted by the impulse model. Figure 16 shows the angular distribution between the proton and the lambda. It shows the proton and lambda tend to favor the same direction of motion. 2-4. The Strange Particles No simple model, such as the impulse model, predicting the behavior of A's exists. Figure 17 shows the cosine of the angle the A makes with the beam. As one would expect, it is sharply canted in the forward direction. In Figure 18i we examine the laboratory momentum spectr=un of the A. For comparison, we have included the lab momentum spectrum of Wangler (1966) from the reaction w P 4 A (Kr)~ at 2550 Mev. This reaction is charge symmetric to the reaction + N (KT)+ and, assuming charge symmetry, the cross sections are equal. Since the wN center of mass energy is not a constant, but ranges from 2600 to 3100 Mev with an average value of 2750 Mev, we must, in addition, make the asstunption that the momentum spectra are slowly

24 varying functions of the center of mass energy. Figure 83 shows oiur A's to be somewhat slower than those from P- P, in spite of the higher average center of mass energy. This may be evidence for a A spectator proton secondary interaction. We will discuss this point in some detail in Chapter 4. Figure 19 contrasts the K meson momentum spectra from the two experiments. They are very similar, except, as one would expect, the T- P events are somewhat slower. Finally, Figure 20 depicts the 4 momentum transfer from the deuteron target to the A-P system. It is clear from the graph that low momentum transfer events predominate.

25!',~.il..'.:l, ~. - -'. ~'.,~. ~,. ~'.' ~, i ~:V,'..-r.~....~,:t,~.'~ /,,.,. ~',;ti?,i;;;'./ x, ~'.':..... "..~tl:.t'~'.''~.'; f.". ~. I'!i ~:'./ ~:'li[ iil':'1 il.,' i'/: i.. l. ~ o,, I [... -. 4!14 i".i,.,'t..'-....'';''..,.: -" i ~. ~ I z~;,.l.~., i ~ I.'1.''I ~1; ~ ~'~':'.''''' ":'.:' i, ",.....-.' _,~'.....''~ -' ~'- l'/,~;i!.~ " i'..~ "~',' ~'~.' i. ~': I iii:t-' i':,'' ~''... -''.;....,.-''~.. ~. ~'., ~.~;:;I~',,: ~..'. \, ~,~'~,,-,..;,./,....... —.!.,.,/! ~i-~;,t..,' ~... _!. v',,~! ~',':-" ~ "',:'"..'.;,'.~ -[' /.'!.~f"l~:! ~', ~ il:l I,: t'~.;..~...t..-, ~:./ ~; ]11;:?'~7_,......'".'::''' "-.'-. ).-'.. ~/. ~,..~-~k~1'.'. I i!''! Ii' I''!':''.'.'",' ~!!'; i.,'.~' i ~' i-'".'-'~'' ~'.'~ i,~....'':.\!iil!:' ~L.j.. i.'.i'......'.'". ~ —!~:li',': ~,,... ~.':....,.!'.: ~.',~i'::l'i/~'. ~,i~,~ ~'..... ~,. ~' -..-. ~.. i.. /~'...,~ ~.' — i?'"'.'.'' ~ -.;.. ~,i;'' i I -;'' ""'~:""" i:J~'''....'.''~i"';~'" ~ "-',..., i.,'::~}11i'i'i,, "'" "'"''""';.-! ~.. i' [,,t'~... ~ 1'1'..'.,... ~:::i~-~.!I i i"' ", "-....-':~J~k!i:.-,';'',;,.' 1:.2.!:' i~!i i I r \ / i'~i i' ~' ~'\"" "'.''t'T,.11~'",' "[ x /'':.. —'.-:.,,r.'.~!\ii~'i'.j[x /''""' j"'''li/ I;"'~'"' ".-:'' -.; "/.~ i~'~:,,'f" ~.',,'. I iiii~i~! ~ i./k / ~ - ~ ~ ~ u,. ~'."..:'. ~'' -",.' t.',~j~,'\,'.t ~ t:t ~ \ / -.:,~, [:..I.,-'. ~ +;~.' v-' ~'"'!~{: ~l'',. i ~....t!~:;.;i. ~..,..........:~,! ~,,.~.,l"'x \\ f'.'...';,?x ~'.~.........~....,,,.,,..,.;~.:~.......:....t-;''":/'; ~i':~..!'.'.x'..........;~:i~.,,,,t!.-, I ~\~-\ \K' DECAY ":.;, \"'?'." ~/:;~'~11''~i:.j'"l -'~ ~ \-IN FLIGHT ~.'....... —.. i.' -f',..!r::ii.'..... ~ -i.'~:;-:~: ~il ~,I', - i; - -'-...'.', —..,...... ~ I, -,;-5;'' -...".' ~.........~>A'!,., i~,.-:..,~1 \ \ ~..',.'-'.'.~.'~:':. "...:.:., 4 ~-.,j ~.' i' 1- l' ~ ~'-~.""I~,'' ~.' P ~ }.', -.-.''71!~:!.'lll'-i.-!'l'u ~ ~ ~ ~..\....i~i 1~'.r';,: ~ ~ "'X/i.~! ~g,'.I~ ""' ""'-; "U~i'i'::!~"i'ii':I ~r+ 2pr & IV. &2V Fig 3. An example of event Fig ~. An example of event topology type 2 pr topology type 2 pr and 1 V. ~ and 2 V's.;~,'' i''' ~'" 1.....''...' -'i ~ ~.' t' ~'' i' -.~: ~. ~ i -'....', t1';' ~.,;',, ~ ~'~....,,~,: -,,' ~'...... ~,., ~' i ~:~,$.',!~!:A~I'i:'..'~', ~..~ i, Ii I....'. ~,';,: ~'.~ L..:.:!~.~-4+.4-'~.', ~ ~,,. ~. ~ - ~,,... \ ~. ~-.., t.tiii.u:~..,..'~,...!,.,.,.,~..71.,~~,,~.:.....,,,...,,,......,,.,!,~ —~.-,-.-,~.,":'' ~! ~' "'"'''" "'' i:' i!'" //': "':',,.','~'p.'!~j ~?'~,'.~r':.','' "'' ~', - i' -, ~...,,,:,.,,.....:~"~/ ~.,.; ~,.:~'!i"q-','-'i-!d-:'..'.,,.',?,.,-', ~i~' /....~-.'i"/ i, " ~''{ ~"''>'~'"'' i.;iJi''!, _... -,~>,i'-' i!i~: ~'?ii: -:..'' ""'''''' "'" ~':~\~.:,- "i~l: a!li~' "''"'. i': --'''"-.,71~'~,;" I~;', -.,,:~'?. ]' i ~.'"' ~' "~f!fr!if! ~......,,,.,,,.,.,:i~..-~,,,,,.,/.. ~.; -.....~:, - Ell,! ~.f /.....,...... t!,ll!~'i ~:i:''.~..k?.1.', / "~'.:. ~., ~!...,,.'[:,~ Ill'', ~'" ~:-]!~"'"..."',zi-,.',,',,t,,i,~'l~,':'.,.r..,/:':-~., "''''"'liJ ~':: ~::','..' -....-A ~.!,,,X,, ~.~.~!~:,.;. U_.'.,~/-'...~''-' ~. ~., $' " ~', II,~l I.'.,i.. ~ " "" i.~ ~''iI,j~..,!i -.. —!:. ~,,,,,,,,~,, ~' -.,, ~';',,~,',,I;, ~......' i.:.!i ~.... \ ~ ~..',:"'.'::....,, i,~ ~.i.~;::~il \/"::, ~'4,!', /,~-''"' "''"t —:..i'.'..",~1!~:~! lb. /Ix. ~'" i\i] I. -.,".- " I ~'.,' —..:.!...,.' II~"[ 7';'"":: ~' "'i "~"....' ".,';-". __\ ~'.,.,F" "'l ~~" "~~~~~ti. il'x' /......' "'.... ~ i'i -,, ~ ~'.,' ".-. ~ -.'i'! ii.', I;!-~!!. li;11. ~i ii~l'i! -' i i'il ll ~; t;;i~ii..:ij-!l ~r+ ~:,-,:,-.:.'.~.- ~ H-~ ill -~ ~ i X\lV/' "''''" ~ i i|% i "- -'.... ~iJ.,i;,J-" ~il; —....'. -'~, ~ ~!'~!il'-. -' * "-..:. —':k' —; ~'"'";.'.)': —' i' ~! i;~:~l 7 ""-,-' -'' t,~'q ~,'~'~''"'"1....., 4pt & IV'',....... "2 i ~" i!l~'ll[ [4pt.6 2~/ Fig 5. An example of event Fig 6. An example of event topology type ~ p r topolog:~ type 4 pr and 1 V. and 2 V's.

26 COPLANARITY ANGLE 240 220 200 180 160 140 120 100 80 60 40 20 -0.8 0 0.8 COS e)

27 MASS OF LAMBDA 140 120 100 80, 60 40 20 1100 1110 1120 1130 M Figo8 The, mass of thei lambd-a. The mass is c2entered. at 1115. Mev and. the wid~th at haf aimmis6Mv

RANGE- MOMENTUM CURVE IN DEUTERIUM 10 20 40 60 80 100 200 400 600 800 to 9 876504z 35R=.O5cm R=.5cm R= 5cm 2I1, I, I I, i1', /', I' I' TPl Fig 9. The range-momentum curve in deuterium.

29 3.4 3.2Tr K P 3.0 2.8 2I.6~2.4 z 2.2uw2.0-J co 1.8 m 1.6'.4 1.2 1.0.5 1.0 1. 5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 MOMENTUM, BeV/c Fig 10. Bubble density vs particle momentum in deuter-~ jurn.

6050w 0.3020-~~~~~~~~~~~~~~~~~~~~ 100 2 4 6 8 10 12 14 16 18 20 22 24 26 C LAMBDA LABORATORY PATH LENGTH Fig II. The lambd~a laboratory path length.

31 100 80 60 z W 40 w UL 0 z 20 0 10~~~~.5 1.0 1.5 Fig 1,2. The life tim of the lambda in its r~st fae ris the averag-e of several published. values

30 20 I0 500 1000 1500 2000 2500 3000 30 ~A(CORRECTED) Fig- 115. The lambd~a laboratory momentum spectrum corrected. for theindteci~blity of short traveling events. (e et

33 140 130 120 110 100 90 80 70 60 50 40 30 20 I0 0 200 400 600 800 1000 1200 1400 1600 Pp MeV/c Fig 14-. The laboratory proton momentum distribution'. The smooth %.curve is the prediction of the spectator model. (See Text)

154 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 302520'5 I0 5

135 70 65 60 55 50 45 40 35 30 25 20 15 I0 5 -1.0 -.8 -.6 -.4 -2 0.2.4.6.8 1.0 Cos (A~p

136 360 340 320 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 -4.O-.8 -.6 -ft -.2 0.2.4.6.8 1.0

157 55 50 45 40 L (135 z > 30 U-25 U rn. K )+ 0 ~~~~0 7rT-n (KW)0 z20 - K7 15 I0 5 500 1500 2500P A Fig 18. A cotnparison of the laboratory momentum spec — t ra

25 0 This experiment Et I -P —> A(~1 ) 15 0 C:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 0 o~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~c 0 z 0 500 1500 2500 Pko+, Mev/c k Fig 19. A comparison of the K meson momentum spectra from the + reactions w D 4 P A K (nw) and w P A K (nA )

40 35 30 25 20 15 10 5 1.0 2.0 3.0 4.0 5.0 6.0 (BeV) A —o AP Fig 20. The four momentum transfer A from the deuteron to the A-P system.

40 CHAPTER 3 MESON FINAL-STATE INTERACTIONS

41 35-1. Reduction of Fitted. Data The e ve n ts we-re ki nematically analyzed by the program GRIND. This prog-ram takes the momentum assignments and. momentum error assignments of TREID, and, after assig-ning mass hypotheses to the tracks, applies the laws of conservation of momentum and. energy. The method. GRIND uses is briefly as follows: The computed. momenta must satisfy not only conservation of energry and. momenta, but als-o the con22 dition thatx for the events is a minimum, X- being- defined. as the we1_1ig-hted. mean square deviation of -the computed quantities from the measured. ones. That is x2 i (P - ~m) G.~ (% P m iyj~~~~where the we1_ —ighting matrix G. 1 is the inverse of the error matrix G.. ~m ~m ij 1 i.e., the product of the measured errors, and P. - the fitted. values of the momentum P. - the measured. values of the momentum n - the number of measured. variables Both the requirements of conservation of energ-y and 2 momentum, and. a minimal X are'satisfied. simultaneously when one minimizes-'the expression

42 2 2 X (Pea)X + ak fk (P) where the fk (P) = 0 are the n't constraint equations. If the constraint equations were linear in the Pi, the "best fit" momenta would be easily obtained by solving the set of linear equations 2 aX2 (P,~) / a p. = 0 However, the conservation of energy equation is not linear in the momenta, so that neither is the above set of equations. Hence, since no general way is known to solve non-linear equations, they are first linearized by writing m P. = Pm + AP.and expanding the constraint equations in 1 1 1 a Taylor series. Thus, the equations 2 6 xjj j 0 a AP 1 are soluble and the process may be iterated to obtain a set of momenta which converges to a set satisfying conservation of energy and momentum. The process terminates after 9 steps, or if the process is found to diverge. In general, there are 4 constraint equations, one for each of the three momentum components and one for the energy. If, however, there is a missing neutral particle, such as a w0, its momentum may be inferred from the conservation of momentum equations and its energy from the relation E = P + M. Hence, in the case of a missing neutral, energy conservation is the only constraint. A fit of this

~43 kind. is called. a one constraint, or ic fit, whereas if there are no missing- particles, it is called. a 4c fit. There are additional constraints, moreover., which may be applied to V events. Since the direction of the line join-. ing, the vertex and the tip of the'V must be the same as the direction of the sum of the momenta of the two prongs of the V, there are two additional constraint equations for each V particle. In ad~dition, the momenta of the tracks of the V must satisfy the relation (p1+ E2) ( + P92= Mv2 where Mv is the mass of the V. When these three additional constraints are applied, the f it'is called. an Nopt 2 fit, or in the case of two Vts, and, hence 6 constraints, Nopt 15. Thus'it is possible to have lc, 4c, 7c, and. l0c fits. In fitting an event, GRhIND perf orms the f ollowing sequence of calculations. Fi-rst., the effective mass of the V, iscomputed along with a xP probability of being- a K or a A. Next, a coplanarity test is mad~e on the V to determine if the \7 particle is associated. with the vertex of the event. If so, the event is f itted. by adding- the prongs of the V to the vertex using the ordinary fittingl procedure., thus giving an Nopt 1 fit. Next, the additional constraints are employed., yielding- Nop~t 2, or Nopt 35 fits.

A successful GRIMD fit for a given hypothesiss'includes as output the fitted momenta, errors in momenta and. predicted. 2 bubble density for the tracks., as well as the X for the hypothesis. It also includes the number of steps taken to converge and. the number of constraints. Most of the 562 events successfully fitted. by GRINTD received good. fits for several hypotheses. In general,, accepting only Nopt 2; or. Nopt 15 fits reduced the number of hypotheses, but in order to assign a unique h'rpothesis, the events were re-examined visually to compare the predicted bubble density with the observed. bubble density for all tracks. In this way 2155 events receiving Nopt 2 fits were found to have only one GRIND hypothesis which was consistent with the observed bubble density, and 96 remained ambiguous and. were separated. fro-m the others by the prog-ram FILE. The remaining 2155 events were run through the prog1ram POLISH, whose calculations were the source of the final data. 3-2. Meson-Baryon and Meson-Meson Resonant Re_~actions. It is interesting- to compare the presence of mesonbaryon and. meson-meson resonant states in this experiment with resonant states in the 7n-P d~ata. Wang-ler (1964), in the reaction

45 sees a substantial N* (1-690) in the A-K effective mass spect rum. W ehave plotted our A-K effective mass spectrum f rom the reaction w+ D P K+ vo w- A along with his results in Figure 21. These two reactions are charge syrmmetric according to the spectator hypothesis. Although the statistics are meag-er, we see no evid~ence of the N* (16-90). Figure 22 compares the A-v effective mass *spectra from the same two reactions. * The v-P d~ata shows clearly a Y* (1385) whereas our data doeI=s not, althoug-h ag-ain, statistics are meager. Th-e K-w effective Thmass spectra from the above reactions, however, shows a clear K* (891) in both the w-P and. +]D events. This is shown in Figure 25. Figaures 24 and. 25 contrast effective mass spectra from the"n reactions K+wv- A and. P K+w7T0 A w+I D ~ P K 0 7T+ A which., according to the spectator model, are charg-e symmetric., Fig-ure 24 shows the K-w effective mass spectra. Both reactions exhibit a strong, K* (891). Finally., Figure 25 shows the A-v effective' mass s p ectra. Both experiments

46 y* (1385) region- is a reflection of the K* (891). We have s ha d.ed events which satisfy 1500 <MAW< 1450 850 < MK < 950 As shows in Figure 25, the number of such events is rouguhly equal to the number of events above background..

47 20 10 Is 0P O 10 1800 2200 MAK _,!................ 1800 2200 MAK Fig 21. A comparison of the A K effective mass spec+~~~ + P K + A — tra from the reactions w D [P K+ + - A (lower Fig.) o + A and the reactions w- P 4 [K+ upper Fig.) h pA(upper Fg) The peak in the upper figure is the N* (1690).

48 40 30.20 10 10 1400 1800 MAnl 1400 1800MAnl Fig 22. A comparison of the A-w effective mass spectra from the reactions O+ 0 wV D <K0iT T (lowe-r f ig) + PK w A (pe i. ndthe peak tinohnperfgrss *18)

49 J30 20 ao 1011 600 1000 1400 MKn Fig, 23. A comparison of the Kw effective mass spectra in the reactions + A TF DrT (lower fig.) and K+ o KwwA The pak ibot fiue is thepk*r(891

50 20 10 20 10 600 ~1000 1400 1800MK Fig 24. A comparison of the K w effective mass spectra in the reactions + PK~W A w D fK0 A (lower Fig. and wr P ~[0w (upper figure) K wT A The peak in both figures is the K* (891)

51'5 10~~1 5~~ 1400 1 02000 2300 Mn Fig 250 A comparison of the A-7 effective mass spectra f rom the reactions + P~~+ 0 Wr K + (lower figure) and K W W ~K 77 A (upperfi) The shaded events are those for which 850 < MKW < 950 Mev,~ and 11500 < MAv < 1450,

52 RESULTS AND CONCLUSIONS

4-1. The Inadequacy of the Spectator Mod-el. The spectator mod-el asserts that the nucleon which is not struck by the incident meson does not participate in the, interaction. This assertion implies a number of consequences which are inconsistent with experimental results. First, the proton momentum distribution. should. be the same after the collision as before. That is, its momentum distribution should. simply be proportional to j~ Pf2 P2 where Oj is the wave function of the deuteron in the momentum representation. It was seen in Chapter 2 that the proton momentum distribution was ill-d~escribed by the Hulthe~n theory of the deuteron, which predicted. far too few protons with a momentum g-reater than 225 Mev/c (Figure 14).. Secondly, since there is no preferred. direction in the lab, the proton's angular distribution should. be isotropic with respect to any fixed direction in the lab. This was shown in Chapter 2 not to be the case. Fig-ure 15 show~s many more protons g'oing7 forward. with respe-ct to the beam than backward. When coupled with the requirement of charg-e symmtry,~ the spectator mod~el predicts- that the A-K-wT systemr in the react ion w- P -4 A(K w)0

54 is identical with the collision products in the. reaction w+ n - A (K )+ for comparable wT-N center of mass energy. Due to the f ermii momentum of the nucleons there is no unique vn-N center of mass energ-y, but rather it is spread, out from 2.6 to 3~.1 Bev [Ben~son (1966)]. Howe-'ver., if we assume a weak depend.ence of the cross section variation on the center of mess. energ7y, we would. expect that the laboratory momentum spe.ctra of the collision products A + (K in)0 in general, and. the A laboratory momentum spectrum, in particular, to be comparable to those observed. in A (K in). This is seen not to be the case f or the A spectrum (Figure 18). The lambdas produce-d in this experiment are somewhat slower than those produced in the in- P experiment of Wangrler, even thoug0h the averag-e effective beam momentum used. in this exp'eriment is slig-htly hig-her. Finally, the two-body effective mass spectra in the.A (K in)0 system should be the same as those in the A (K w)+ system as reg-ards the production of resonances. Althoug-h the meson-meson resonant states K* (891) and. 0 K* (891) proved to be as prominant in w+ ID as in in- P., this.was not true, for the Y* (11385). Moreover, no N* (1690) was observed in the A-K effective mass spectrum. However, the failure to detect strong2 N* (1690) and. Y* (15385) sig'~nals

Thus, there is considerable evidence to indicate that the spectator model is not completely valid and that the nucleon that I s not struck: in-itially does indeed. subsequently participate in, the interaction. It is to this question we' now turn. 4- 2. The A-P Interaction. A number of possible resonances in the A-N system have been reported by various researchers. Melissinos et al (1965), after examining- the spectrum of K+ mlesons in P-P collisions, found the indication of a singularity in the A-P S matrix near the A-P threshold. The energy above threshold. of the sing-ula'rity was given as +4 +10Mev -5 A resonance with half width +10 l5.- Mev is one interpretation of this singularity. Piroue et al (1964) observed anomalies in the K~ momentum spectrum resulting from the bombardme(n,1 —nt of a beryllium, targ-et by protons. One explanation is a resonance in the A-P system at an effective mass of 2560. No attempt was made to assigrn a width. Buran et al (1966) observed. the A-P effective mass

56 They report an enhancement at 2220 Mev, the width-being-C.estimated. at 20 Mev. By examiningr the A-n effective mass spectrum resulting from K- absorption at rest in helium, Cohn et al (1964) report a resonance at 2098 Mev with a width of 20 Mev. Figure 26 shows the A-P effective mass spectrum for our experime nt plotted. ag-ainst a backg-round. of non-interactingr events which was computed, according to the spectator model, as follows: Proton-neutron pairs were generated with equal and. opposite momenta distributed, according to a Hulthe"n probability density. In the rest frame of the neutron, lambdas were created. with a momentum distribution griven by — that in the experiment of Wangler:, W-P 4A+ (Kw7) 0 A Lorentz transformation was then perfo~rmed to carry the la-mbda momentum into the lab and. the effective- mass of the A-P system was computed. A visibility criterion to be described. below was applied to the proton, and those events deemed to be visible were histogrammed. Approximately 15,000 events were thus generated, of which one-third were adjudg'ed visible. The smooth curve drawn through the histogram of visible events is- shown in Figure 1.

.57. of momentum P leaves) an ionized-track of lengrth R given by arange energy relation where in deuterium b 10156 m 35.615 The units of b are such that R is in cm when P is in Bev/C. The leng-th projected. on the window of the bubble chamber is approximately the length seen by the scanners and dle-pends on the orientation of the particle trajectory with respect to the plane of the window. This is always less then or equal to the leng-th of the track. *As shown in the appendix the probability-of having- a projected. length gareater than a minimum length Rmi is *Pr 1 By multiplying the visibility probability by the Hulthe~n momentum probability density, a -momentum distribution is obtained which predicts the shape of "tspectator" proton distribution which will be picked up by the scanners. As discussed. in the appendix, we chose the value Rmn.14 cm since this value yield~ed a momentum distribution curve which ag-reed with the spectator proton distribution of an.ear-lier experiment.

58 Those events for which the probability was larger than the random number were deemed visible. The A-P effective mass curve as seen in Figure 26 reveals none of the above mentioned resonances. However, there is a large accumulation of events above background in the region of 2125 Mev. As expected, the curve of figure 26 disagrees badly with the data, indicating the failure of the pure spectator model. The disagreement is most pronounced for the low effective mass events, and implies that the low effective mass A-P systems interact more readily. Since the A-P elastic scattering cross section decreases. as a function of energy, as shown in Figure 1 in Chapter 1, one might suspect that the deviation from the spectator model might be accounted for by the elastic scattering between the lambda and the proton. The background curve of Figure 26 is not a phase space for the A-P system since it is not proportional to the number of events in an effective mass interval which are capable of interacting. Figure 27 shows the A-P effective mass of the 10,000 events generated in the same way as those mentioned above, but deemed invisible. According to this curve, there is a large phase space for A-P events in the region 2100 - 2200 Mev. Thus, according to this model there is an extreme sensitivity to any interaction in this effective mass region.

59 In Figure 28 we have calculated. percent interaction in this effective mass range. The percent interaction is d~efined. as the percentage of the invisible events which.must be ad~ded to the vi-s-ible events to reproduce the experimental data. It is presumed that events'in which the Ainteracts with the proton yield a visible proton. The normalization is such that lOO% of the events in the mass interval 2050 - 2075 are presumed to interact. The errors are statistical only. One might expect that this curve would be proportional to the total elastic A-P cross section if this was solely responsible for the spectator's role in the interaction. Fig-ure 29 shows the same percent interaction points normalized. so that the 2075 point falls on the A-P elastic scattering curve of Ali (1967). This curve was calculated. to the best fit (according to a least squares criterion) to the low energ-y A-P elastic scattering- d~ata. We see from. this that, according- to this analysis the percent interaction points. are, within errors, consistent with A-P elastic scattering results, which show a smooth non-resonant variation with energ-y. Althoug-h this procedure does s eem to d~escribe events with MA < 2200, it fails to d~o So for the higher effective mass events, for which it predicts more events to be visible than are actually observed.

60 about the proton momentum spectrum as a function of the A-P effective mass. Although the exact A-P elastic scattering- ang-ular distribution is not known, as discussed. in Chapter 1,. the experimental d~ata in the reg-ion 4o0 < P < 1500 Mev/c, ie, with an effective mass satisfying- 2085 < MA < 2370 Mev, shows an angular distribution consistent with isotropy. We heve fed in the hypothesis of isotropic scattering in the A-P center of mass and. calculated the resulting-C laboratory proton momentum spectrium. Figure 50 shows the experimental momentum spectrum compared with that predicted. by assuming- no' interaction (the spectator. mod-el) and. the momentum spectrum predicted by S wave (i.e., isotropic) scatterin~g. The spectator curve is normalized. at the momentum value 100 Mev/c, whereas the S wave scattering- curve is normalized in accordance with Figure 28. That is, l00% of the events in the effective mass interval 2050 - 2075 Mev are presumed to have S wave scattered, 50% in the interval.2075 - 2100 Mev., etc. The results show g-enerally poor agreement above 2100 Mev indicating- that this method of analysis is not free from internal inconsistency. One interesting- feature of the data is the large number of events in the 2100 - 2125 Mev range'in which the

61 These events may be due to an interaction characterized by a peripheral angular distribution, or they may be spectator events. In an attempt to determine what sort of distribution must be assumed to account for these events we have calculeted the angular distribution of the events whose effective mass lies between 2100 and 2125 Mev und.er two separate assumptions: First, we have calculated. the cosine of the angle made by the A in the A-P rest frame with the direction of the f communicating with the laboratory frame. This angle is the scattering angle, i.e., the angle between the initial and final A direction in the A-P center-of-mass if the proton is initially at rest in the laboratory. We have generated background events by calculating the cosine of the same angle with visible Hulthen protons replacing the experimental protons. Figure 31 (a) shows the angular distribution with a background curve normalized to 51% of the slow proton events (P < 225 Mev/c), or, 19 p events (see Figure 16). By subtracting 19 background events, we obtain the angular distribution shown in Figure 31 (b). For comparison, we have superimposed a curve describing n-P elastic scattering at a proton momentum of 575 Mev/c. [This curve was taken from the work of Hess (1955)] Figure 32 shows the same scattering angle, now smeared in a statistical manner, under the assumption that the proton before

62 the collision is distributed isotropically in the laboratory with its momentum distributed acc-ording to a Huithen probability dlensity.* Ten initial protons were generated for each final proton, and. the cosine of the ang-le between the initial and final proton was calculated. The result, along- with a background, curve similar to that shown in Figure 31 (a), but normalized. to 190 events, is shown in Figure 52 (a). Fig-ure 52 (b) shows the angular distribution with the 190 back~ground events subtracted. The n-p elastic scattering angrular distribution is also shown. It is clear f rom both Figure 51 (b) and. 52 (b) that af ter a background subtraction is made, the ang-ular distribution is comparable to the n-P distribution in the forward. reg-ion. Thus, w-e. conclude that the peak in the A-P mass spectrum(Figlure 26) at 2100 - 2125 Mev is consistent with beingC made up of 26% non-interacting- A-P events and, of 74% events in which the A elastic scatters off the proton with an ang-ular distribution similar to that shown in Figures 51 (b) and 52 (b). It is possible that the basic assumption that the A momentum spectrum is a slowly varying function of the wF-n center of mass elnerg-y is not valid. For this reason another *V Thi distr-ibuinissoninApndx1 igr 6

6`3 backg~round. curve, independent of Wangler's data was calculated as follows: Our experimental M's from events whose proton momentum'lay below 225 Mev were compounded, with Hulthen protons. Although some of these M's may have interacted., it is believed. that any interaction undle-rgone will not alter the A momentum. spectrum appreciably, since.the protons associated. with these events are not fast enough to be inconsistent with the spectator mod-el. Figure 35 shows the experimental A-P effective mass spectrum alongl with the curve, so.calculated, depicting the non-interaction.background in which only events dleemed visible by the aforementioned. visibility criterion are employed. The curve results from d~rawing- a smooth curve throlugh the histogram of of approximately 6,000 events, and normalizing so that the area enclosed equals the experimentally observed. number of events. Any inconsistency of the curve and. the data must then be reflected in a departure of the observed proton spect ra from the Hulthe"n prediction for P < 225 Mev/c. p That this is indleed. so f or the M - 2100 - 2125 region can p be seen In Figure SQ. The enhancement at. 2125 Mev is d~ramatically in evidence among- the slower proton events. This is not inconsistent with the f ind~ingrs of Cohn et al, whose nucleons were slow enough to be consistent with a spectator modl The lower effective mass value(29Me)osrd miga-ht be due to the upper kinematic limit of 2100 Mey in

.64 In Figure 54 we Show the A-P effective mass spectr;um,for the events whose proton momentum is in the interval 100 < P < 225 Mev/c. This figure shows the enhancement p C.centered at 2125 Mev to have a width at half -maximum of 40 Mev. Since this enhancement occurs so close to the Z-N threshold at 21350 Mev,'it is possible that the exces's events are the result of the interaction of the Z-N system with the A-P s y SItem. This possibility is explored. in Appendix TI where cusp phenomena and Z-A conversions are discussed.. 4-3. Summing, Up In conclusion, a number of observations cnan be mad~e. First, the spectator model is not. completely valid for A-P events. Secondly, there seems to be a vigorous interaction betwe~en the lambda. and proton in the effective mass region of 2100 - 2150 Mev. Moreover., this interaction is not accounted. for by a monotonic decrease in the elastic scattering cross section as a function of energry. Since this interaction i~s most readily apparent among- the slower pro-ton events (P < 225 Mev), it is not pure S wave in nature p (F igure 30), -but must contain a forward peak in the centerof-mass ang-ular distribution (Fig-ures 31 and. 52). The enhancement whos-:e center is at 2125 Mev and. whose width at half maximum is 40 Mev is possibly related. t o the pDresen-e of the 3-N-T threshold at 2150O Me~v. TPheP 9r —,n dtiI le

65 scIattering of lambdas near 600 Mev/c off free protons.,

40w 0 z 503 0> 2100 2400 2700MAMe Figr 26. The A-P effective mass spectrum. The background. curve,, a prediction of the spectator mod~el, is described. in the Text.

Co * - *\ * - O \ proton is not observable.

68 150.= z I00-. 0 05! — ~.O.. DI 2100 2300 MAP (MeV) Fig 28. The percent interaction as a function of MAP. This figure is described in the Text.

69 Imb) 50 41 2100 2200 (MeV) Fig 29. The percent interaction is compa elastic scattering behavior.

70 MAP~2OS 20 ~~~~~~~~~~~2075 (MAP ( 2100 U)10 w U 0 5 ~~~~~~~~~~~~10zw 0 500 ~~~~~~~z Pp (Mev/ C) E 500 1500 PP (Mev/C) 20 2IOO<MAPK2I2S IS ~~~~~~2125<,MAp <2150.0- ~~~~~~~~~~~> lo0 C ~~~~~~~~w 0~~~~~~~~~~~~ > o 0 0 z 5z 500 10 500 1500 Pp (Mev/C) Pp (Mev /C) IS 2150<MAP <2175 40 ~~ 10 2175 <MAp<~2200 w 10-~~~~~~~ 0~~~~~~~~~~~~ z~~~~~~~~~ 500 1500 Pp (M ev/C) 500 1500 Pp (Mev/C) Fig 150. The proton momentim spectra as a function of MAP.- The curves represent the predictions of

20 20 0 L<~ | 101 (/3 > ~ ~ ~ ~~~~~ ~~~~~~- IO,=I IIOI z~~~~~~~ II 0 o0 6~~~~~~~ w z~~~~~~~ 0~~~~ -I 0 I -I 0i COS ( A)Cos (,) os (Ap,A) Fig 31.a The scattering angle in the Fig 31.b The angular distribution of fig 31.a in the center of mass assum- after a background sutraction.The ing the proton is initially results are compared with n-p elastic at rest. scattering.

(I, W R) 4-. 44- ~~~~~~~~~~0 0 0 6 ~~~~~~~z z Co ~~~~~~~~~Cos(F~~ Figr 32.a The scattering ang-le under Fig 32.b The angular distribution offi 2a the assumption that the pro- atrabCkgonDutrcin h ton is initially di'stributd eults are compared -with n-p lsi isotropically with a Hulthen scttrig mome-ntuam probability.

f D 30 Pp<225 20 (IJ 0 6 10 2100 2400 2700 MAP (Mev) A Fig 33. The A-P effective mass spectrum of events with P < 225 P Mev/c. For a discussion of the background curve, see text.

20 21 220 2300 2400 MAp ( Mev) C 44 — 0 z 2100 2200 2300 2400 MA (Mev) Fig 34. The A-P effective mass spectrum of events with 100 < P < 225 Mev/c. The shaded events have 100 < P < 150 Mev/c. P P

75 Appendix I: The Hulthen Theory of the ]Deuteron Huithen describes the static interaction between the proton and the neutron phenomellnologically with the potential V (r) = -r _ V (1 e'Ir e~~ where r is the relative distance between-the nuclei and. V0 and p. are adjustable parameters of the theory, altholugh p.is often taken as the inverse pion compton wavelength The potential is both central and short rang-e, and for small values of pLr since 1 e-r approache's p~r That is, the Hulthe~n potential reduces to the Yukawa potential for small p4r. However, unlike the case at the Yukawa potential, the resulting- Hamiltonian 2 -p4r HL P e M- Mn MP 2m 1- ep Mn:+ Mp may be solved by ordinary matrix methods., or the corresponding radial Schroeding-er equation 2_ 1 d(2 14 v pr + /(/~) t2 2mr r dr o 1- ~

76 may be solved by making a change of variable. Setting u 0 the resulting- wave function is e e-Ir where N is a normalization constant 2 _2c cc_. 2+a N CC 2~~~~~~~~ E = 2.23 MevThe binding energ of the deuteron. 1/a.= 4.3 x 10 -13 cm The wave functi~on may also be written -a~r er where + a +[t. The expectation value of the inter-nuclear distance is given by F-a r -6r r2 e -e, r ~~~~dr This is easily evaluated to yield: 1 22~l) __+.) 2 2 2 2~~c~.+ 2

77 choosingo= 7a we find. < r > 3 xlO15cm That'is to say, the average internuclear separation distance is 5 fermis. We may estimate the size of the individual nucleons as seen by the incoming pion f rom pion nucleon scattering cross sections by equating the total cross section to the geometrical cross seto 2R n ov ing f or R. The w-N crosG section in the rangae 2.6-. Bev is 31.5 mb, from which we obtain a w N radius of about 1 fermi. Thus, we may crud-ely picture the deuteron, as seen by an inc~id~ent pion of momentum 13.65 Bev/c as the dumbell shown in fig.,- 35 with the separation betwleen the centers of the two parts about 5 fermis, and. the radii of each of the end~s about 1 f ermi. This "static picture" of the deuteron, however, is -misleading since the nuclei oscillates about this mean distance of separation 3 fermis. This may be seen by evaluating the wave function in momentum space 1 r (IP) = 2Q3/ fp (r) e 1 dxr" r $r JiPr 3/2Sr — ecor

78 A-straightforward evaluation gives(P) N' (_212 2 1 h2 where N' is a normalization constant. 2 2 Thus, j(~ P dP gives the probability that a nucleon will have a mnomentunm in the interval dP about P. 2 2 The curve (P) P is shown in Figure 36. Note that the curve peaks sharply at about 50 Mev/c, and f alls to on'e-tenth of its peak value at about 225 Mev/c. The expectation value of r2is r2> 3_[1(2t52/(ct+~)2+1/ (2~)2 20.4~I f 2 So that the root mean square deviation is V<r2>-<r7> 1-3.18f.which gives a measure of the magnitude -of the oscilla-tions about the equillibrium position. Finally, since the time dependence of the wave function of a stationary state is g'ive nby> the pceriod. of the -deuteron oscillation is

79 if the neutron prot'on bond is broken and. one nucleon removed. in a period. of time short with resp-e-1ct to the period. of the deuteron's oscillation, the remainingC nucleon will retain its initial momentum in accordance with the "Sudden approximation" of quantum mechanics. Thus, if a neutron is' struck by an incident-projec-tile and. removed. from the presence of the proton, the proton will travel a distance of R in a deuterium chamber,, where R is g-iven by the rang-e momentum relation R =bp with M 3.615 an d. b15 The units of b are such that R is in cm when p is in Bev/c. Whether or not the proton is visible depend~s on the length of the ionization track as seen by the scanner. if the scanner looks in the Z direction, he sees atrack of length Rsin", where e is the polar ang-le s~hown in fig.. 57. The probability that this projected..length will be grae ha mn the shortest visible length, is g-iven by: Pr number of ways that Rsin >Ri numb of a5-ll possible orientations But this quantity is just the ratio of the area between the two hemispherical caps shown in fig. 3~8 to the

8o 2w arcsin(Thnin/R) Pr- 2F- d.m r deosO 4w Evaluating the integral gives VrTi (Rmin/R) In practice., there is not a def inite leng-th Rmin below which a track is never seen and above which it is always seen., due to the individ ual scanner's ability to detect extremely short tracks.and due to the statistical nature of bubble formation. A sIpec-tator mnomentum distribution, found. by multiplying the above I C~~~~~~~~~~l~ ~ probability in which Rmin.14 cm, with a Hulthe/n probability density, was found. to agree fairly well with a sample of protons from a different sample of events in the same exposure as ours (Lovell (1967)) for which the protons approximated, the behavior of true spectators. This comparison is shown in fig,.359

THE HULTHEN "PICTUIRE" OF THE DEUTERON Fig 155. A schematic representation of the d~euteron based. on the Huithen theory. (See Text)

82 150 140 130 120 110 100 z 80 cr70 H60 a:<50 40 30 20 I0 200 400 600 800 1000 1200 PMeV/c HULTNEN MOMENTUM SPECTRUM

83

84

160 120 (0 0 =) 80' 0 z40 0.2.4.6.8 Pp (B ev/C) Fig 39. Comp rison of the observable spectator distribution with the protons from an earlier experiment. (See Text)

86 Appendix II Cusp Phenomena and. Z-A Conversions It is tempting to speculate on the relationship of the enhancement at 2125 Mev to the Z-P threshold at 2130 Mev. Two types of threshold phenomena may be responsible for an enhancement in the A-P effective mass spectrum: a cusp in the A-P elastic scatteringo cross section, and a conversion of Z's to A's upon interacting with a nucleon. A number of authors have predicted cusp phenomena in A-nucleon processes at the Z threshold. Dullemond and DeSwart(1961,1962) have calculated the A-P elastic scattering cross section using phenomenological potentials derived from previous research on the two nucleon problem. The hyperon nucleon system is described by a two component wave function dealing with the A-N and Z-N channels simultaeously: OAN "YN = ( ) The potential, then, is a 2 X 2 matrix MV V AA AZ Vt V2 v= vEA vZZ where the elements of the matrix depend on the relative distance, the relative angular momentum, and the spin orientations of the two hyperons. Fig. 40 shows the results of their calculation for two sets of nucleon-nucleon potential. In order to more readily com

87 pare the-predictions of their work with our data, we have multiplied, their curves by a "phase spc" curve in which-the experimentally observed. A's from events with p < 225 Mev/c,, were folded. into Huithen protons in the momentum range 0-225 Mev/c, so that both visible and. invisible protons are included. The results are shown in fg 41. It is noteworthy that although a cusp in the A-P cross section at the Z-P threshold, is capable of producing a resonance-like peak in our data, the center of the peak is slightly above the Z-P threshold, whereas the observed. value at 2125 Mev is slig-htly below. This is due to the characteristic rapid. rise of the cross section just below the cusp, and its relatively slow decline above, as exemplified, in fig. 40. It is possible that the hyperon produced in the w-N collision is not a A, but a 7. which subsequently converts to a A. This is depicted, schmatically in fi~g. 415. The propensity of Z's to convert to A's in-the presence of other nucleons is well known. Webb et al (1958) found. that for K.: absorbtion stars in nuclear emulsions, 58% of the hyperons converted. to A's. lDahl et al (1961) found. that the process Z N - A P

88 tribution peaked in the forewa-rd direction for the. process i n -+ A P. As pointed, out by Karplus and Rodberg,= (1959), moreover, the conversion may occur below the Z-N threshold.. This follows from the fact that the Z need. only travel on the average 5 fermis before interacting and hence., on the basis of the uncertainty principle, may be as much as 65 Mev off the mass shell. Karplus. and RodbergD (1959) have derived 7 —A conversion amplituid-es for the process Z N F-A N. They find, that the Z A conversion probability is of the formn: kl - ~~~~ M >2130 Mev (l+ka) ~(kj) A where k is the relative momentum and. T, and a are parameters. In a certain rang-e of these Para-meters there is a peaking'in the conversion probability slightly below the Z-P threshold.. Fig. 42 shows the conversion probability, as a. function of MAP for Some representative values of the parameters in this range. The theory admits, a bound state in the Z-N system which quickly decays into the A-P system with a bindingenerg-y given by

89

40 30 20-'(mb) IOMAP (Mev)., I I, I I I I II 2070 2100 2130 2160 Figf 40. The A-P elastic scattering cross section near the EN threshold as predicted by Dullemond and. De Swart (1962). The two curves result from different choices of the potential energ-y.

7050U,ll 4~~~~~~~_-I C) I Ll_~M 0 0 I0,_ I II,,I, l.tl l-, - - 2100 2400 2700 MAP (Mev) Fig 41. A comparison of the predictions of Dullemond and De Swart (1962)with our data. (See Text)

en C) 15- 4 - 0 10...I I 1 I 1I! 2100 2150 MAP Fig 42. The Z 4 A conversion probability of Karplus and Rodberg (1959) for certain values of their parameters.

cu ci)'H 4~~~~~~..p 4-) 4r-i

94 REFERENCES G. Alexand~er, J. And~erson, F. Crawford., W. Lasker., and L. Lloyd, Phys. Rev. Letters 7,148 (1961) G. Alexand~er, U. Karshon., A. Shapira., G. Yekutielil, R. Eng-lemann, H. Fllthuth, A. Fridman, and. A. Mingruzzi, Phys. Rev. Letters 115, 484 (1964). G. Alexand~er,, 0. Benary,, U. Karshon, A. Shapira,, G. Yek-. utieli, R. Englemnann, H. Filthuth, A. Frid-,,an and, B. Schiby, Phys. Letters 19 715 (1966) S. Ali, M. E. Grype-.os and L. P. Kok, Phys. Letters 24B 5415 (1967). B. A. Arbuzov, E N. Klad~nitskaya, V N. Peenev, and R. N. Faustov, JETP 42, 979 (1962), Soviet Phys. JETP 15,'676 (1962). D. Bassano,, C. Chang,. M. Goldberg-, T Kokuchi, and. J. LeiterPhys. Rev. 160, 12359(97 P. Beilliere, J. L. Gomnez, A. Lloret, A. Rousset, K. Myklebost,, and J. M. Olsen, Phys. Letters 12, 1550 (1964). G. Besn Mesons and. Spectator Protons in wr + d.-. Tw pp at 15.65 Bev/c, University of Michigoan technical report coo. 11/2-4. (1966) T.Buran, 0. Eivindson, 0. Skjeggoestad,, H. Tofte and I. Vegge, Phyics Letters2 151 (196)

95 G. Cew nd. WckPhys. Rev. 85 6356 (1952~) D. Cline, R. March, M. Sheaff., Physc. Letters 25 466 (1967). H. 0. Cohn and. K. H. IBhatt, Phs. Rev. Letters 135 668 (1964). F. S. Crawford., M. Cresti, M. L. G.-)od., F. T. Solmitz, M. L. Stevenson, and H. K, Ticho., Phys. Rev. Letters 2,174 (1959) 0. ]Dahl., N. Horwitz, D. Miller, J. Murray, P. White, Phys. Rev. Letters 6, 142 (1961) J. J. IDeSwart and.2C., Dullemond Ann. Phys.,, 16, 263 (1961). J. J. DeSwart and. C. IDulleno-nd, Nouvo Climento, 25, M.5, 1072 (1962) T. H. Groves, Phys. Rev. 129, 1372 (1965). W. Hess., Rev. Mod.. Physics,~ 150, 1568 (1958) L. Huithen and M. Sug-awara, Handbuch der Physik (SpringerVerlagBri, 1957),~ Vol. 159, P. 1 R. Karplus., L. Rodberg-, Phy. Rev. 11 08 (199 T. Kotani and M. Ross, Nuovo Cimento 14, 1282 (1959)

96 A. C. Melissinos, N. W. Reay, J. T. Reed, T. Yamanouchi, E. Sacharidis, S. J. Lindenbaum, S. Ozaki and L. C. L. Yuan, Phys. Rev. Letters 14 604 (1965). W. Moebs, University of Michigan technical report COO - 11/12 - 3 (1965). L. Piekenbrock and F. Oppenheimer, Phys. Rev. Letters 12, 625 (1964). P. A. Piroue, Physics Letters 11 164 (1964). A. Rosenfeld, N. Barish-S-hmidt, A B rbaro-Galtieri, W. Podolsky, L. Price, P. Sod.ing, C. WDhl, M. Roos, and W. Willis, Lawrence Radiation Laboratory Report UCRL8030 (1967). B. Sechi-Zorn, R. A. Burnstein, T. B. Day, B. Kehoe, and G. A. Snow, Phys. Rev. Letters 13, 282 (1964). V. F. Vishnevskii, Tu Yuan-Chtai, V. I. Moroz, A. V. Nikitin, Yu. A. Troyan, Chien Shao-chun, Chang Wen-yu, B. A. Shakhbazyan, and Yen Wu-kuang, Soviet Journal of Nuclear Physics 3 511 (1966). T. Wangler, University of Wisconsin Thesis (1964). T. Wangler, Private Communication (1966). I would like to thank Drs. A. Erwin and W. Walker for making Wangler's data available to me. F. Webb, E. Iloff, F. Featherson, W. Chupp, G. Goldhaber, and S. Goldhaber, Nuovo Cimento 8, 899 (1958).

97 ACKNOWLEIDGEMENHIS It is a pleasure to acknowledgeth el f h following people, to all of whom I am deceply grateful: Dr. John Vander -Velde — for slerving as chairman of my doctoral committee, as well as for his patient guidance throughout the experiment, Dr. T. Murphy for the interest showvn in the prog7ress::-, of the experiment, Drs. M. Ross, R. Lewis, and. F. Shure for servingC as doctoral committee members, our technical staff, particularly ID. Moebs, V. French, M. Rauer, and A. Locleff, my fellow g-radiuate students for assistance and many interestingo discussions; in particular,, the lateG. Benson, L. Lovell, A. Fisher, ID. Falconer, M: Church, and C. Arnold, G. Kane and' M. Ross for helpful discussions, J. Besancon and N. Higbee for drafting most -of the fig-ures in this report,

98 the experiment.

CA) CD~ (0 co - _ COz 01 c - ) —o _IO 0 COD A r