THE UNI V E R S I T Y OF M I C H I G AN COLLEGE OF LITERATURE SCIENCE AND THE ARTS Department of Physics Technical Report No. 28 - p ELASTIC SCATTERING AT 180 DEGREES FROM 1.6 TO 5~3 GeV/c Stephen W. Kormanyos ORA Project 05306 under contract with: DEPARTMENT OF THE NAVY OFFICE OF NAVAL RESEARCH WASHINGTON- D. C. CONTRACT NO. Nonr-1224(23) NR-022-274 administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR April 1967 Distribution of this document is unlimited

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 ix I. INTRODUCTION 1 II, EXPERIMENTAL EQUIPMENT AND PROCEDURES 3 A. Circulating Proton Beam and Internal Target 3 B. T Beam Intensity 4 C. it Beam Geometry 5 D. Et Beam Tuning 7 E. Hydrogen Target9 F. Counters 13 G. Scattering Analysis 18 H. Electronics and Timing 26 III. EXPERIMENTAL CHECKS 37 IV. CORRECTIONS AND UNCERTAINTIES 42 A. Nuclear Interactions 42 Bo Decay of Pions 43 C, Muon Contamination 44 D. Electron Contamination 45 E. Counting Losses in Beam Counters 46 F. Events Occurring in the Beam Counters 47 G. Inelastic Contamination 48 H. Bin Size 48 I. Counter Efficiency 48 J. Beam Attenuation in LH2 Target 49 K. Uncertainty in the Pion Jacobian 49 V. RESULTS AND CONCLUSIONS 51 APPENDIX 65 BIBLIOGRAPHY 69 iii

LIST OF TABLES Table Page I. Scintillation Counter Sizes 13 II. Center of Mass Cross Sections For '-p Elastic Scattering at 180~ 53 III. The Experimental Parity and X(J + 1/2) for the N* Resonances 62 IV. Input Parameters for the Determination of X(J + 1/2) 63 V. Proton Beam and Internal Target Parameters 66 VI. Zero Degree t- Production by 12.5 GeV/c Protons on Copper 67 VII. T- Fluxes in the Range 4.0 GeV/c to 5.2 GeV/c 68 v

LIST OF FIGURES Figure Page 1. The beam layout. 6 2. Pion beam profile. 8 3. Q1 and initial B1 tuning curves. 10 4. Q2 and Q5, Q8 tuning curves. 11 5. Q6, Q7 and final B1 tuning curves. 12 60 Layout of t-p elastic scattering at 180~..4 7. The hydrogen target..5 8. The ':;2 and t'3 counters..7 9. Electronics logic diagram. 17 10. Interior of trailer showing the electronics. 19 11. High voltage curves. 1 12. Delay curves. 2 13. Cherenkov pressure curve. 33 14. Scalar readings as recorded on Polaroid camera. 36 15. Proton magnet curve. 38 16. Pulse height analyzer time of flight spectrum. 59 17. Differential cross section. 54 18. Resonance amplitude in the complex plane. 57 19. Constructive interference of background and resonance amplitudes. 59 20. Destructive interference of background and resonance-ampli~tudes. 21. The assumed background cross section. vii

ABSTRACT We have measured the differential cross section for ~-p elastic scattering at 180~ in steps of 0.10 GeV/c or less in the region from 1,6 to 5.3 GeV/c. There is considerable structure in the cross section. This may be interpreted as an interference effect between the resonance amplitude and the nonresonant or background amplitude. There is a dramatic destructive interference at Po = 2o15 GeV/c.which' is quite interesting as 'the cross section drops almost two orders of magnitude in this region. Another interesting feature of the experiment is' the large narrow peak in the cross section at Po = 5.12 GeV/c. We believe that this is firm evidence for the existence of a nucleon resonance with a mass of (3245 + 10) MeV. This N* (3245) has a full width at half-maximum of less than 35 MeV. The width of the resonance is about 1% of its mass. Parities and the quantity X(J + 1/2) are given for various N* resonances where X is the elasticity and J is the spin of the resonance. ix

I. INTRODUCTION In recent years many high energy physics experiments have been done to investigate the existence and properties of resonances. Traditionally the mass, width, and isotopic spin have been investigated in total cross section measurements. The resonances yield structure in the total cross section and from this structure some properties of the resonances can be learned. The spin and parity has been studied in angular distributions. In this experiment we have employed a different technique to measure the properties of the N* resonances. We measured the differential cross section at 180~ as a function of energy. Because of the interference of the resonances with the background, quite a bit of structure was present in the cross section. From our data we were able to determine the parities and the quantity X(J+1/2) (where Xis the elasticity and J is the spin of the resonance) for various N* resonances, This method of probing resonances appears to be more sensitive than looking for bumps in the total cross section, We have measured the differential cross section for E p elastic scattering at 180~ in steps of 0.10 GeV/c or less in the region from 1,6 to 5.3 GeV/c. This experiment was done at Argonne National Laboratory on the Zero Gradient Synchrotron, The differential cross section for ~T"p.elastic scattering in the backward hemisphere has been measured by other experimenters, However, none of them has taken measurements as far back as 1800. Our data agrees with other experiments having measurements near 180~,1-7 1

There is considerable structure in the cross section. This may be inter-reted as an interference effect between the resonance amplitude and the non-resonant or background amplitude. There is a dramatic destructive interference at P0 = 2o15 GeV/c which is quite interesting as the cross section drops almost two orders of magnitude in this region. Another interesting feature of the experiment is the large narrow peak in the cross section at Po = 5.12 GeV/c. We believe that this is firm evidence for the existence of a nucleon resonance with a mass of (3245 + 10) Mev, This N* (5245) has a full width at half-maximum of less than 35 Me-V The width of the resonance is less than 1% of its masso It seems remarkable that such a massive particle should be so stable. Assuming a smooth background amplitude we found the parities of various N* resonances. We also calculated the qunatity X(J + 1/2) for various N*'s where X is the elasticity and J is the spin of the resonanceo 2

II. EXPERIMENTAL EQUIPMENT AND PROCEDURES A. CIRCULATING PROTON BEAM AND INTERNAL TARGET Figure 1 shows the beam layouto The 12o5 GeV/c circulating proton beam struck a 90% copper, 10% aluminum internal target 1/8" x 1/8" x 3o85" long with a beryllium lip. This internal target was a pop up typeO During the acceleration cycle the target was out of the beam envelope. After the acceleration cycle the target moved up and the beam was brought onto the target. The circulating proton beam made many passes through the internal target during the spillo For example the duration of a typical spill was 150 msec. The time for a proton to make one revolution was approximately 640 nsec. So in the spill time the beam made on the order of 235,000 passes through the target. The circulating proton beam was brought onto the internal target during flat top by increasing the frequency of the accelerating voltage, This is called the radio frequency (RF)o As the RF frequency increases the particles get out of step with it, lose momentum, move in a smaller circle and are thus brought onto the target. There was a feedback loop which kept the spill as constant as possible. The internal target waamplaced at various positions from 3 to 5 feet back into the field of the ZGS ring magnet. Its position was determined by the selection of two parameters and the use of appropriate graphs given in ZGS Users Handbooko These two parameters were the pion production angle, which was zero or as close to zero as we could get in order to have maximum pion 5

production, and the pion momentum. After the 3.5 GeV/c run we added a beryllium lip to the leading edge of the copper target in order to remove the sensitive dependence of targeting efficiency on the target angle. Measurements had indicated as much as a 15% decrease in beam counts for a 1% change in target angle. The thickness of the beryllium lip was sufficient to jump the circulating proton beam about 0005 inches per pass through the lip. The internal target coordinates were calculated before the experiment was run1ro During the experiment as we went to a new pion energy the internal target was moved to its appropriate position and angleo The internal target was mounted on a drive mechanism which moved it into our desired positions. The reason for placing the target back into the ZGS ring magnet was to obtain zero degree pion production, that is maximum pion production, for most of our experimento In addition, the ZGS ring magnet, which bent the pions produced at zero degrees through 17~ into our beam line, selected negatively charged particles and also partially momentum analyzed these particleso B. 3 BEAM INTENSITY The "- beam intensity was 3.5 x 105 pions per 5 x 1011 circulating protons in the region 2.0 to 4.0 GeV/c. At higher and lower momenta the intensity dropped off, At lower momenta more beam pions decayed while at higher momenta the pion production cross section decreased. Throughout most of the experiment we had intensities in the range of 1 x 105 to 3.5 x 105 pions per pulse. In the course of the experiment the zero degree Et production for 12,5 4

GeV/c protons on copper was measured. The results are given in the appendix. C. t BEAM GEOMETRY The pion beam line is shown in Figure 1. It consists of three quadrupole doublets for focusing and two bending magnets for momentum analysis. There is an intermediate focus at the second beam collimator and a second focus at the liquid hydrogen (LH2) target. The beam had a momentum bite of AP/P = + 3/4% and subtended a solid angle of 1 x 10-4 steradians at the internal ZGS target. This gave the beam particles an angular divergence of less than 3 milliradians at the target. The beam bending magnets were 18 inches wide, 6 inches high, and 72 inches long. We calculated the currents needed by using graphs of central magnetic field versus current, supplied by the ZGS Users Handbook for these magnets. The quadrupole magnets were 10 inches nominal diameter and 36 inches long. For the quadrupoles we also used magnetic field gradients versus current curves from the ZGS Users Handbook. For the beam bending magnets we had symmetrical bending through 8.50~. That is with respect to the magnet axis 9initial = efinal = 4.25.. So then the magnetic field Bo was calculated from the equation: BoLeff = 1313.22 P(sin ein + sin eout) (1) where Bo is in Kg., P in GeV/c, Leff in inches. For the values of the gradients we used an iterating beam design computer program. We specified the positions of our two beam foci, and intermediate focus at the 1" x 1" beam collimator and a second focus at the LH2 target. We 5

/P2 P MAGNET 6 3,P COLLIMATOR B2 a-H2 TARGET, "T COLLIMATOR 3TT>a T' ~ " TT MAGNET Q A / / X^^,~/BEAM V8 BBEABEAM, COLLIMATO HERENKOV COUNTER BEAM a Q COLLIMATOR o 4 8 12 16 ZGS TARGET SCALE (FEET) ZGS RING MAGNET Figure 1. The beam layout. 6

selected the particle momentum, the orbit starting values, and the approximate values of the gradients. The program then iterated the gradients until our focal conditions were satisfied. By slightly varying our starting orbits and our initial gradients we arrived at a satisfactory focus and beam angular divergence at the LH2 target. There was a solid angle beam collimator between the second quadrupole and the first bending magnet. Its dimensions were 3.5" wide, 4.5" high, and 24" long. We wanted as small a beam angular divergence as possible since we wished to study elastic scattering as close to 180~ as possible. We settled on a beam which gave us an angular divergence of less than 3 milliradians. We worked out the beam design for 4.0 GeV/c and linearly scaled the other gradients from this value. At 4.0 GeV/c the beam profile is shown in Figure 2. After passing through the permanent 17~ beam magnets the incident rC beam passed through the it-magnet which deflected it by 2.3 to 1.3 degrees onto the LH2 target. The Ec magnet gap was 84" wide, 14" high, and 30" long. Its magnetic field integral was measured by a wire orbit technique. D. it BEAM TUNING At each new incident beam energy we tuned the beam. We had a beam monitor consisting of three small scintillation counters mounted on a stand which we placed on the outside of Q1 inside the ZGS ring shielding. We counted the triples coincidences of these counters. This beam spill monitor output was directly proportional to the beam spill. In tuning we maximized the number of pions relative to this beam monitor. The number of pions coming down our beam line was determined by the coincidences between the three beam counters 7

x (Inches) 2.0- Q2 B HORIZONTAL 1.0 - FIRST HYDROGEN /FOCUS TARGET 200 400 600 800 1000 120 1400 1600 18 Z -1.0 p Q 5 8 Y (Inches) 3.0- 01 VERTICAL 2.0 - Q2 BI -2.0 - Figure 2. Pion beam profile 8

v V B1' B2, B3, and the Cherenkov counter C. This quantity is denoted by BC. In tuning we used a TSI Preset Count Control built by the ANL Electronics Division. This was connected to the monitor scalar. At a preset'; number of counts on the monitor scalar, say 105 or 106, the Preset Control would turn off all the scalars. With this the ratio BY/M would be directly readable as M would be a power of 10 and no division was necessary. This was a great help in tuning. In changing to a new energy the internal target was moved to a new position, The quadrupoles and bending magnets were set at their calculated values. The tuning was done as follows. First B1 was tuned, then Q1, Q2, Q6 and Q7, Q5 and Q8' then B1 was recheckedo Typical tuning curves are shown in Figures 3-5. B2 was not tuned but was set and held at its calculated value. This magnet gave us our final momentum selection. The rest of the beam was tuned around B2o The central magnetic field of B2 as a function of current or shunt voltage was measured with nuclear magnetic resonance techniques over the entire range of the values used in the experiment. Hysteresis was found to be negligible. By this measurement the laboratory momentum of the pion beam was known to +0.03 GeV/c. E. HYDROGEN TARGET The source of the target protons was a liquid hydrogen (LH2) target. The cylindrical target was 12" long and 1-1/2" in diameter with its axis along the beam axis. The LH2 target was carefully surveyed into position. During the course of the experiment the LH2 target was moved and surveyed into a new 9

x103 540- Initial BI Tuning Curve 510 -480 Set At 45.75 Un 450 420 -390 360l 330 300 -45.2.4.6.8 46.2.4 B, (mV) x103 540- Q| Tuning Curve 510- 480- S et At ~0 450 - o 420 390' 360 -330 300,' ' — I.6.8 38.2.4.6.8 39 QO (mV) Figure 3. Q1 and initial BI tuning curves. 10

x103 540 _ Q2 Tuning Curve 510 Set At 480 > 450 ~ 420 - m 390 360 330 300 l 34 35 36 37 02 (mV) x103 540 - Q5 and 08 Tuning Curve 510 - Set At 480+ f 41.88 In 450 0 <3 420 - 390 360 -330 300 40 41 42 43 Q5 Q8(mV) Figure 4. Q2 and Q5, Q8 tunning curves. 11

x103 540_ 6 and Q7 Tuning Curve 510 -X80: /-Set At 480 48O0 -~ ~ 30.88 UI 450 0 < 420 390/ 360 \ 330 \ 29 30 31 32 Q9 Q7(mV) xi03 540p Final BI Tuning Curve 540 510- T-^ 480 SetAt 45.75, 50 420 390 360 330 300 ---{- -l,..,1 -, I, I I 300 45.2 4.6.8 46.2 BI (mV) Figure 5. Q&6 Q7 and final B1 tuning curves. 12

position two more times, so that the scattered pions would not have to be bent through too large an angle. Thus in the experiment we had three beam "geometries." The experimental layout is shown in Figure 6. The LH2 target is shown in Figure 7. F. COUNTERS The counters consisted of sheets of Pilot scintillator B with tapered lucite light pipes. These were cut and polished by the Pilot Chemicals Company. Both the scintillator and light pipe were wrapped with aluminum foil and black masking tape to give internal reflection without light leaks. The counter sizes are shown in Table I. TABLE I.SCINTILLATION,COUNTER SIZES Size Counter width x height Thickness Energy Range (inches) (inches), (GeV/c) Tt2 14 x 14 1/2 1.6 -5.3 `3 16 x 16 1/2 1.6 -5.3 8 x 8 1/2 1.6 -2.5 6 x 6 1/2 2.6 -5.3 p2 12 x 12 1/2 1.6 -5.5 12 x 12. 1/2 1.6 -5.15 p x9 x 9 1/2 3.15-4.5 8 x 8 1/2 4.5 -5.3 B1 1 x 1 1/8 1.6 -5.5 1 inch in 1/8 1 B2 5'B diameter m/e 15

o o o // I4) L O) Jct i (D,0 ( OI ~~~ // S I I I - 1T' E 0 *-= -1'^*0 — ^ ^)^~ Io3 ---- /~~rON- ^~~~~~r c: 'F I 0) Ill co iH Q) 0 14 00 0 H ),(.d ---~._

LSI:::::i;:i ;::::::-:_::-ij_;il ii:i::_:::;::Ri::i3:9::::_:::z i —i:-2-:::::il-:-;;::::-, _F L:s — i 1":-_8:a:::: — i: i::: 1 "~:::.~: :::+:::: -i i-- C8 f:;X Bli~: C:X Ic:::: i+Q ': -:,:,i-:::::,j:-::::;::: "-_: -":r::-::-;i;:::jj::-:::_ -,_;: —_:_::::::_::::::::::i:.i:;:i-::;i;i,::;:-:,:wi~~: ::~-:I:i:i:s:~ kEWXZ_' i"lQ;""":ns": i: 2 z:_-;2i:-i": :~:ia:-:j:1:::-1::::::j;:::;:_:-:j::::::-j:-:.: -j~::i:j: i:-~:i-::i:i:-:::::j_\;: :;:::: '-4:-i~mksn6 s ~~:tik'4::3SiCh;lBSSSF ja "i':;B ":-:i:i::: B dRI:'i&#~,BiS`B8849 e:,g;:: L;4 -:i s-:::i i x 1::::-:::::i i.:::::i:i:_ -::::::::;-::::::i-:::-,:;:3P-:::- "::::: -:::::-_i_-:;::i 'aS-s ~-:::::::~i:-::::-:li::::_-:: a-C:e:: ~-::;a:-:~:i: j:::::; 15

The light pipes were optically connected to RCA 7746 photomultiplier tubes. These are fast 10 stage tubes. The time between the light pulse and the voltage pulse was stable to less than a nanosecond. The rise time itself was about 2 nanoseconds, but by triggering on the rising edge of the voltage pulse we got stability of better than one nanosecond. The tubes were encased in Mu-metal shields to eliminate stray magnetic fields. The anode voltage on each tube was set by running a high voltage curve and setting the voltage about 150 volts above the knee of the plateau as shown in Figure 11. The phototube bases were Model 531 S manufactured by Nanosecond Systems. Because of the high counting rate, the bases of the beam counters were modified so that the voltage would remain more stable when a large current was being drawn. The wavelength of the maximum light output of the Pilot Scintillator B is 4000 Anstroms and at this wavelength the relative sensitivity of the RCA 7746 photomultiplier is 90%. The counters were attached to lateral adjusters and then mounted on transit stands. In this manner they were very stable and could quite easily be positioned very accurately. By means of a plumb bob hung over the center of the counters they could be horizontally positioned with respect to survey lines laid out by the Argonne survey crew. Vertical positioning was done using a transit. A view of the j counters is shown in Figure 8. Since the refractive index of the scintillator is 1.58 light transit times from one end of the scintillator to the other of about one or two nanoseconds could be expected. The resolving time was improved by having all 16

k ~~~ oQ ro ON~~~~~~~~~~~~~~~~~~~~~~~~~c Ell~~~~~~~~~~~~~~r.".8( i~~~~~~~~E OD"& IBM' ~~~~~~~~~~~~~~~~~~~~~~~~~~~~.v~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~lj~~:h:~;~r ">~l> i> k7~~~~~~~~~~~~~~~~~~~~~~~~~~k

the counters in a telescope pointing in one direction so that the particle then passed through the same part of each counter and the light transit time was approximately equal for each counter, To further improve resolution, since we were accepting scattering angles in a small range about 180~, the counters in the p telescope all pointed toward + x while the counters in the E telescope all pointed toward -x. By doing this the light transit time of both the Tr and p telescopes can be made approximately equal. The two beam counters B2 and B3 were pointed in opposite directions' with overlapping scintillators so that the pions would have to go through both scintillators in order to be counted. This was done because had the counters pointed in the same direction, pions could have gone through both light pipes, given off Cherenkov light, been counted as a beam pion, and yet miss the LH2 target. G. SCATTERING ANALYSIS We have an incident g- beam elastically scattered from protons in a LH2 target. This elastic scattering has five independent variables: Pinc the incident laboratory momentum of the j-, Pt and Pp the final laboratory momenta of the A and p after scattering, and ~ and ~p the laboratory angles of the 7t and p. Conservation of 4energy and momentum give us three constraints P sin e = Ppsin p Pinc = Pcos e6 + Ppcos Ep (2) m + (Pin +2)1/2 = (p2 + 1/2 + (p2 + 1/2 p nc+ me p p%/18 18

For 180~ scattering these reduce to P- =Jj 1/2 _ LAB = (P) / where J. = (3) i Td i CM P. = P P inc p Et mp + (Pinc 2 + P 22 1 + + + 2)/2 So there remain only two independent variables. One of the strong points of our system is that we experimentally determine all five quantities and thus have three constraints on the system in addition to coplanarity. We detected and counted the incident beam pions, the 180~ backscattered -C and the 0~ forward scattered po We counted incident beam particles with scintillation counters B1, B2, and B3 in coincidence with a gas threshold Cherenkov counter containing 80-140 psig of ethane. This beam coincidence will V be referred to as BC. The Cherenkov counter discriminated against antiprotons and K's which comprised less than 1% of the beam. As we increased the energy we decreased the Cherenkov pressure so that we would discriminate against K's. See Figure 13. The first counter B1, at the first focus was a 1" square-1/8" thick counter. The beam counters B2 and B3 were 1" diameter by 1/8" thick circular counters. The liquid H2 target was 12" long by 1-1/2" in diameter. However, the interaction region was defined by the 1" diameter circular beam counters (B2, B3)o With this arrangement we were sure that the detected incident beam particles did indeed impinge on the LH2 in the target. By visual observation it was seen that the mylar bag containing the LH2 was never completely full 19

of LH. There was approximately a 1/8" space at the top which did not fill with LH2 Our detection system for the scattered particles was a double spectrometer, a 7t arm, and a p arm, in coincidence. Let us now follow an elastic scattering event. The incident t passes through the T magnet and is bent through a small angle depending on the geometry in use, passes through the t collimator, through B2 and B3 beam counters and then into the LH2 target. We were interested in 180~ elastic scattering. After such a scattering the backward scattered ET passed through the it magnet in the opposite direction to the beam and was deflected so as to pass through the i telescope counters t2 and 53. Thus the scattered it was cleanly separated from the incident 7 beam. The forward scattered proton passed through the p magnet which deflected it through the p telescope counters p', pp. p3 The < particles which did not interact, the great majority of the beam, being of opposite electrical charge to the protons, were bent in the opposite direction. In this way the scattered protons were also cleanly separated from the non-interacting E beam. The incident and scattered pions passed through the it collimator while the scattered proton passed through the p collimator. These collimators were considerably -oversized so that the scintillation counters rather than the collimators would define the solid angle. The collimators were made of accurately machined steel plates surrounded by lead bricks supported on adjustable steel tables. The p-magnet was a standard bending magnet (18 VI 72). The n-magnet was 20

a large gap bending magnet 30" long, 14" high, and 84" wide. The momentum bite of the Tr telescope was about AP/P = + 30%, while for the p telescope AP/P was about + 10%. The term momentum bite in the above means how much the momentum of the particle under consideration can very and still pass through its telescope. The current settings in the it p magnets and the counter telescope angles were determined as followso For a given geometry and incident beam momentum the magnetic field integral for the Jt-magnet necessary to bring the incident i- beam onto the LHO target was calculated via the equation P(siniN + sine ) =. - d(sin + sinOUT 1313.22 once the field integral was calculated the angle of the 7t telescope was fixed as the momentum of the backscattered i" was determined by kinematics. The magnetic field of the p-magnet was adjusted so that the forward scattered p would be bent into the proton telescope and at the same time cleanly separated from the negatively charged i- beam. An advantage of the experiment was that in going from one energy to the next higher one in the same geometry only small changes were made in the system. This was because P was close to 0.400 GeV/c throughout the experiment. As we went to a higher energy the current in the it magnet was increased so that the higher momentum incident beam still passed through the LH2 target. The current in the p magnet was increased.so that the higher momentum protons still passed through the p telescope. The only physical change in going from one incident momentum to the next was to increase the i telescope angle 21

by about 1~. This consisted of moving the two t counters by about one inch. Also small timing changes were made due to the difference in time of flight of the E and p. Not having to move the LH2 target, the magnets, or the p counters removed possible systematic errors to misalignment. The solid angle subtended in the center of mass was defined by the 16 x 16 inch 73 counter at a distance of 200 inches from the LH2 target. The p3 counter (9 x 9 inch) was 500 inches from the target and was overmatched to subtend a somewhat larger solid angle in the center-of-mass. The matched size of the p3 counter was calculated from the equations AH = RH AH p H rc AV = RV AV AH and AV refer to the horizontal and vertical extent of the counters, and FH and Rv are the horizontal and vertical matching ratios given by H (L + D)Hff Jsing (5) (L + D)ev sinp (L + )eff sineV in terms of the effective distances, Jacobians, and laboratory angles. There is a horizontal and vertical focusing effect for both the it and p. Thus in calculating solid angles these effective lengths rather than the measured lengths must be used. They are defined below. L refers to the distance from the H2 target to the center of the magnet in question, D refers to the distance 22

from the center of the magnet to the counter in question. Now at 180~ scattering we have sin (J 1/2 sin (p J So at 180~ the matching ratios become (L + D) H, p I RH = eff ()2eff etf JT (L + kD)yf J. (7) (L + D)V ( /2 (L + D) V. J eff it AH. and AV. for the 3 counter were both selected as 16 inches and then AHp and AVp for the P3 counter werecalculated. The effective lengths were calculated using the magnet matrices given by Penner.9 The effective lengths are given by H cos B2 cos I1 (L + D)H = I + d- + + [p + Fd] sin (P1 + P2) eff cos P1 cos P2 + F [l-cos(1 + 2)] [p + d tan 2] (8) (L + D)eff = + d + (p1 + P2)[P - ~ tan P1 - d tan P2] - d (tan P1 + tan P2) where p R sin P1 + sin P2 = RL sec d = D - sec 2 R = the effect length of the magnet 23

1 = the incident angle = the final angle L = the distance from the H2 target to the center of the magnet in question. D = the distance from the center of the magnet to the counter in question. and F = is the focusing factor given in general by *1. P F = - and is zero for both t and p for 180~ elastic scattering. Horizontal and vertical effective lengths for both the ET and p were calculated using a computer program. The horizontal effective lengths (L + D)ef and (L + D) H differed at maximum from the measured lengths by less than 1%. eff differed at maximul That is (L + D)HiT (L + D) -_' ---- = 1.004; = 1.002 (L + D) H (L + D)H'P While for the vertical lengths the maximum ratios were (j + D)V"t= 1.104;,(L + D)V,P 1.031 (L + D)Vt (L + D)VP eff eff So there was more vertical than horizontal focusing. The center of mass solid angle subtended by the t3 counter was calculated as follows. (n)QM = (9) where S;

1611 16" LAB H V (L + D) H, (L + D)V't eff eff Typical laboratory solid angles subtended were 7 millisteradians. The solid angle in the center of mass system, defined by the 13 counter, varied from 1.5 to 0.5 millisteradians as we increased the energy. The p3 counter was overmatched to subtend a somewhat larger solid angle in the center of mass than the 3 counter. The over matching was calculated to allow for such things as the momentum spread and angular divergence of the incident beam, a 1% variation of the magnetic field of the p magnet, a 3% variation of the magnetic field of the i magnet, the H2 target size, and the multiple Coulomb scattering of the scattered particles. The horizontal overmatching is given by 5H r(A )2 + (B AeO) + (C. ) ( + (E — I)2 '0 Ip ) (10) + (G xo)2 + ()*)2 The vertical overmatching is given by v = [(BAT)2 + (G'Ayo)2 + * (2 (11) P aP where A = pDp p B: (L+D) H Lp 1 - JP)/ B. = (L+D)V+ [1 (_)1/2j C = Dpop 25

E = Dro(I (12) G = 1 RH G' = 1 + RV (f)2 = a2 + (RHA.) (*) = 2 2 + (RVi)2 The above.contribution of the multiple scattering includes both the multiple scattering of the proton and the image of the multiple scattering of the pions. By overmatching the proton counters in this way, in-scattering is equal to outscattering and no correction to the raw data was necessary. The various terms making up the overmatching are assumed to be independent of one another and are combined in quadrature. The above overmatching represents about one standard deviation. For most energies we had at least two standard deviations of overmatching. H. ELECTRONICS AND TIMING The electronics logic is shown in Figure 9. The three monitor counters (M1M2M3) formed the M coincidence. The three beam counters (B1,B2,B3) formed the B coincidence which was put in coincidence with the Cherenkov counter forming the Bl coincidence. The number of BC coincidences after corrections yielded the number of pions impinging oh our H2 target. The scattered protons were counted by the p telescope pl, P2, p3 in coincidence. The scattered pions were counted by the x telescope -c2,V3 ini'hoidenc. The BC'coincidence and v.; the p coincidence were put in coincidence forming the pBC coincidence which formed with the Ec coincidence the jcp fast coincidence and jcp slow coincidence. 26

MI Delay M2 Delay _- caler W-^ -^ Mz Disc.} M Coin. M3 _ --- - M3Disc. B |- - -----. B Oisc. Delay Scaler ="^f^ B Disc. )-B Coin. Im I 8 Dela"y I B83 Disc. coler, - - _ 8 C Coin. C Delay v De C Disc. ______ S'-t ^ Delay,,~~~~. _______.~ ~ ~~S | 1_ Saler PSrHA PI Delay c ler --- ~ —^fJL "^P, Disc 7 PBC Coin. r^ o II -. —, P Disc. PC Coin..LL~~.., ~~~~TASc DiscI Q P-ost 7r P Slow 7o Delay Delay 2 g -ff2 ODisc. Scaler e____ ~ - ' -- ^ ^. P2 - ---- Stretch I.7r Coin. D. 7r,, DeaI "-DiscZGS --— ate — Figure 97 Electronics logic diagram,

The jtp fast coincidence had a resolving time of 5 nsec while the irp slow had a resolving time of 30 nsec. These different resolving times were used to check for accidentals. A pulse height analyzer (PHA) was also used to check for accidentals. Stretched signals from the 3t2 and p2 discriminators were fed directly into a time-to-amplitude converter (TAC) which was gated by the rp slow coincidence. This gave us an output pulse whose voltage was proportional to the overlap time of the -3 and p pulses. This output was fed into the PHA which gave us a plot of number of events versus the c-p time-of-flight difference. Any significant accidental background would appear as a broad uniform plateau under the elastic peak which could be subtracted from the peak. We set the pulse height analyzer so that the time difference from one channel to another was approximately 1/3 nsec. We used the first quarter of the memory (100 channels) of the PHA to record the events of a run and the second quarter of the memory to store all the events of a certain energy. The stretched irp coincidence signal which triggered the TAC was 160 nsec longo The P2 stretched. signal was 30 nsec long and the t3 stretched signal was 50 nsec long. Channel 50 on the PHA corresponded to the normal time of flight difference between the rt and p. This gave us a possible range of events of from channel 5 to 95. All the electronics and the beam magnet controls were housed in an airconditioned trailer on the ZGS floor, The interior of the trailer with the electronics is shown in Figure 10. This eliminated dirt and noise from the ZGS floor and helped considerably in running the experiment. 28

0 H ~I),,~~~~~~~~~~~~~~~~~~0 o12 H~ H ho 29

The pulses from the counter phototubes were carried by 50 ohm RG 213 U cables to a trailer panel, Inside the trailer and throughout the electronic logic the signals were carried by 50 ohm RG 223 double shielded cables.. The signal cables from the counters were cut to specified lengths. The pulse transit time was calculated and independently measured for each cable using reflected pulses. The measured pulse transit time of all the signal cables were within one half a nanosecond of the calculated time. The logic cables were made to specified lengths by EG and G. The timing of the electronics logic circuit including the logic cables and intrinsic discriminator and coincidence circuit delays was first calculated, and then checked by feeding pulser signals into the discriminators and tracing them through the circuits. Thus the approximate delays which we had to insert could be found. These delays were further checked by running a complete set of delay curves at 1.6 GeV/C, our first experimental point, where the counting rate was high. They were all found to be quite close. Delays were then calculated for highei energieso Typical high voltage curves and delay curves are shown in Figures 11 and 12 respectively. The counter pressure curve is shown in Figure 135 The dip on the blow up at 84 psig corresponds to 0.6% K's in the beam. The timing procedure went as follows. First of all the monitor telescope was set up by means of high voltage curves and delay curves on each of the three monitor counters. Then the magnets in the line were set at their calculated values for 1.6 GeV/c momentum, and the beam counters and Cherenkov counter were timed in. For the delay curves, delays were inserted by means of delay boxes 50

HV CURVE ON P, ' ~ Set P. at 1800 volts P12 B, I!, I I I I 1.4 1.5 1.6 1.7 1.8 L9 2.0 2.1 HV P, in K volts HV CURVE ON I3 Set I3 at 2250 volts i, I, i I.. I 1.4 1.5 1.6 1.7 1.8 L9 2.0 2J 2.2 2.3 2.4 HV 1i3 in K volts Figure 11. High voltage curves. 31

DELAY CURVE ON FP 12 Set Pi delay -+4ns. -2 0 2 4 6 8 10 F, delay in nsec. DELAY CURVE ON H1 ~23 | |~1i3 delay -6 nsec BC -2 -4 -6 -8 -10 -12 -14 UI3 delay in nsec 'igure 12. Delay curves. 32

1.0.8 BC /w C.6 I Cerenkov counter curve B. at 52 GeV/c.4.2 20 40 60 80 100 120 140O 160 CPRESSURE (psig) I 5 I I ' | | I | 5 | 5"I erenkov counter curve at 5.2GeV/c!,.995 " BC B..990.985 980 -' -" -,I -. I, I ~ II.....,. ) 20 40 60 80 100 120 140 C PRESSURE (psig) Figure 13. Cherenkov pressure curve. 33

made by Nanosecond Systems, Inc. The use of these plus the fact that the scalars could be turned off at any preset number by a preset count control made the high voltage and delay curves easy to run. After a delay curve was run and the correct delay determined, a delay cable was inserted in place of the delay boxes. After the beam counters and Cherenkov counter were timed in the beam was tuned for 1.6 GeV/c momentum. After the beam was tuned a Cherenkov counter pressure curve was. run. Next the counters in the p and -T telescopes were timed in. Then the beam telescope (B1B2B3C) was timed in with the p teleV scope. These two telescopes formed the pBC coincidence. Then the it telescope v was timed in relative to pBC, to form the final Tp fast and slow coincidences. After we were timed in we ran a p-magnet curve. This consisted in varying the magnetic field of the p magnet around the calculated value and at each point plotting the ratio (ip coincidence)/BC against the p magnet field (Figure 15). It was found that the maximum value of this ratio occurred at the calculated value of the p magnetic field. Throughout the experiment we could vary the magnetic fields of all our bending magnets and quadrupoles from with our trailer. This was very convenient and timesaving for us. Periodically during the running of the experiment high voltage and delay curves were run on all the counters. The electronics coincidence system used was a Chronetics Nanologic 100 System. The pulse height analyzer used was a model k04C 400 channel analyzer made by the Technical Measurement Corp. The scalars used were made by TransV istor Specialties, Inc. The most important quantities: B, BC, cp fast and gp slow, were double scaled on two different 100 Me scalars to insure accuracy, The magnet shunt voltages and the counter high voltages were also monitored by two digital voltmeters in parallel to insure accuracy. 34

All discriminators except those of the monitors were-.-turned on and off by a gate circuit which was triggered by an Argonne Preset Interval Timer. This timer is synchronized with the ZGS and will give a pulse at any predetermined time after the start of the beam acceleration cycle. The gating times were determined by viewing the gate pulse and the beam spill given by the monitor counters which were simultaneously displayed on a RM 561 A Tektronix oscilloscope. Thus we could bracket the good spill and gate out spikes in the spill. 8 WH The run consisted of an integer number of 10 BC coincidences. At the end of a run (about 1-2 hours and about 4-6 x 108 BC depending on the counter rate) the scalars were automatically turned off at some preset integer number of 108 beam particles. We had a Polariod camera (Pathfinder land camera 110A) with a 10 second picture development time permanently mounted with the scalars in focus. At the end of a run we would simply take a picture of the scalars and print out the PHA spectrum. The beam energy, date, run number, and time (from a 24-hour clock) were also recorded on the picture as shown in Figure 14. This method of data recording was straightforward, accurate, and very rapid so we lost little useable beam time. 35

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III. EXPERIMENTAL CHECKS At 1.6 GeV/c we ran a p-magnet curveo We purposely detuned the p-magnet and plotted the number of (utp coincidences)/BC versus the magnetic field (see Figure 15). This ratio reached a peak at the calculated value of the magnetic field and decreased on both sides as we went.away from the calculated value. This may be regarded as evidence that we were indeed seeing elastic scattering. We had two methods for studying possible background due to accidental coincidences. The first method involved using two independent rep coincidence circuits; one (up fast) had a resolving time of 5 nsec and the other (tp slow) had a resolving time of 30 nsec, Both circuits gave essentially the same number of coincidences. This indicated that none of the coincidences were accidental, This was not surprising since the single telescope rates were very low; nc was typically 50 counts/pulse and p was about 1 count/pulse. The alternative method was to feed the signals from the T7 and p2 counters directly into a time-to-amplitude converter (TAC). This gave out a pulse whose amplitude in volts:was.proportional to the overlap time of the t3 and p2 pulseso This output was fed into a TMC 400-channel pulse-height analyzer (PHA), which gave us a plot of number of events against the U-p time-of-flight difference. The peak was typically about 3 nsec wide (see Figure 16), Two nsec of this was due to the fact that the H2 target was 12" longo The additional time spread was caused by small time differences in light transit time in the scintillators and light pipes, small time differences in the photomultiplier tube responses, and small time differences in the various logic circuits. 37

II I1 40 c 20 I 0 -I0 0 LLJ w 4 z PROTON MAGNET CURVE AT 116 GeV/c (ARBITRARY UNITS ) Figure 15. Proton magnet curve. 38 58

0 I o 0) HOF| HO -- Ha — cO LLJ O: 0 i LL OD () L4 b-, o I-I I: 0 I II ch< - I,,i I I ist^ Pi Z 0 o 13NNVH3O 3d SIN3A3 39

Any significant accidental background would have shown itself as a broad plateau under the elastic peak which could be subtracted from the peak. The events which were outside of approximately a 15 channel range (e 5 nsec) about the peak we regarded as accidental and disregarded in our cross section calculation. There were only a small number of these, typically 1 or 2 per hundred events, We wanted to show that there was no contamination due to inelastic events of the type -"- + p + p + o (13) This was done by taking data runs with a 2-1/2" long carbon target placed just behind the empty LH2 target. This carbon target had about three times the number of protons as the LH2 target but the protons in the carbon nucleus had some Fermi momentum. The Fermi momentum is distributed isotropically and has a range of up to a maximum of about 0.230 GeV/c. Suppose our constraints on angle and momentum were sufficiently lax that with the LH2 target we were observing E p events that were in fact smeared by o~ production, Then the additional smearing of angle and momentum introduced by the Fermi momentum of the protons in the carbon nucleus would not remove the counting rate, But if our kinematic constraints were sufficiently tight that the smear of the Fermi momentum removed most of our event rate, then we have evidence that g~ production smears things too much to be detected much by our double spectrometer. This is true because the gto production introduces a greater smear than the Fermi momentum for any reasonable distribution of t~ mesonso We took several runs with a carbon target at different energies and 40

obtained two events. In equivalent runs with a H2 target we obtained over a hundred events, This conclusive evidence for a 1% upper limit on inelastic contaminationo It also showed that we had no accidental eventso This is seen as follows, With(the carbon target in place of the LH2 target the number of coincidences in the it telescope remained the same but the number of PBC v V coincidences increased. The ratio of PBCcarbon/PBCLH2 was 2 at 2,8 GeV/c and lo5 at 4l1 GeV/co Therefore, if we were counting accidental events we should have seen more with the carbon target. However, we saw only two events compared to over a hundred with the LH2 targeto Thus we conclude that we had no accidental events. The carbon runs simultaneously served as empty-target runs as the carbon target was placed just behind the empty LH2 target. 41

IV. CORRECTIONS AND UNCERTAINTIES This section describes the corrections and uncertainties which were applied to the data. A. NUCLEAR INTERACTIONS Some of the desired events were not recorded because the pion and/or proton did not travel completely through their respective telescopes because of nuclear interaction in the hydrogen target, air, or scintillators. The number of events lost in this manner can be calculated if the relevant cross sections are known. A good approximation to the actual cross section is the natural or geometrical cross section defined by anatural = -rn where rn = (a/m c)Al/3 is the nuclear radius, -/m c = 1.4 Fermi, and A the mass number of the material. We can improve this formula by remembering that in the energy region we are dealing with a nuclear collision can be thought of as occurring between the incoming particle and the individual nucleons of the nucleus, p-p and at-p collision cross sections are experimentally known. So the collision cross section for other materials can be better approximated by multiplying the natural cross section by the ratio of the p-p (or c-p) experimental cross section to the natural cross section for A = 1. Thus we have _ - _ 2/3 a = A2/ 42

where b' and c are the average proton-proton and pion-proton total cross PP iP sections in our energy range and are taken to be 45 and 30 mb respectively.l0-11 Some of the interacting particles yield forward going charged particles that are still counted. We estimate that of those interacting in the hydrogen target 20% + 10% are still counted; of those interacting in the air 30% + 10% are still counted; of those interacting in the scintillators 50% + 15% are still counted, So we have for the proton correction pLP pLp exp 0 No (o70+.10) + ( lSCIN).50+ 15) PP 0 1/3 AIR A1/ Pt/2 + (X)LH (.8o.10) (15) where N = Avagadro's number = 6.023 x 1023 p = density of the various materials in g/cm3 L = path length of proton in the various materials t = H2 target length = 30.5 cmo There is a similar expression for the pion correction. Combining these two expressions we have a total nuclear interaction correction of (12.5 + 2.5)%. B. DECAY OF PIONS The pion is unstable decaying into a muon and a neutrino with a mean life of 25o5 nsec12 in its rest frame, As many as 30% of the backward scattered pions decayed before reaching the final counter in the pion telescope. However, the muons were emitted by the relativisitic backward scattered pions in a narrow forward cone with a maximum half angle of from 6.4 degrees at 1.6 - GeV/c incident beam energy to 5.4 degrees at 5.3 GeV/co The backward scat43

tered pion momentum varies slowly over the energy range of the experiment. At an incident beam energy of 1.6 GeV/c the momentum of the scattered pion is 0.3552 GeV/c; at 5.3 GeV/c it is 0.420 GeV/c. Thus the coincidence was completed in many cases by the muons. Also events lost by the muon missing the pion counters were somewhat compensated for by pions which would have missed the counters being counted by decaying and sending a muon through the counter, We assume that all those back scattered pions which decay in the first 80 inches before the <t-magnet are lost that is their muon does not go through the pion counter telescope. We also assume that the pions which decay in the remainder of the path are counted via their muon or by a compensating muon coming into the telescope. Since the momentum of the scattered pions does not vary much, this correction is practically energy independent. With these assumptions the correction for the decay of the scattered pions is (9+5)%o Admittedly this is a somewhat rough calculation. To do it more accurately would require a complicated Monte Carlo program and still one could not properly fold the beam divergence and momentum spread into the program. Since the correction is small anyway, the above calculation is sufficient. Some of the incident beam pions decay from B3 to the liquid hydrogen target. However, this distance is only a few inches so this correction was well below 1%. C. MUON CONTAMINATION To get a rough idea of the magnitude of the muon contamination we did the following experiment. We inserted 30 inches of brass (about 6 collision lengths using the geometrical cross section) into the beam and measured the beam with 44

and without the brass in the beam. Since pions interact strongly they should be removed by the brass while the muons which interact electromagnetically for the most part pass through the brass. We did this measurement at three different energies and from the ratios of the scalars got for muon contamination the values 6.8% at 5.2 GeV/c, 6.1% at 3.6 GeV/c, and 4o.9% at 2.6 GeV/c. This measurement is rather difficult to do accurately. There will be multiple Coulomb scattering effects of the muons depending on their laboratory angular distribution. Some of the pions which undergo strong interactions. will be forward scattered and counted as muons. At higher energies less pions decay but they are restricted to a smaller forward cone. At lower energies more pions decay, but their forward cone is larger. These effects work against each other but it is difficult to accurately calculate them, As a final correction we decided on a muon contamination of (6 + 2)% for all energies, Do ELECTRON CONTAMINATION Since the range of electrons in copper is 7 to 9 cm in an energy range of 1 6 to 6.0 GeV/c clearly the electrons in the beam, if any would be stopped by the 30 inches of brass which we inserted into the beam to measure the muon contamination. We measured the electron contamination in the beam by running a C pressure curve down to zero psig of ethane and established that there was less than 1% electron contamination in the beam. 45

E. COUNTING LOSSES IN BEAM COUNTERS More beam particles than we count hit the H target while the coincidence circuitry is activated. The pulse width of all our logic electronics was 2.5 nsec. If, during this time, 2 or more beam pions pass through our beam counters only one will be counted yet all of them hit our H2 target, can interact to produce an event, and be counted by the activated coincidence electronics as an event, We are not concerned about beam pions which pass through the beam counters during any dead time of the beam counters or the beam logic circuits. Since the beam telescope is in coincidence with both the Ec and p telescopes, we must get a beam coincidence in order to get an event. So those beam particles which arrive at any portion of the beam circuit dead time except during the 2.5 nsec while the coincidence circuitry is activated are completely excluded from the cross section measurement and we need: not concern ourselves with them. The probability of two particles separated in time by less than 2.5 nsec both interacting to give events is extremely small. Therefore to a very high degree of accuracy only the number of beam particles impinging on the LH2 target should be modified. The counting loss can be written as loss = 1P + 2P3 + 3P4 + o 254 Consider for example the second term on the right side in the above expression. P3 is the probability of 5 beam pions in the time T, the pulse width of our electronics, given one event. The coefficient 2 arises because we count the first pion but miss the next two. So 46

= absolute probability of 2 events in time T ( absolute probability of 1 event in time T Using Poisson statistics we have.(m2/ 2' e" m m a (17) 2i (m/l ) e- 21 where a is the average counting rate and T is the time interval under consideration. Also 2?P5 m (18) and so on. Using the above the loss becomes 2 5 m ml m> loss =. +=- m - m19) 2 - While the protons are accelerated they form RF-bunches 8 nsec, long every 80 nsec. During the spill the beam still has this approximate structure, therefore the effective spill time will be 1/10 of the measured spill time. Assuming no ZGS magnet ripple, a measured spill of 150 nsec, and a beam intensity of 2.0 x 105 pions per pulse we get a beam counting loss of (2 + 1)%. The measured denominator (BC) is too small by approximately (2 + 1)%. It should be increased by (2 + l)%. Therefore the cross section should be decreased by approximately (2 + 1)%. F. EVENTS OCCURRING IN THE BEAM COUNTERS A (2 + l)% subtraction was made for interactions occurring with the hydrogen of the polystyrene of the B2 and B3 beam counters. Our system detected these interactions. In fact these events can be seen as high channel events on the PHA time of flight spectrum (Figure 16). Their high 47

channel number and thus their relative time of flight difference (pion early, proton late) as well as their relative number correspond to expected events from these two beam counters. G. INELASTIC CONTAMINATION As was mentioned earlier we measured the inelastic contamination to have an upper limit of 1%. H. BIN SIZE In a counter experiment it is impossible to measure the differential cross section at exactly a given point because of the finite size of the counters. Thus in this experiment we measured the average cross section within an angular spread Ae around 180~. Our CM subtended angle Ae varied from 1~ to 0.4~ as we increased the energy. Although there is structure in the differential cross section as a function of angle close to l80~ it is not sufficiently violent to change much over this range. I. COUNTER EFFICIENCY Early tests of the counters with both cosmic rays and with the t beam showed them to to be essentially 100% efficient. High voltage and delay curves were run periodically on all the counters in the system. Throughout the experiment we assumed the counters to be 100l efficient and thus have no correction for counter efficiency. As was mentioned earlier we ran periodic high voltage and delay curves on the counters to check the timing and efficiency. 48

J. BEAM ATTENUATION IN LH TARGET 2 As the incident pion beam moves through the target, pions are removed by interaction with the target protons so that fewer pions are available to interact at the downstream end of the target than at the upstream end. This effect is an overall reduction in the effective beam intensity. The effective beam intensity, I ff is given in terms of the incident beam intensity I by t Iefft = f I(x)dx or (20) I: = I / e-PX'x dx eff t o where t is the target length, 'p is the average J p total cross section in our energy range and p is the number of protons per cubic centimeter in the liquid hydrogen target. The x-axis points along the beam direction with its origin at the upstream edge of the target. The resulting expression of If eff is o pt I = I (1-,- (21) eff 0 2 Taking p = 30mb in our energy range and assuming that all pions which interact once are lost to the beam, we get If = 0.99 I eff o K. UNCERTAINTY IN THE PION JACOBIAN The solid angle in the center of mass subtended by the defining pion counter is given by: (AQ) = (A )B. (22) CM J 49

At 180~ 1 2 ' -;, /: CJ - Cd I (23) EI (g.1)2 where = inc; g (24) CM E:.+.mp E m +-mpEc inc inc ET Because of the uncertainty in the pion beam momentum Pin of + 0.03 GeV/c there is an uncertainty in J. This uncertainty varies from + 1.5% at 1.60 GeV/c to +0.5% at 5.3 GeV/c. 50

V. RESULTS AND CONCLUSIONS The differential cross section in the center-of-mass was calculated from the formula (rcpB)/BC) ' (abcdefgh) d:o Nopt En (25) --- =... l where dQCM A J where (jpBC) = total number of elastic events at a given energy (BC) = number of beam coincidences at a given energy N = Avagadro's number = 6.023 x 1023 p = density of liquid hydrogen =.071 g/cc t = length of the H2 target = 30.5 cm An = solid angle subtended by the r3 counter in the laboratory J = the pion Jacobian A = atomic weight of hydrogen = lo01 a = correction for nuclear interaction = 1.12 +.02 b = correction for decay for rc = 1.09 +.05 c = correction for muon and electron contamination in beam = 1.06 +.02 d = correction for counting losses in beam counters =.98 +.01 e = correction for events occurring in B2 and B3 beam counters =.98 +.01 f = correction for inelastic contamination =,99 +.01 g = correction for beam attenuation in LH2 target = 1.01 h = correction for uncertainty in the pion Jacobian = 1.00 +.01. Combining all the corrections and errors we get a net correction to the 51

raw data of 1.25 with a maximum error of + 12%. That is (abcdefgh) = (1.25 +.12). The above systematic error appears primarily as a normalization uncertainty. As was previously discussed we used essentially the same layout in measuring the cross section at adjacent energies. In view of this there should be no relative systematic errors. However, in addition to the 12% normalization uncertainty, there may very well be an energy dependant uncertainty of 3% in going from 1.6 to 5.3 GeV/c. The statistical errors which represent one standard deviation are for the most part in the range of 10% to 15%. The uncertainty in the beam momentum is + 0.03 GeV/c. The angle subtended by our counters around 180~ varied from 1~ to 0.4~ as we increased the energy. The cross section for f7p elastic scattering at 180~ as a function of laboratory pion momentum is given in Table II and is shown graphically in Figure 17. Only the statistical errors corresponding to one standard deviation are shown. The line is a freehand fit to the data. The positions of the known N-* resonances are shown. Given below them are their masses in MeV and their quantum numbers: isotopic spin, spin, and parity. Other groups have measured the i p elastic scattering cross section at angles between 160 and 180~ in the center of mass'-7 although they did not get back as far as 180~. Our data agrees fairly well with them. In elastic scattering each resonance appears as an intermediate state in the process + p -+ N*+ t5 + p. 52

TABLE II CENTER OF MASS CROSS SECTIONS FOR i-p ELASTIC SCATTERING AT 180~ pa S dc/d/ da/dt Errorb (GeV/c) (GeV)2 (kb/sr) ib/(GeV/c)2 (%) 1.60 3.91 220 1200 7 1.70 4.10 127 643 10 1.80 4.29 89.8 424 10 2.00 4.66 15.5 64.5 12 2.10 4.85 3.15 12.4 23 2.20 5.04 3.29 12.2 23 2.30 5.22 8.04 28.3 18 2.40 5.41 21.6 72.4 11 2.50 5.60 33.3 106 9 2.60 5.79 31.9 97.4 10 2.65 5.89 36.9 110 11 2.70 5.98 41.3 121 10 2.80 6.16 42.1 118 11 2.90 6.35 40.1 108 11 2.95 6.45 27.5 72.7 12 3.00 6.54 20.8 53.9 11 3.10 6.73 23.7 59.2 10 3.15 6.82 20.1 49.3 12 3.20 6.91 15.9 38.3 11 3.30 7.10 14.5 33.7 12 3.40 7.29 13.5 30.4 12 3.50 7.48 13.0 28.3 9 3.55 7.57 12.6 27.0 15 3 60 7.66 16.9 35.6 10 3.70 7.85 14.2 29.1 11 3.80 8.04 14.0 27.8 12 3.90 8.23 16.9 32.6 12 3.95 8.32 16.6 31.6 12 4.00 8.41 16.0 30.0 12 4.10 8.60 13.2 24.1 12 4.20 8.79 11.9 21.1 13 4.30 8.98 10.1 17.5 14 4.40 9.16 9.44 15.9 15 4.50 9.35 9.60 15.8 16 4.60 9.54 10.7 17.2 15 4.65 9.63 7.58 12.0 12 4.70 9.73 9.50 14.9 15 4.80 9.91 6.77 10.4 15 4.90 10.10 7.07 10.6 17 5.00 10.29 6.38 9.37 18 5.05 10.39 8.21 119. 19 5.10 10.48 10.7 15.4 15 5.15 10.57 10.4 14.8 17 5.20 10.66 7.25 10.2 22 5.30 10.85 6.73 9.28 20 aThe laboratory momentum Po is known to + 0.05 GeV/c. bThe errors quoted are statistical corresponding to one standard deviation. There is also a maximum normalization error of + 12%. 53

1000 _ \ TT-P ELASTIC SCATTERING,~~~ Hi~ ~AT 180~ 400 2 BERKELEY Hellond et ol (160~) 200 ~[ \~ ~ NIMROD Duke et ol (165~) 1- 00 THIS EXPERIMENT 340 20 10 4 - 2-1 I I I I I I 1236 1518 1688 1924 2190 242 2649 2850 3245 (3/23/ (3 )/2 5()(3(/2,9-) (3/2?, ) ('/2,. ) (3/2, )?.? ) 0 1 2 3 4 5 PO (GeV/c) Figure 17. The center of mass cross section for 7tp elastic scattering at L80~ as a function of laboratory pion momentum. The cross section is in Cpb/sterad. The pion momentum in GeV/c. Only the statistical errors corresponding to one standard deviation are shown. The line is a freehand fit to the data. The positions of the known N* resonances are shown. Given below them are their masses in Mev and their quantum numbers; isotopic spin, spin, and parity. 54

In this type of process there are effects due to two types of amplitudes, the resonance amplitude and the non-resonant elastic amplitude or background amplitudeo These two amplitudes may interfere constructively or destructively or not at all, There is a dramatic destructive interference at Po = 2.15 Gev/c which is quite interesting as the cross section drops almost two orders of magnitude in this region. Another interesting result of the experiment is the large narrow peak in the cross section at P = 5.12 GeV/c. We believe that this is firm evidence 0 for the existence of a nucleon resonance with a mass of 3245 + 10 Mev. This N* (3245) has a full width at half-maximum of less than 55 Mev and rises about 4Lb/sterad above the non-resonant cross section. The width of the resonance is about 1% of its mass. This means that the particle is quite long lived in spite of its large mass. The paritiesj. and the quantity X(J + 1/2) of the N* resonances were calculated as follows, Using the idea first suggested by Ross and Heinz, at 180~ the elastic <-'-p differential cross section in the region of a resonance can be written as13,14,22 dc ANF + tCX(J + 1/2) (-1)2 (27) dR B ~ - i since at 180~ the spin-flip terms are zero. In equation (27) C is the ClebschGordan coefficient C = 1/3 for I = 3/2 C = 2/3 for I = 1/2 55

X = the elasticity of the resonanc - Fe/F r = the full width at half maximum of the resonance e r = the partial width for decay into the elastic channel J = the spin of the resonance = IR - S/MerR M = the mass of the resonance S = the square of the center of mass energy NF AB' = the non-spin-flip background amplitude We can write (-1)~ in terms of the parity of the resonance, PR. the ~-p system P- = (-1)(+l)(-l), and since the resonance formation and decay are parity conserving reactions PR = P-p= - (-) (28) So we can write the resonance amplitude R as aCX(J + 1/2) PR ( R = - (29) C - i If the partial widths of the various channels have the same energy dependence (usually a good approximation in the energy region ER + 3/2 FR) the above resonance amplitudes trace out circles in the complex plane., The diameter of the circle is equal to the magnitude of the pure imaginary part of the resonance amplitude when e = 0, that is at the resonance energy. The circle is above or below the real axis depending on the parity of the resonance. See Figure 18. Starting at an energy below a resonance and increasing the energy, the circles are traversed in a counterclockwise direction starting at the 56

Im R at the Resonance Energy Odd Parity,/ i Increasing Energy _- 1__-"//' Starting Below the a/ ^. Resonance Energy Re ~I ~ Even.~\ v ~/ Parity Figure 18. Resonance amplitude in the complex plane. 57

origino At the resonance energy, R is a maximum, is pure imaginary, and is at the top, or bottom, of the circle depending on the parity of the resonance. If there is also a non-resonant background amplitude present, the circular trajectory is still traced out but the starting point is displaced from the origin and the resonance energy is no longer at the top, or bottom, of the circleo That is the maximum intereference, constructive or destructive, does not occur at the resonance energy but is displaced from ito See Figures 19 and 20~ For the background cross section we used the empirical form _ = A(Pi )a jib/sr (30) d 2 LAB where P = is the momentum of the incident -" in the laboratory LAB A = 420 a = -2 58 This was obtained from a straight line fit to the data on a log-log ploto The assumed background cross section is shown as a dashed line in Figure 210 It is assumed that the sign of the real and imaginary parts of the background amplitude do not change sign as a function of energy. We can determine the quadrant of the background amplitude as follows. The N* (1688) and the N* (1924) both interefere constructively with it near their resonant energies. They are knownl6 to have positive (+) parity. From this we assume that the background amplitude does not lie in the first or second quadrant because if it did it would not interefere constructively with the positive parity reso58

A'lm Re 'do"'1/2 \ \ \ d / Background 59 Even Parity Figure 19. Constructive interference of background and resonance amplitudes.

Im Re ~d-o * A \Odd ( Xs \\V/2 Parity Background A - Figure 20. Destructive interference of background and resonance amplitudes. 60

000 \ - TT-P ELASTIC SCATTERING AT 180~ 400 + BERKELEY Hellond et ol (1601) 200 -I NIMROD Duke et ol (165) 1T00 ^ THIS EXPERIMENT E 40 - BACKGROUND \ 20 (3/O3-/2-+(1^^)(l2y)(3/2). (1/2,?~-) (/2.. ), /2,~ (^ ),. ) 0 1 2 3 4 5 PO (GeV/c) Figure 21 The assumed background cross section. 61

nances near the resonance energy. Also because the mimimum cross section near the 2190 resonance is at a greater energy than the 2190 resonance energy leads us to assume that the resonant amplitude is not in the third quadrant but that it lies in the fourth quadrant. The imaginary part of the background amplitude is negative and the real part is positive. The parities and the quantitites X(J + 1/2) are listed in Table III. TABLE III THE EXPERIMENTAL PARITY AND X(J + 1/2) FOR THE N* RESONANCES N* I J P r X(J + 1/2) X 2190 1/2 7/2 - 200.46 + 20%.12 + 20% 2420 3/2 + 275.31 + 60% 2650 1/2 - 300.058 + 70% 2850 3/2 + 300.12 + 70% 3245 + 355.073 + 8o% C The parities are determined by noting whether the resonance intereferes constructively or destructively with the background. Constructive intereference indicates positive (+) parity while destructive intereference indicates negative (-) parity. The quantities X(J + 1/2) for the resonances are determined from Figures 19 and 20 by trigonometry. For example, referring to Figure 20 we have by the Law of Cosines 2 2 2 a = b + c - 2bc cos A (50) 62

where a = (d)l/2 dQ( Background b = (d)/ + pure imaginary dQ Minimum 2 Rpure imaginary 2 Im R) A = 2 arctan (k-) Re R At minimum cross section = 2arctan (M ) M2 - S At minimum cross section R = 19 73 A C (J + 1/2) X (t barns) / pure imaginary From the above we solve for X(J + 1/2) consistent with the uncertainties in the values of the input parameterso These are shown in Table IV. TABLE IV INPUT PARAMETERS FOR THE DETERMINATION OF X(J + 1/2) N* (d - (d) r M dSQ Background dQ Maximum (Mev) (Mev) Minimum 2190 60 + 15% 2.5 + 5 200 + 10 2190 + 5 2420 28 + 15% 42 + 2 275 + 10 2423 > 10 2650 19 + 15% 14 + 1 500 + 20 2649 + 10 2850 12.5 + 15% 17 + 11. 300 + 20 2850 + 12 3245 653 + 15% 11 + 1 50 + 15 3230 + 20 63

In many recent papers Barger and Cline17-20 have given a phenomenological analysis of the cross section at 180~ with a Reggized non-resonant background amplitude having both a real and imaginary part of the same order of magnitude. In the course of their calculations they have given parity, spin, and elasticity assignments to the resonances. In a recent T+p elastic scattering experiment near 180~ by Dobrowolski, et al.,23 the N* (2420) and N* (2850) were confirmed to have positive (+) parity, 64

APPENDIX 0~ K- PRODUCTION CROSS-SECTION During the course of the experiment the 0~ c- production cross section on copper at 12,5 BeV/c was measured. For details see reference 21. dc/dMdP was calculated from N A = A2AT PtN No da Ell A dQdP where T = fraction of surviving pions at the H2 target, No = number of calculating protons, and T = target efficiency factoro Other quantities are given in Table Vo In Table VI the zero degree K- production by 12.5 GeV/c protons on copper is shown. The following fluxes were obtained in the range 4.0 GeV/c to 5.2 GeV/c (Table VII). Since the target could not be moved further into the octant, we allowed the target to remain at the 4.0 BeV/c point which gave a range of production angles from 1/2~ to 4~ at the expense of the beam going off axis about 2 mrad. To stay on axis would have meant that the high momentum production angle would have been about 6-1/2~. The fluxes tabulated can be expected to vary about + 15% 65

TABLE V PROTON BEAM AND INTERNAL TARGET PARAMETERS 1o Beam Parameters ao A2 = 10 x 10-4 sr b, AP c. Beam length = 48 meters 2, Target Parameters ao 3585" long x 1/8' x 1/8" target (90% copper, 10% aluminum) b, 0~ production angle PN= 8.06 x 1023 cm-3 A 5, Fluxes and Cross-Section a, Fluxes are for the average of several thousand pulses and the cross-section is normalized to a (55 + 15)% targeting efficiency. bo Above 3.5 GeV/c normalized to (86 + 15)% because of the addition of the beryllium lip on the target. c. Internal beam averaged 5 - 6 x 10 per pulse. 66

TABLE VI ZERO DEGREE i- PRODUCTION BY 12.5 GeV/c PROTONS ON COPPER Nt-/1011, No /(GeV/c)/sr/circ., d (mb/sr/(GeV/c), PGeV/c d.dp protons protons nucleus 1.6 25 x o13 1.o4 x lo-1 398 1.7 33 1.30 478 1.8 335.3 1.23 440 2.0 40.6 1.35 445 2.1 40.7 1.29 419 2,2 41.3 1.25 400 2.5 43 1.25 392 2.5 46 1.23 375 2.6 45.5 1.17 351 2.7 46. 4 1.15 340 2.8 42.9 1.02 299 2.9 47.1 1.08 309 3.0 47.4 1.05 300 351 4.1 0.93 5261 3.2 45 0.94 264 3.3 45.8 0.93 257 304 43.7 0.86 238 305 44.9 0.86 235 3.5 67 l128 235 5.6 62.1 1.15 212 307 66.2 1.19 216 308 65.9 1.16 210 3.9 61.0. 04 188 4.0 64.0 1.07 191 67

TABLE VII E- FLUXES IN THE RANGE 4.0 GeV/c to 5.2 GeV/c,. PGeV/c NJ-/1011 circ. protons Produion ff Axis Angle P Nit- Angle'Angle 4.0 64 x 103 0.50 0.2 mrad 401 64 1.0~ 4.2 65 1.5~ 4.3 62 2.0~ 4.4 56 2.4~ 4.5 51 2,7~ 4.6 47 2.9~ 4.7 45 3.1 4.8 40 3.4~ 4.9 36 3.6~ 5.0 33 3580 2.0 mrad 501 30 3,85~ 5.2 29 35.9 68

BIBLIOGRAPHY lo W. R. Frisken, A. L. Read, H. Ruderman, A. D. Krisch, J. Orear, R. Rubinstein, D. B. Scarl, and Do H. White, Phys. Revo Letters 15, 313 (1965). 2, P. J. Duke, D. P. Jones, M.A.R. Kemp, P. G. Murphy, J. D. Prentice, J. J. Thresher, H. H, Atkinson, C. R. Cox, and K. S. Heard, Phys. Rev. Letters 15, 468 (1965); and private communication. 3. Co T. Coffin, N. Dikmen, L. Ettlinger, D. Meyer, A. Saulys, K. Terwilliger, and D. Williams, Phys. Rev, Letters 15, 858 (1965). 4. D. E. Damouth, L. W. Jones, and M. L. Perl, Phys. ReVo Letters 11, 287 (19635) 5. W. F. Baker, A. Lundby, et alo, private communication, 6. M, L. Perl, Y. Y. Lee, and Eo Marquit, Phys. Rev, 138, B707 (1965). 7o J. A, Helland, C. D. Wood, T. J. Devlin, D. E. Hagge, M. J. Longo, B. J. Moyer, and V. Perez-Mendez, Phys. Rev, 134, B1079 (1964). 85 S. W. Kormanyos, A. D. Krisch, J. R. O'Fallon, K. Ruddick, and L. G. Ratner, Rev, Letters 16, 709 (1966)o 9. S. Penner, RSI, 32, 150 (1961)o 10. Do V. Bugg, D. C. Salter, G. H. Stafford, R. F. George, K. F. Riley, and Ro J. Tapper, Phys. Rev. 146, 980 (1966). llo A Citron, Wo Galbraith, T. F. Kycia, B. A. LeonticQ R. H. Phillips, and A Rousset, Phys. Rev. Letters 13, 205 (1964)o 12o J. Askin, T. Fassini, G. Fidecaro, Y. Goldschmidt-Clermont, N. H. Lipman, A. W. Merrison, and H. Paul, Nuovo Cimento 16, 490 (1960). 135 R. M. Heinz and M. H. Ross, Phys. Rev. Letters 14, 1091 (1965); and private communication, 14. W. Layson, Nuovo Cimento 27, 724 (1963); J. D. Jackson, ibido 34, 1644 (1964). 15. Robert Do Tripp, Annual Review of Nuclear Science 15, 325 (1965). 16. Ao H, Rosenfeld, A. Barbaro-Galtieri, W. H. Barkas, PO L. Bastien, J. Kirz, and M. Roos, Rev. Modo Phys. 37, 663 (1965). 69

BIBLIOGRAPHY (Concluded) 17. V. Barger and D. Cline, Phys. Rev. Letters 16, 913 (1966). 18. V. Barger and D. Cline, Paper submitted to the XIIIth International Conference on High Energy Physics at Berkeley, 1966. 19, V. Barger and D. Cline, Phys. Letters 22, 666 (1966). 20. V. Barger and D. Cline, Fermion Regge Pole Model for the Structure of PionNucleon Elastic Scattering in the Backward Hemisphere, to be published, 21. L. G. Ratner 0~jr" production cross section on copper at 12.5 GeV/c and some t- fluxes in the 17~ beam line, Argonne National Laboratory internal report. 22. B. Jacobsohn and C. No Yang, private communication. 235 T. Dobrowolski~ et alo, Paper submitted to the XIIIth International Conference on High Energy Physics at Berkeley, 1966. 70

Unclassified Security Classification DOCUMENT CONTROL DATA - R&D (Security claeeilication of title, body of abstract and indexing annotation muet be entered when the overall report is cleessiied) 1. ORIGINATING ACTIVITY (Corporate author) 2-. REPORT SECURITY C LASSIFICATION The University of Michigan Unclassified Department of Physics 26 GROUP Ann Arbor, Michigan 3. REPORT TITLE ot-p Elastic Scattering at 180 Degrees from 1.6 to 5.3 GeV/c 4. DESCRIPTIVE NOTES (Type of report and inclusive dates) Technical Report S5 AUTHOR(S) (Last name. first name, initial) Kormanyos, Stephen W. 6. REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OF REFS April 1967 76 | 23 Ba. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER(S) Nonr-1224(23) 03106-28-T b. PROJECT NO. INR-022-274 ____. c. 9b. OTHER R PORT NO(S) (Any other numbers that may be assigned this report) d. Technical Report No. 28 10. AVA IL ABILITY/LIMITA TION NOTICES Distribution of this document is unlimited. 1. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Department of the Navy Office of Naval Research Washington, D.C. 13. ABSTRAe have measured the differential cross section for jrp elastic scattering at 1800 in steps of 0.10 GeV/c or less in the region from 1.6 to 5.3 GeV/c. There is considerable structure in the cross section. This may be interpreted as an interference effect between the resonance amplitude and the nonresonant or background amplitude. There is a dramatic destructive interference at P = 2.15 GeV/c which is quite interesting as the cross section drops almost two orders of magnitude in this region. Another interesting feature of the experiment is the large narrow peak in the cross section at PO = 5.12 GeV/c. We believe that this is firm evidence for the existence of a nucleon resonance with a mass of (3245 + 10) MeV. This N* (3245) has a full width at half-maximum of less than 355 MeV. The width of the resonance is about lo of its mass. Parities and the quantity X(J + 1/2) are given for various N* resonances where X is the elasticity and J is the spin of the resonance. D iJAN64 1473 Unclassified Security Classification

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