AI1STRACT A MEASUREMENT OF THE DIFFERENTIAL CROSS SECTIONS FOR THE REACTIONS rr + p K + AND n + p 4 K + Y (1385) NEAR ZERO DEGREES AT 3.0, 5.0 AND 7.0 Gev/c by Parviz Kalbaci Chairman: C. Tristram Coffin The differential cross sections for the reactions ++ + rrp 4 K E and rr p 4 K Y have be ehn'e'asured for kaon laboratory angles from 00 to 3.:.;.n-T..gsi.e,-ei'-m, missing-mass spectrometer determined.-he-..:di't'ction.; o nd-,,mXomentum of forward going ka,ons. The spec ropio re. t -,on.s-st.f bending magnets, scintillation counters, '.gas;ihre-bold'erenkov counters and wire spark chambers concted '.i' ayi.. -on Tne computer. The differential crof.s c' st'ons. Tor rrp 4 K E rise exponentially to tmin at 5.0 arid-*7>.~,'-"Gev/c. However, the cross section at 3.0 Gev/c deviates from a. simple exponential shape indicating a possibility of an s-channel contribution to the cross section. There is no evidence of a dip at very small -t indicating that the spin flip contribution to the cross sections for this reaction is small. The results at high energies are compatible with double Regge pole models in the forward direction. The reaction rrp 4 K+Y shows a sharp dip at very small -t indicating the dominance of the spin flip contribution to the cross section. The 'p-photon analogy' has been employed to interpret this forward dip.

UM HIE 71-41 A MEASUREMENT OF THE DIFFERENTIAL CROSS SECTIONS FOR THE REACTIONS Tr + p K + E AND + p - K + Y (1385) NEAR ZERO DEGREES AT 3.0, 5.0 AND 7.0 Gev/c by Parviz Kalbaci A dissertation submitted in pa.rtial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) in The University of Michigan 1971 Doctoral Committee: Associate Professor C. Tristram Coffin, Chairman Professor Wilfred Ka.plan Professor Dona.ld I. Meyer Assistant Professor Brian E. Springett Associate Professor Yukio Tomozawa

ACKNOWLEDGEMENTS I wish to thank Professor C. Tristram Coffin for his calm, patient advice and encouragement at all stages of my thesis work. I would like to thank Professor Donald I. Meyer for his many helpful suggestions and continuous assistance throughout the experiment. I am indebted to Professor Carl W. Akerlof for his invaluable contributions and guidance during the experiment and also for his perceptive comments on my thesis work. Thanks are due to Dr. Kenneth C. Stanfield for his assistance from the very beginning to the final data analysis. I would like to express my gratitude to Dr. Peter Schmueser for both his advice and building of most of the spark chambers. I appreciate the assistance of Dr. Paul K. Caldwell in running the experiment. I would like to thank Professors Yukio Tomozawa and Gordon L. Kane for helpful discussions. I would also like to extend my thanks to Professors Wilfred Kaplan and Brian E. Springett. I wish to thank Dr. David R. Rust, particularly for building the high voltage pulser. Finally, acknowledgement is extended to the staff of the Argonne National Laboratory. ii

TABLE O0F CONTENTS Pag; e ACKNOWLEDGMENTS................................... ii LIST OF TABLES..........................O iv LIST OF FIGURES...................v............. O v LIST OF APPENDICES................................ vii I. INTRODUCTION..................... II. EXPERIMENTAL METHOD....................... 8 A. The Incident Beam and The Target...... 10 B. The Fast Electronics.................. 12 C. The Spark Chambers.................... 19 D. The On-Line Computer................. 23 III. DATA ANALYSIS.................... 29 A. Track Reconstruction and Spark Chamber Efficiency................... 30 B. Event Reconstruction and Cut Requirements.................. 32 C. Solid Angle Acceptance of the Spectrometer.................. 40 D. The Incident Beam Correction.......... 42 E. Nuclear Interaction and Decay Corrections of Kaons.44 F. The Differential Cross-Section........ 47 IV. DISCUSSION OF THE RESULTS......... 51 A. Consistency of this Experiment with Other Experiments.................... 51 B. Differential Cross Section for nT + p K +...................... 53 C. Differential Cross Section for + + * y + p 4 K + Y (1385). 60 D. Determination of the Spin Flip and Spin Non-Flip Amplitudes............. 66 LIST OF REFERENCES.............................. 93 iii

LIST OF TABLES Tab le Page I. Incident beam pion parameters.............. 11 II. The summary of the corrections applied to the data................................ 45 III. doa/dt in fb(Gev/c)- 2 for reactions (5) and (6)................... 48 IV. The results of the best least squares fit to the equation (20).................... 67 V. Comparison of Wood-Saxon model with experiment 81 VI. Total cross section for various elements... 84 iv

LIST OF FIGURES Figure Page 1. The Feynman diagram of two-body reactions.. 2 2. The differential cross section for some of the two-body reactions.................. 3. The experimental layouts.......... 9......... 4. The flow chart of the fast electronics logic.................. 13 5. The schematic diagram of the C1 Cerenkov counter.................................... 15 6. The pressure curve for C1 Cerenkov counter at 5.0 Gev/c incident beam momentum......... 17 7. The details of the physical construction of a single gap wire spark chamber......... 21 8. The flow chart of the different input-output devices to the computer.................. 25 9. The distribution of events versus the separation between the incoming and outgoing trajectories through the magnet....... 33 10. The missing mass plot for the Z and the Y production after target out subtraction.... 35 11. The X distribution of the target events before and after Y cut requirement......... 36 12. The missing mass plot for the Z and Y production............................. 38 13. The missing mass spectrum for the Y production................................ 39 14. An end view of the downstream end of the analyzing magnet........................... 41

LIST of FIGURES (cont'd) Figure Page 15. The four momentum transfer acceptance for 5.0 Gev/c.............................. 43 16. The differential cross section for the I+ +p 4 K + Z reaction.................. 49 17. The differential cross section for the + p + K + Y (1385) reaction............ 50 18. The comparison of this experiment on Kn production at 5.0 Gev/c with others........ 52 19. The results of the least square fitting program 55 20. The comparison of the up 4 KE cross section data with the Regge pole model........... 57 21. The comparison of the up 4 KE cross section data with the Regge pole model............ 58 22. The comparison of the up 4 KE cross section data with the Regge pole model............. 59 23. Comparison of this experiment with others on Y*............................. 62 24. The Feynman diagram for the isobar productions............................. 63 25. The comparison between experimental data and a Regge pole prediction.................... 65 26. Thyratron pulser power supply.............. 73 27. Avalanche driver........................... 74 28. Thyratron power circuit.................... 75 vi

LIST OF APPENDICES Appendix Page I. Interference between the t-channel and s-channel resonance........................ 69 II. The high voltage pulser.................... 72 III. Nuclear interaction correction............ 76 vii

I. INTRODUCTION The strong interactions are responsible for such processes as the scattering of mesons by baryons, of baryons by baryons and for the forces that bind protons and neutrons together in the nucleus. Much of our knowledge of strong interactions comes from the two-body reactions of the form a + b 4 c + d The most successful theories for such reactions are based 1 on the concept of particle exchange. Figure 1 shows the Feynman diagram for a two-body reaction mediated by the exchange of one particle. The behavior of the two-body reactions has been found to depend on the quantum numbers exchanged between the interacting particles. If the exchanged quantum numbers are such that a particle with these quantum numbers exists, the cross section for the corresponding reaction is large; otherwise it is relatively small. For instance, the reaction K + p 4- n + + requires a meson exchange with quantum numbers I=1/2, S=-land Q=O. Since there exist meson resonances with these quantum numbers such as K (m=890, JP=1, I=1/2, S=-l)and K (m=1420, JP=2+, 1=1/2, S=-l), one expects a forward peak in the cross section and it is observed. However, the reaction K + p 4 w + E 1

a c J s-channel --- (a) t-channe 1 (b) Figure 1. The Feynman diagram of two-body reactions a) a + b 4 ~ + d as viewed from s-channel. b) a + c5-b + d as viewed from t-channe l.

in the forward direction requires the exchange of a meson with I=3/2, S=l and Q=2. Since there are no doubly charged mesons, the forward cross section should be much smaller than the forward cross section for K- + p 4 I- + E+ and it is.2'3 Before proceeding further with examples of relationship between cross section and quantum numbers exchanged, it is convenient to define some kinematic variables. The two-body reactions are described by two independent Lorentz invariant variables. The most common variables used are the Mande lstam variables s and t which are defined as follows: =-(P + Pb)2=E 2 t=-(pa - Pc) Where p's are the four momenta of the corresponding particles, p(p,iE). E is the energy in the center-of-mass system and t is the square of the four momentum transfer from a to c. The following set of reactions illustrates the relationship between the structure of the cross section and the quantum numbers of the exchanged particles. -rr + p 4 —+ P (1) + + + p, Tr + p (2) Tr + p T r +n (3) - +p + p n (4) The dominant exchanges of the quantum numbers for the elastic scattering reactions (1) and (2) are the quantum numbers of the vacuum (B=I=S=O), or the pomeranchucktrajectory in the language of the Regge pole theory.4 However, the leading trajectories for the charge exchange reactions (3) and (4)

are the p and A2 trajectories respectively. Figure 2 demonstrates the structure of the measured cross section for some of the two-body reactions with different exchanges. The differential cross sections for the elastic scattering (1) and (2) are measured at different incident pion energies, for pions production at different angles in the final states, by many authors.5'6 The general features of these two reactions are the exponential decrease of the cross section as a function of t followed by a second maximum as shown in Figure 2 (a and b). The second maximum starts to disapear as the incident pion energy increases. The charge exchange reactions, (3) and (4), show a peak in the small momentum 7-9 transfer. Such a peak is not steeply decreasing from the forward direction, as is the elastic peak, but rather it is flat up to -t-.l (Gev/c)2 and then decreases exponentially with a slope b10 (Gev/c)-2 for the reaction (3) and a slope b-4 (Gev/c)-2 for the reaction (4). Figure 2 (c and d) shows the behavior of the cross section for the reactions (3) and (4). The study of the reactions 1 through 4 has provided information for determining the corresponding exchanged trajectories. Another class of reactions of interest comprises the hypercharge exchange reactions. The following processes are of special interest because they are convenient to study experimentally. + p K + + (5) r+ p - K+ Y (1385) (6)

5 too w'p- 'ptoo too r* " CL~b too -Jtoo P~ I00 - Ov~~~~~~~OV/C loco so i000,oc:,1 5,, -p,. e ~~~~. 0' 1*;;;.;;~,,i3 %..... d~l!......S.1. c t~ ~,t. 10 ~~~~~~~~~ 1OG@VC~~~~~~~~~~~~~~~~ N.5 N' MI-PS DT N. 1.0 1.g, *0 I a)~~~~~~~i o43 -,l Tog!lf~AN.1o * * $ 0 ',o:-i ~~ "", 1' M o oo~~.~~~C u~~~N,- SII VO S~ -t. 98 1. 92 W C4).olC ~~~ ~ I 0. O to to 45 2 0.C tootvef 0,.,.8o.2 1.6 2.0 10 I F1 ttY~r r I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 9 C d w 5 16 A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~()C V'p -*' l,~nOW/,oo ~-. 2..,. PRUSS el a 14 GW IC CH a~~~~~~~~~~~~~~~~~~~~~~~~~a 4GsVAt 's-] eie~~~~~~~~~c 70GeV/c cI 0..I 'o') J W 0.' - W '""= ~ ~ 2. 3.0 0 0. 04-.-06I. el...[. - e ) 1:1.4 r —i 4O(b.,L '1~~~~~ \ \ 6 t~/,.us, eI f vI~~~~~~~~~~~~~~~~~~~~~~~~C 2'~~~~~~~~~~~~~~~~~~~~~, -! (OeV/c] -t~~~~~G~~~V/cf] ~~~~~~~Itl (eeV/c)Z D-~

6 The exchanged trajectories for both these reactions are K (890) and K (1420). The differential cross section for reaction (5) has been measured for pion energies from 3 Gev/c to 14 Gev/c. 10-12 The cross section for this reaction shows an exponential decrease with t followed by a secondary maximum similar to the one for the charge exchange reaction (3). Figure 2 (e) shows the dependance of the cross section for reaction (5) on t and on beam momentum. The cross section for reaction (6) falls off exponentially 12,13 with t and it has a dip in the forward direction.12,13 Figure 2 (f) shows the general features of the reaction (6). 10-12 None of the above mentioned authors have measured the cross section for the reaction (5) near zero degrees to demonstrate whether the cross section rises exponentially to tmin(minimum) or whether it is flat ( or perhaps even dips ) as in the charge exchange reaction. The dip in the forward direction in the reactions (3), (4) and (6) is due to the dominance of the spin flip amplitude, which goes to 14 zero at zero degrees. This thesis describes an experiment which was performed to measure the differential cross section for the reactions o o (5) and (6) for laboratory kaon angles from 0 to 3.5 The incident pion energies were 3.0, 5.0 and 7.0 Gev/c for reaction (5) and 5.0 Gev/c for reaction (6). One of the motivations for doing this experiment was to study the relative amount of spin flip and spin non-flip amplitudes

in the reactions (5) and (6). Another objective was to provide more detailed information on the K (890) and K (1420) exchanges through a study of the energy and angle dependence of the cross section. Section II will describe the apparatus used in this experiment such as wire spark chambers, detectors, fast electronics logic, buffer system and the on-line computer. Section III will describe the method of analyzing the data. Section IV will discuss the results obtained from this experiment and compare it with other experiments. It will also discuss two theoretical models, the Regge pole and the Ip-photon' analogy, that are used to explain the experimental data.

IIo EXPERIMENTAL METHOD This experiment was done with a single-arm, missingmass spectrometer to determine the direction and momentum of forward going kaons (Figure 3). The spectrometer consisted of bending magnets, scintillation counters, gas threshold Cerenkov counters and wire spark chambers with magnetostrictive readouts connected on-line to an EMR 6050 computer. The wire spark chambers were triggered on events preselected by the scintillation and Cerenkov counter system. The identification of the K Z and the K Y final states among the large variety of other processes was done * by calculating the mass of the final Z or Y, and requiring that this mass agree within experimental uncertainity with the known masses of these particles. The mass is calculated as follows from the conservation of energy and momentum for two body reactions: Pa + Pb = Pc + Pd (7) The missing mass can be defined as: (Missing mass)2 MM2 = md2 = _(pd )2 -= (P + Pb - Pc)2 (8) In the laboratory rest frame of particle b, equation (8) reduces to: MM2 m 2 % m 2+ 2mb[(ma2 + p2)1/2_ ( 2 + c2)1/2] 2 + 2)1/2 2 + 2)1/2 Icos (9) Whr ' a Pa ) P C co (9) Where p's are the three momentum of the corresponding

O 2 METER STEERiNG, IMAGRET WSC ~ BM2 BM3 CZC CPI2, BM4 'H, 4 BEAM TARGET KA-4 Figure 3. The experimental layout.

10 particle and 0 is the laboratory angle between ~a and Pc. Therefore for a kinematically well defined initial state, the measurement of the scattering angle and momentum of the particle c was necessary to determine MM. The wire spark chamber in the beam-line determined the direction of the incident pion beam and the spark chambers in the spectrometer determined the direction of the produced particle c in the final state. The intersection of these two direction lines defined the scattering angle. The momentum of the particle c was found from angle of bend in the analyzing magnet. A. The Incident Beam and the Target The extracted proton beam of the Zero Gradient Synchrotron (Z.G.S.) at Argonne National Laboratory was used to produce a secondarybeam of pions from a beryllium (Be) target. These pions were focused onto a momentum slit of 3/4 in. width, by a beam transport system consisting of two quadrupoles and two bending magnets. Two scintillation counters pi and p2, at the momentum slit, (not shown in Figure 3) were used to divide the accepted momentum into three regions. The momentum of the beam was defined to +3/4% at the first stage of focusing.. In the second stage of focusing, a set of two quadrupoles and two bending magnets recombined the momenta and focused the beam onto the hydrogen target. The characteris tic parameters of the positive beam pion were

11 Table I. Incident Beam Pion Parameters Spot size.28 in. x.22 in. RMS Momentum spread.63%6 RMS Horizontal divergence 3.4 mrad RMS Vertical divegence 5.3 mrad RMS Pion intensity 2 x 104 per pulse ~ Length of the beam spill 500 msec found by using a wire spark chamber in the beam-line. These parameters are summarized in Table I. The reason for running at low intensity was to avoid having double tracks within the resolving time ( which was about.6 microseconds ). The pions were tagged by two threshold gas Cerenkov counters, CPI1 and CPI2, and their positions were defined by scintilation counters BM1, BM2, BM3 and i4 The liquid hydrogen was contained in a target vessel 24 in. long and 2 in. in diameter, surrounded by a vacuum jacket 27.5 in. long, with a cross section of 5 in. inner

12 diameter. The H2 was cooled by an A.D. Little Company refrigerator which reliquefied any hydrogen which boiled off the target reservoir and returned it to the target. B. The Fast Electronics An EVENT was defined as a coincidence between an incoming pion andan outgoing kaon produced at the hydrogen target. Figure 4 shows a flow chart of the fast logic. There were four scintillation counters BM1, BM2, BM3 and BM4 to define the beam. BM1 was downstream from CPI1 and about 40 ft upstream from the hydrogen target at the first focus of the beam. BM2 and BM3 were on either end of CPI2. BM4 (9 in. x 12 in.) with a square hole 3/4 in. x 3/4 in. in the middle was located immediately before the target to limit the spot size of the incident beam. The coincidence BEAM = BM1 x BM2 x BM3 x BM4 indicated the number of particles entering the target. The pressures in the gas threshold Cerenkov counters, CPI1 and CPI2, were set to detect pions and not heavier particles. The coincidence, BPI = BEAM x CPI1 x CPI2, defined the pions entering the target. The only contaminations in the BPI were muons and positrons, which caused 3% of the BPI pulses. The BPI pulses were counted in two independent scalers for later use in calculating the cross section. The spectrometer was designed to accept kaons which o0 o were produced in the target at angles between 0 to 4.5

BEAM ) ( Bpi BM 1 — > - BM2 BM3> BM4 CPI2 (EVENT) K1GA K2 K3 S IOK4 -> - C1 OFAN FAN M Ul 6 our OUT SAC START W KlKM -~ r, _, E_ X,SCOPE TRIGGER d C2 KR1 KR2~ / F > I W.S.C. TRIGGER KR3. I | MODE PULSE FAN OUT Figure 4. The flow chart of the fast electronics logic.

14 in the laboratory system. Incident pions which did not interact also went through the spectrometer. The ratio of the K events to the number of incident pions was about 10-5; therefore a pion rejection of the order of 10-5 was necessary in order to avoid triggering the apparatus on direct pion beam. A rejection ratio of this order of magnitude was also necessary to kinematically separate the K events, as is explained later. There were three gas threshold focusing Cerenkov counters, Cl, C2 &nd C4, detecting kaons and suppressing the pions in the beam and pions due to elastic and inelastic scattering. The optics and sizes of C1 and C2 were identical. Figure 5 shows the details of C1. The windows of Cl were made of aluminum domes with thickness of.1 in. and.15 in. C1 was designed o o to detect kaons coming from the target between OQ - 5 by producing Cerenkov light with a cone angle of 4.5. The solid lines in Figure 5 show the paths of the Cerenkov rays. These rays are reflected on two spherical mirrors and are focused near the photocathode of a 5 in. RCA-4522 photomultiplier, after passing through an iris of 4.5 in. diameter. This iris rejects the Cerenkov rays of a cone angle larger than 4.5. A ray tracing program was written to check O whether all the Cerenkov light in a 4.5 cone produced by the charged particles would go through the iris. It was found that 100% of the rays of 4l.' cone go through the iris and as the cone angle was increased fewer rays went through the iris.

15 4522, 5" RCA PHOTO-TUBE IRON SHIELDING 20" FOCAL LENGTH 2 O \ ELDT ALUMINIZED MIRROR PLEXIGLASS MIRROR. in. THICK ALUMINUM.15in.TIICK ALUMINUM ENTRANCE WINDOW EXIT WINDOW Figure 5. The schematic diagram of the C1 Cerenkov Counter.

Figure 6 shows the pressure curve for C1 for 5 Gev/c incident pions. Freon 13 was used in C1. The solid line is number of events versus pressure while C2 and C4, which were detecting only pions, were taken out of anticoincidence. The solid line shows that pion detection efficiency of C1 started to fall off at 140 psig (pound per squared inch) 0 which corresponded to a cone angle of 7.2 and it was very inefficient at 180 psig (8.5 cone angle) in detecting pions. The dashed line is the number of events versus pressure with C2 and C4 in anticoincidence to reject pions. Cl1 started counting kaons as well as pions at about 60 psig. It's kaon detection efficiency increased with pressure increase while it's pion detection efficiency remained constant, until the pressure reached about 140 psig. The fall-off of the dashed line at 140 psig is due to the inefficiency of C1 in detecting pions for cone angles larger than 70 The pressure of C1 was therefore set at 180 psig for detecting 5 Gev/c kaons, where the detection efficiency was independent of pressure for kaons and very small for pions. C2 was set to detect only pions, and it was in anticoincidence with C1. C4 was a boiler vessel with three spherical mirrors to focus Cerenkov light on the photocathode of three 5 in. RCA-4522 photomultipliers. C4 was used onlyin tagging bit unite and not in the trigger. This was desirable since C4 was not as efficient as C2 and also about 7% of the kaons interacted in thle walls of C4. It

17 1600 1400 i ij ~203 ir i- ' vLeft Scale 1000 C lxKxKRxBPI m~ //"'t',' '10 BPI Fq E- 800 800x103I 600 r' 600x103 400 X 400x103 Right Scale 4 200C 1200x103, i PSIG Figure 6. The pressure curve for Cl Cerenkov counter at 5.0 Gev/c incident beam momentum.

18 will be shown in chapter 3 that the combination of C1, C2 and C4 Cerenkov counters gave a pion rejection of the order -6 of 106. There were three sets of scintillation counters, K1234=(K1, K2, K3, K4) at the entrance of the analyzing magnet, KM at the exit of the analyzing magnet and KR = (KR1, KR2, KR3) behind the last set of the spark chambers K4. This set of scintillation counters was used to detect produced particles and to suppress the triggers on the spurious particles which were coming from different directions. The coincidence, K = HODOS x Cl x C2, indicated thata kaon passed through the spectrometer. ( HODOS s K1234 x KM x KR.) The coincidence between K and BPI formed the EVENT signal, EVENT = BPI x K. A buffer system ( to be explained in detail later ) conveyed information from different elements of the experiment to the computer. The EVENT signal triggered the spark chambers and prepared the buffer for a new event. The event signal was set in coincidence with P1, P2, Cl, C2, C4, K1, K2, K3 and K4 counters and the computer was told which one of these signals was present when the EVENT was formed. Some of these counters such as P1, P2 and C4 were only in tag bits and not in the trigger. A dead-time of 40 miliseconds was provided by an EVENT GATE module after each evenlt. During thli. time the ions in the spark chambner were cleared and thle thuffer system had accepted

19 all the data and these data were transferredto the computer. Every ten ZGS pulses, the computer pulse was used to change the trigger requirement (by changing the Cerenkov counter requirement) to select beam pions going through the spectrometer. During the time of this ZGS pulse, scalers were gated off and the wire spark chambers were triggered on the incident beam. These"Mode pulse events" were used to check the magnetic fields of the magnets as well as the apparatus survey. The angular resolution of the spectrometer and the beam momentum and beam mom'entum resolution were determined from the data accumulated during the mode pulse. This data was also used later to find the wire spark chamber efficiency. C. The Spark Chambers: In this section the wire spark chambers are explained in detail and their superiority to optical spark chambers for this experiment is discussed. A spark chamber consists of two parallel conducting plates, which are connected to a high voltage pulser. The high voltage is turned on after the charged particle has passed through the plates. The charged particle creates positive and negative (electrons) ion pairs and high voltage accelerates these ions. The collision of these ions with the molecules creates many more ions, which causes the spark break-down between the plates. For optical spark chambers, cameras take pictures of this spark for later

20 analysis. The wire spark chamber15-1 s the natural descendantof the usual parallel plate spark chamber. The major difference is the method of extracting the information. In order to make the spark discharge immediately available for processing, the conducting planes are replaced by a layer of parallel wires, typically 0.1 milimeter in diameter and spaced 1. milimeter apart. The discharge current flows through the wire. This current may be detected and used to find which wires have been struck by the spark and thus where the particle has passed through the chamber. The virtue of using the wire spark chambers in this experiment are; a) they can be triggered on events which have been preselected by a scintillation and Cerenkov counter system; b) they can be connected to an on-line computer, which does a major part of the analysis while the experiment is in progress, where optical spark chambers can not be connected on line to a computer; c) they measure the trajectories accurately. Five sets of spark chambers were used in this experiment. Each set consisted of four gaps. The sizes of the chambers were from 19 in. x 11 in. to 80 in x 32 in. Figure 7 illustrates the different layers of materials from which a single gap chamber was constructed. There were 30 wires per inch, which were bonded to a mylar film of.002 in. thlickless. A 3/8 In. glass epoxyed laminate spacer

21 ACLAR GAS WINDOW Spacer Ground S tr ap, Ai luminum Strap,,~,a 'Acking Mylar - Backing 'Y' Wires. ---.. ',. * * * * * * * * * * * * * * * * * Copper Tape Y, w -ITeflon Tube 'X' Wires* MH.Y.,- - -. -1Ma'gnerostricrive Strap Wire ACLAR GAS WINDOW WI.V. PULSER Aluminum Backing W. v S rr7 H V. PULSER — 'y' Wires 'Y' ur-pu Damping lad // X / X //////' ~, Ground Strap ~~~Fidu~cial. /~~,Pick-up Coil Points "~ M,Preamplifier,agnerostricrive Wire 'X' out-put Figure 7. The details of the physical construction of a single gap wire spark chamber.

22 separated the two planes of mutually perpendicular wires. A continuous sheet of aluminum was bonded to the other side of the mylar sheet. The aluminum sheet and layer of wires, which are separated by the mylar, form a capacitor. The high voltage was applied to the aluminum sheet and by inductance the high voltage was transferred to the wires quickly and uniformly everywhere. A 1/8 in. spacer with an aclar window was epoxyed to the chamber. The gas, which was a 10% helium and 90% neon mixture, filled the space between the two layers of wires and between the aclar window and the aluminum sheet at a pressure slightly higher than atmospheric pressure. 19 A magnetostrictive ribbon, Remender,was magnetized and placed close to and perpendicular to the chamber wires. The discharge current pulse caused a sonic wave in the magnetostrictive ribbon7. This wave propagated with the velocity of sound( 5 milimeters/microseconds ) in the ribbonto the both ends, where it was damped by clamping the ribbon between rubber pads. At one end of the ribbon a small pick-up coil was located which was connected to a preamplifier. When the sonic wave arrived in the pick-up coil, it induced a voltage in the coil which was of a few tens of milivolts in amplitude. Two fiducial wires were placed across the ribbon, one between the pick-up coil and the wires and one beyond the wires. The fiducials for horizontal and vertical wire planes were connected

23 in series. The fiducial wire was pulsed at the same time as the wires of the chambers; these fiducial wires also generated sonic pulses. The pulses from fiducials and spark discharges arrived at different times at the pickup coil. Those time differences were proportional to the differences in distance between fiducial marks and sparkstruck chamber wires. The spark positions were determined by measuring the delay time of the sonic pulses caused by the 'sparkdischarge relative to the same pulses from the fiducials. A narrow gap chamber requires a current of about 1000 amperes and a potential of several thousand volts and the rise time of the high voltage pulse must be short. A fast rise time is needed to prevent the high voltage pulse from acting as a clearing field, during the rise time, and sweeping away primary ions ( caused by the traverse of the charged particle through the gas)before spark discharge develops. Hydrogen thyratron tubes were used to construct a high voltage pulser for these chambers. The schematic diagrams of the high voltage pulser, with a brief discription, are given in Appendix II. D. The On-line Computer: One of the great advantages of a wire spark chamber, as mentioned before, is the feasibility of being connected to an on-line computer. The outputs of the individual chamber were transferred to the computer through the buffer

24 system. The on-line computer used in this experiment was an EMR ( Electro-Mechanical Research, Inc. ) 6050. The size of the memory was 16K words, each word being 24 binary bits. Figure 8 shows the different input-output devices such as data buffer, teletype, oscilloscope etc. which were communicating with the computer. Any input has to be digitized and transferred to the computer sequentially. For this reason a data buffer was used to digitize the analog output of the magnetostrictive read-outs of the spark chambers. A 20 megacycle clock was used to digitize the analog outputs. The buffer accepted the data, digitized and stored the signals from 32 spark chamber read-outs as well as from scintillation and Cerenkov counters and then sent these signals to the computer. The data from the magnetostrictive lines were accepted in parallel by the buffer, but were transmitted serially to the computer. The buffer system used was the MIDAS ( Multiple Input Data Acquisition System ) from Science Accessories Corp. There were two SAC units ( Enenekontakaihex Scaler Model 1124 ) which received the signal from 32 magnetostrictive read-outs. One of these SAC units had 96 scalers and the other had 32 scalers. There were four scalers reserved for each magnetostrictive read-out. These four scalers allowed for a maximum of three sparks and one rear fiducial.

ZGS COUNTERS _ ITELETYPE SCOPE PROGRAM MODE INTERRUPTS TAPE FAST PUNCH LOGIC TAPE ____i~~~~~~~ ~READER TAG EMR 6050 BITS EVENT CARD TRGER READE1COMPUTER __CARD 16 K 24 BITS R INTERRUPT v~~~~~~~~~~~~~~~~, ~TAPE I SAC DATA o,, IBUFFER 169 WORDS T PULSE MAO C~IW~~~~ a~~~~~,, ~~~TAPE LINE PRINTER 1 Figure 8. The flow chart of the different input-output devices to the computer.

26 The EVENT signal, in the fast logic, was set in coincidence with individual counters, K1, K2, K3, K4L, C1, C2, C4, P1 and P2. The outputs of these coincidences were sent to the SAC buffer ( model 1105 Gated Tagging ) and then to the computer. In this way when the EVENT was formed, it could be found which of the above counters had pulsed. A Multiplexer ( SAC Model 1118 ) was connected to the Differential Voltmeter (DVM) output for magnet current and also to the Analog to Digital Converter (ADC) for transferring pulse height information on C1 and C2 Cerenkov counters to the computer. When the EVENT GATE module, in the fast logic, received the event signal, it turned off the fast logic gates for 40 milliseconds and no data, was accepted during this period of time. The EVENT GATE sent a signal to the buffer and a signal to the high voltage pulser to pulse the spark chambers. The arrival of an EVENT signal from fast logic to the buffer caused the scalers to reset to zero and to clamp there for 15 microseconds. The reason for this dead time is that when the chambers are pulsed, there will be an electromagnetic noise broadcast, which can be picked up by the pick-up coil and be mistaken as a fiducial or spark pulse. When this clamp was lifted, the scalers stayed at zero until the fi rst pulse from the chamber reached the blaffer. The first pulse, which was assumed to be from the

27 first fiducial, started all four scalers reserved for that magnetostrictlve line. The computer program checked the last spark to see if it was close to the expected rear fiducial position; if it was not, the computer used the rear fiducial position from the previous set of sparks. The successive sparks locked the successive scalers. These scalers generated a binary number corresponding to the position of the spark. The content of these scalers were read by the master control unit of the buffer (SAC Model 1204) and transmitted to the computer. When the computer had received all the data during the spill time, it first sent these data to the magnetic tape for future off-line analysis and then started the calculation. Along with the calculation, it sent the results to the display oscilloscope. The display oscilloscope was very essential for diagnostic purposes. It displayed various histograms, such as missing mass, four momentum transfer distribution of the cross section, etc. It also displayed a computer simulation of the tracks through the chamber. These histograms and the computer simulation were helpfull for understanding how the different parts of the equipment were functioning and what results the experiment was producing. A test pulse was provided for testing the buffer and the on-line computer communication. The computer, after receiving a signal from the ZGS, sent a pulse to the buffer

28 through a Test Generator (Model 1110). The Test Generator sent a sequence of signals, resembling the signals from the chambers, to the buffer. These signals were sent to the computer by the buffer in the same way that event data were produced. Later, the computer checked this test pulse to find out whether the buffer had responded properly to the test pulse. This was a check of the communication line between the buffer and the computer. The buffer and the computer started accepting data after the test pulse, during the 500 milliseconds of the ZGS spill time. The test event took about one millisecond.

III. DATA ANALYSIS A number of steps are required to derive final differential cross sections from the spark coordinates stored in the computer. The major steps will be outlined here and then discussed in detail in the various subsections of this chapter. The first step in the analysis consists of assembling the sparks in each chamber into tracks if possible, and if not possible, in rejecting that set of sparks as an event candidate. This procedure and corrections introduced by it are discussed in section A. The tracks from the first step are then connected up to form possible orbits for the spectrometer particle and the beam particle. At this point,a number of geometric and kinematic criteria (cuts) are imposed on good events. We discuss the cuts and corrections required by them in section B. Section B also describes the calculation of kinemetic quantities such as kaon production angle and momentum from the orbit information. The analysis described so far is done event by event on line by the computer. At the end of each run the computer printed out histograms in missing mass, four momentum transfer and in other variables of interest. The final step in the analysis consisted in applying corrections for geometrical acceptance and various nuclear 29

30 absorption and decay effects to the raw computer histogram. These corrections and the calculations of the differential cross section are described in sections C through F. A. Track Reconstruction and Spark Chamber Efficiency: There were four sets of spark chambers ( each set consisted of four gaps ) in the spectrometer and one set in the incident beam-line. These chambers did not always form detectable sparks for the desired charged particles which went through the system. There were some occasions when there were spurious spark tracks. These spurious sparks took the discharge energy of a good track, sometimes they reduced the amplitude of the magnetostrictive readout to below the threshold of the buffer and therefore that good track was either completely lost or there were two adjacent tracks, which confused the filter program. To define the trajectory, there was required the presence of tracks in each of the four horizontal views ( K1, K2, K3,K4 ), two vertical views ( K1 and K4 ) and tracks in the horizontal and vertical views of the beam chambers. A good unique track has only three or four detectable sparks in a set, that can be fit to a straight line within a given accuracy. If a set had a good track ( 3 or 4 sparks ), the program fitted a straight line to these sparks and compared the measured position of each spark relative to the expected position. The distance

31 between measured and expected position must be within a given accuracy. The horizontal view efficiency of one set was found by finding the probability that the corresponding set had a good unique track while at least two other sets also had a good unique track (this included two spark tracks too). The horizontal view efficiency varied from 96% to 99% for all the chambers and it was fairly constant over the range of -t acceptance. The Mode pulse, which was explained previously, was used to find the spark chamber efficiency;since most of the mode pulse events contained single non-interacting tracks going straight through the chamber, the determination of this efficiency was relatively easy. The two chambers K1 and K4 determined the vertical position of the trajectory as well as the horizontal position. The vertical view efficiency of each set was determined by finding the number of times that it had a good unique track while all the horizontal views ha-d a good track. The vertical view efficiency was from 97% to 99%. Beam chamber efficiency was found by asking the number of times that each view, horizontal or vertical, had a good track while the spectrometer chambers had a good trajectory. The beam chamber efficiency was from 94% to 97%. The overall efficiency of five sets of chambers were the products of the efficiency of each set. The final chamber efficiency correction applied to the cross section was 80% for 5 Gev/c and 85% for 3 and 7 Gev/c incident beam momentum.

32 B. Event Reconstruction and Cut Requirements: The major background in this experiment was from particles produced in the C1 Cerenkov counter or upstream of the hydrogen target. In order to reduce this background, it was required that the kaon had originated in the liquid hydrogen target. The computer program chose a center value for every good track in every set of chambers. The center values of K1 and K2 sets formed a. line indicating the particle trajectory entering the momentum analyzing magnet (BM-109) and the center values of K3 and K4 formed a line indicating the particle leaving the bending magnet. These two lines are expected for kinematic reasons to intersect at the center of the magnet. A good event was required to have tracks intersecting within +.5 in. Figure 9 shows the distribution of the separation between the incoming and outgoing trajectories through the magnet at the center of the bending magnet. The magnet cut rejection was negligible. The momentum of the spectrometer particle was found from; f0.d eP = d1313.2(sine1 + sine f) (10) where 0i and ef are the plan view angles that incoming and outgoing particle trajectories make with the longitudinal axis of the bending magnet. ~B.dl is the magnetic field integral of the magnet. The momentum resolution of the spectrometer, which is due to measurement error in ei and e was found to be +3/4%. The momentum resolution of the incident pion beam was found to be.63%. Therefore, the total momentum resolution of the system was.98%.

5600 4800 4000, 3200 'u 2400 1600 800 - -30 _20 -.10 0.10.20.30 X in. Figure 9. The distribution of the separation between the incoming and outgoing trajectories through the magnet.

34 The missing mass of every event was calculated from equation 9 after the event was momentum analyzed. The mass resolution of the spectrometer was found to be 40 Mev. The missing mass of KE candidates were required to be within the mass limit; Mass ( 1 +.195 ). This mass limit was three times of the RMS of the mass resolution of the spectrometer for the E peak. There were practically no events outside the mass cuts for Z events after target out subtraction. Figure 10 shows the missing mass plot after target out subtraction at 5 Gev/c. The particle trajectory was traced back to the hydrogen target and the production point of the particle was calculated. In order to reduce background from out of target production, the X and Y coordinates of the production point were required to be within + 1.2 in. and the Z-coordinate within the + 24 in. of the center of the target. Multiple coulomb scattering in C1 and C2 Cerenkov counters caused a displacement of the production point, in tracing back the trajectory to the hydrogen target, by.12 in. (one standard of deviation). The cuts of + 1.2 in. in both X and Y directions were ten times larger than the coulomb scattering effect. Therefore there were practically no true events outside of the cuts. Figure 11 shows the X distribution of the events before and after Y cut requirement. The effect of the Y cut in eliminating out of target background is clear.

35 840 720 600 480 360 240 120p \ t Y*(1385) 6. 85 1.1 1.35 1.60 1.85 2.10.6.85 1.1 1.35 1.60 1.85 2.10 MM2 ((ev/c2) Figure 10. The missing mass plot for the Z and the Y* production after target out subtraction.

EVENTS -., C::) 0 0: I-J C) ~~~~~~~0 ~C) C7 C~~~~~~~~~~nC Y, CIJ~~~~~~~~~~~~~DC ct — C~~D P-,(C O (q X ~ ~ ~ ~~~~K' XX '.... c+ Xx c~ c+ (D Ct. Omn C C:) - u ~ ct c - o- 0 ~.X" ct-~~~ X (DDC (D C C c+ ~ - c~ r i3 iD vl~I.~ct o~~~E

37 The target cut requirement eliminated most of the background due to Cl and sources upstream of the H2 target. Th)e target empty runs indicated that about 40% of the events in the zero degree production bin were not produced in the hydrogen target. The target cut requirement could not eliminate these zero degree background events because the Z coordinate of the event origin could not be determined for these events. There were from O. to 10% target out events at larger angles. The residual background mentioned above was eliminated by subtracting the events from target empty runs. Figure 12 shows the missing mass spectrum without target out subtraction and Figure 10 shows the same missing mass spectrum after the target out subtraction. The computer printed out several histograms of events at the end of each run. One of these was the squared four momentum transfer distribution of the desired reaction after fulfilling all the cut requirements. This histogram was used to calculate the cross section for the E production. In order to subtract the background, in the case of Y production, it was convenient to use the-missing mass histograms for a variety of angular ranges. Y* events were divided into five angular ranges O.-1.4, 1.4-2.1, 2.1-2.8, 2.8-3.5 and 3.5-4.2 degrees. Figure 13 shows the missing mass plots in the above angular ranges. It is clear that the Y* peak sits on a large background at smaller angles. The Y* peak increases and the background decreases at larger angles. To find the number of

38 1000 750 $ 500 '' x10 \, Figure 12. The mIssing mass plot for the and the Y I It: I,t 1,I,.6.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 MM2 (GeV/cZ)2 Figure 12. The missing mass plot for the 2 and the *

39 10 3.5 ~- 4'20 5- - 0 15 -I 2.8 o- 3.5 10 - 5 -15 2.1 o2. 10 35 -O'- 1.4" 30 5 -'0 5.6 1.8 2.0 2.2 2.4 2.6 MM 2(GeV/c2) 2

40 events in the above angular ranges, a mass distribution consisting of a Gaussian with a fixed width and center and a superimposed straight line was fitted to the events in each angular range. The width of the Y Gaussian was calculated from the Y* resonance width folded by the mass resolution of the spectrometer. The smooth curves in Figure 13 represent the fit and the histograms represent the data. C. Solid Angle Acceptance of the Spectrometer: Figure 14 shows an end view of the down stream end of the analyzing magnet as was seen by a particle leaving the H2 target. Consider particles that left the target with polar angles between 0 and 0 + d0. These particles could have any azimuthal angle, but only those particles which passed through the solid shaded section of the annular region between e and 0 + de would have been accepted by the spectrometer (Figure 14). Therefore, only the fraction a/27r of particles with production angle e was accepted. The spark tracks of the good events had to be within the fiducial line boundaries which was set on the last spark chamber. These fiducial boundaries were determined from the dimensions of the analyzing magnet aperture. The squared four momentum transfer, -t, is related only to the polar angle 0 and not azimuthal angle cp. By knowing the number of particles accepted between e and 0 + dO, it is easy to calculate the number of particles which are accepted with

41:"Bne e +d. c BJ eam 4i Figure 14. An end view of the down stream end of the analyzing magnet as was seen by a particle leaving the H2 target.

42 -t between -t and -t + d (-t). A Monte Carlo calculation was performed to find the angular acceptance of the spectrometer. Some additional factors, aside from the fiducial boundaries, which were considered in this program were the angular, position and momentum distribution of the incident beam and also the multiple coulomb scattering. The angular and position distribution of the incident beam were found by using the information from the beam chamber. The horizontal and vertical angular distribution of beam particles were consistant with Gaussians having RMS angles of 3.4 and 5.3 miliradians. The position distributions were also (consistent with Gaussians having RMS distances of.28 and.22 in. in X and Y planes. The distribution of the beam density was considered to be uniform along the 24 in. hydrogen target for the purposes of the acceptance calculation. The momentum distribution of the beam was consistant with Gaussianshaving RMS of.63%. The multiple coulomb scattering in the hydrogen target and the two Cerenkov counters C1 and C2 were also considered in determining this angular acceptance. Figure 15 shows the acceptance of the spectrometer as a function of the squared of the four momentum transfer for 5 Gev/c incident momenta. D. The Incident Beam Correction: The incident pion beam had a contamination of muons

43 1.00.80.60.40.20_:10.08.06 -.05.015.045.075.105.135.165 -t (Gev/c)2 Figure 15. The four momentum transfer acceptance for 5. Gev/c.

44 and positrons. This contamination was taken to be 3%.20 The last pion Cerenkov counter in the beam, CPI2, was at a distance of 80 in. from center of the target. A correction was made for the decay of pions in this distance. In the case of the target empty data, the distance from CPI2 to the center of C1 Cerenkov counter was considered for the decay of pion beam since the effective target was C1. Table 2 shows the summary of all the major corrections which was, applied to the data. For calculating the absorbtion of pions and kaons in the target, it was assumed that on the average a pion travels half the length (12 in.) of the hydrogen target and produces the kaons and the kaons travel the second half. The same assumption was made in the case of the target out data except that C1 was considered as the target. E. Nuclear Interaction and Decay Corrections of Kaons: The produced kaons interacted in the hydrogen target, Cerenkov counters, scintillation counters, air and wire spark chambers. The major interactions were in the C1 Cerenkov counter and the target. The number of good beam pions and kaons eliminated by a material can be readily calculated once the nuclear cross section for that material is known. The wood-Saxon potential was used to calculate the total cross section for various nuclei ( Appendix III ). The results of this model were in good agreement with experimental data on the total cross sections of pions on various nuclei.

45 Tab le II The summary of the corrections applied to the data Nature of theion 3. Gev/c 5. Gev/c 7. Gev/c correction Muon and positron contamination 3% 3 3 Decay of pions bectween CPI2 and 1.2%(2.3%).73%(1.3%) 52%(.98%) H target (C1) Absorption of pion(kaon) in 12in. 3.51%(2.21 %) 3.51%(2.21% 3.51(2.21 Of H target Absorption of pion(kaon) in | 5.85%(3.83%) 4.05%(2.71% 2.75%(1.95$) half length of C1 Absorption of kaon in the ma terials of the 13.91% 11.49% 9.77% spec trometer Decay of ka~on |34.81% 21.57% 15.63% Spark chamber efficiency 80% 85% 85% Nuc lear interaction in C4 6.o90 6.68% 5.67% Target out subtraction near 0. degree, 40% 40% 0% at larger angles 0.-10% 0. -10% p.-10%

46 A correction was also necessary for those events for which the kaon was misidentified by C4. The C4 Cerenkov counter was only in tag bits, counting only pions, as explained previously. The walls of C4 were made of 3/8 in. steel. The kaons produced at the hydrogen target, which satisfied the trigger condition, can interact in the walls of C4 and produce particles which might be counted in C4. Because C4 was set to detect pions, the computer program rejected the events for which the C4 tag bit was present, but it saved these events in a missing mass histogram. By using the number of Z events in this missing mass histogram and the number of Z events in the missing mass plot 12, it was found that about 7% of the time the kaon interacted in the walls of C4 and was counted as a pion. There was a distance of about 330 in. from the center of the target to the last hodoscopes KR for the kaon to travel and fire the trigger system. A correction for the decay of the kaons in this distance was applied to the data. The corrections for the absorption and decay were applied separately to the target full and target empty events. It was assumed that most of the target empty events result from interaction of beam particles in the C1 Cerenkov Counter. Therefore the geometry of these counters was used in calculating the corrections.

47 F. The Differential Cross-Section: The differential cross section was calculated from; d_ ne dt nb x nt x dt( corrections ) where ne is the number of events in an interval dt, nb is the number of beam pion entering the hydrogen target and nt is the number of protons per centimeter squared in 24 in. long target. The cross sections for the reactions rrp4E and pp-KY (1385) are summarized in the table III. Figure 16 shows the 't distribution of the cross section for the reaction rrp4KE and figure 17 shows the -t distribution of the cross section for the reaction uTp4KY from this experiment together with results from a previous experiment at larger angles.1013 The error bars are statistical only. The possible systematic errors are less than 10%.

TT + p K+ ++ rr K + Y(1385 3.0 Gev/c, 5.0 Gev/c 7.0 Gev/c 5.0 Gev/c - dac/dt -t da/dt - da/dt -t d/t/d t.0291 685~34 i.0246 405~17.030 229+12 1.0365 7.9+5.5.0331 672+40!.0446 31218.070 153~11.0515 10.7*6.4.0381 619+33 1.0646 305~20.110 112+10.0720 28.8~6.6.0o441 543+38!.o846 220+20.150 67~8.0990 27.0+6.5.0511 486+32. 1046 183~18 1.1320 24.7~5.7.1246 170~18 1 A=713.4~+23.5 A411.7~12.2 A=274.9~8.6 b=14.68+.92 lb=9.37+0.16 b=9.01+.21 Table III. da/dt in b (Gev/c)-2 for reactions (5) and (6) and best fits to the do/dt=A*exp [b*(t-tmin)]

49 1000 1 ' 4:.. (713.4* 23.5)e (14'88's92)(t'tM.,) (399.2-14.0)e (6.06-.20)(t-tMN) 1000 o 33. Gev/c (9.37~0J6.l6t-t, Ot ~ (411.712.2) e(937-6)(t-t) -1000 5. GeV/c 100F~ \ (274.9~8.6)e(9.l_.21)(t tM~.) \u. ~7. GeV/c...... THIS EXPERIMENT..... PRUSS eta l 10 ___- I,..,,,,, I', 0.1.2.3.4 -t (GeV/c)2 Figure 16. The differential cross sectuon for the reaction rr+ p * K +,.

50 100 i { +.....THIS EXPERIMENT......YING etal 0.1.2.3.4.5.6.7.8 -t (GeV/c)2 Figure 17. The differential cross section for the 4~ + Y*( 1385). reaction u + p -* K + Y (1385).

IV.. DISCUSSION OF THE RESULTS The discussion will be divided into four major parts. A) We compare our results with the other cross section measurements on the reactions rn + p 4 K + E and n + p 4 + * K + Y for the purpose of testing the relative normalization of the different measurements. B) We survey the general features of our data on KE production and compare the data with the Regge pole model. C) We compare our results on the + + * reaction IT + p 4 K + Y with other measurements on this reaction and survey the general features of this reaction. D) We discuss quantitatively the helicity flip and helicity non-flip amplitudes for the above reactions in the final section. A. Consistency of This Experiment With Other Experiments: Figures 16 and 17 show the consistency of this experiment 10'13 with a previous experiment on the same reactions which was done at larger angles. The agreement between these experiments at 5 and 7 Gev/c, in the region for which the data overlaps, is excellent. The data, of this experiment and the larger angle datal~ were therefore used together to find the slope and amplitude of the cross section as a, function of -t. The two sets of data were also used together for comparison with theoretical models and for comparison with measurements of this reaction by other groups. The Stony 12 Brook group has measured the differential cross section for the reactions (5) and (6) for energies from 51

52 500 400 #I eTHIS EXPERIMENt aPRUSS et-al 300_ f + STONY BROOK " 100 80 60 40 4 20.O05 ~21.2 5 3 -t (Gev/c)2 Figure 18. The comparison of this experiment on KC production at 5 Gev/c with others.

5.3 3.5 to 14. Gev/c. Figure 18 shows the results of this experiment at 5 Gev/c incident momenta, compared with the Stony Brook data at the same energy. The error bars in Figure 18 are statistical only. They also estimate 20% systematic errors. These two experiments agree within statistical and systematic errors. B. Differential Cross Section forrr + p 4 K + E: Figure 16 shows that the differential cross section for the reaction (5) at 5 and 7 Gev/c incident momenta, rises exponentially as t - tmin with slopes 9.37 and -2 10 9.01 (Gev/c)2, consistent with the previous experiment.10 We observed no evidence for a forward dip and conclude as is explained in section D that there is no strong spin flip contribution to the differential cross section for this reaction. The cross section for the reaction (5) at 3.0 Gev/c falls off more rapidly from tmin to t -.1 (Gev/c)2 than at larger angles (Figure 16). It is possible that there is an s-channel effect interferring with t-channel exchange forces thereby giving a rapid rise to the cross section. The total energy in the center-of-mass system at 3 Gev/c is 2.56 Gev. There are several resonances near this energy, such as A(2420) and A(2850), which may decay into KE and contribute to the cross section. To investigate the possibility of such a interference, the Breit Wigner terms due to the resonance (m=2420,JP=(11/2)+)

54 were added to the t-channel amplitudes and the resulting expression for the cross section was fitted to the data. The cross section will be: 2122 2 2 +f ~ ~s + gj+_ dt |ifs++ + f ++l + Ig+ g whe re ++ K2, +1 (t + 1) ae+, + 1/2 o (Q) ft = a e(b/2)t lCp 1 ++ e 5 1 4 rr g-+ = K/ 2-t+l /' ( +1 ) a t,) + 1/2 (n) t -_ c / t e(d/2)t ic 2 g+- e and m as,, +1/2 2 m -s-irm 1 Where m = 2420 Mev, Fe = 34.1 Mev, r 310 Mev and Ir is not known. f++ and g+_ are the scattering spin flip and spin nonflip amplitudes. 1pl and cp2 are the phases between f++ and s amplitudes and their corresponding Regge pole amplitudes, t t f++ and g+_ (The details of the calculations and the definition of some of the parameters are given in Appendix I.) The solid line in Figure 19 shows the results of the least square fitting program. 2 (Chi-squared) was 22 for 7 degrees of freedom. One can note in Figure 19 that the very forward data points are al:.l. hiher than the solid line nmaking the fit a poor one. The spin:f lip and spin non-flip amplitudes and the slopes obtained from this fit were unrealistic in comparison to the corresponding

800 600 3.0 GeV/c If K+ + 4...THIS EXPERIMENT 0..PRUSS et al oc =22.16 for 7 degrees of freedom 200 4'0' 6-o '100 80 60 40 - 0.05.10.15.20.25.30.35.40 -t (GeV/c) 2 Figure 19. The results of the least square fitting program.

56 amplitudes and slopes at higher energies. It is apparent therefore that the simple Regge amplitude plus this Breit Wigner term will not explain this phenomena. It is possible that the resonances with higher spins might fit better to the data, but there is no direct evidence that such resonances exist. We will next compare the data, with the Regge pole theory. The Regge pole theory has been used more extensively to explain high energy collisions of strongly interacting 4523 particles than any of the other theoretical models. One of the several Regge pole models for hypercharge exchange reactions is the double Regge pole exchange of Reeder and Sarma. 2425 This model is expected to be applicable to the forward direction. In this model the exchanges of K`-(890) and K**(1420) trajectories are assumed for reaction (5). They assume exchange non-degeneracy because the SU(3) symmetry is broken, i.e., the masses in a given multiplet are not degenerate. K* and K** trajectories are obtained from p and A2 trajectories by taking into account the SU(3) breaking. There are fourteen parameters in their model to be found from experimental data. These parameters are four residue constants, four energy scale factors, one 'cross over' factor and five parameters to define the K* and K** trajectories. Figure 20, 21 and 22 show the results of the Reeder and Sarma, model compared with the data of this experiment. As is shown in Figure 21 and 22, there is a good agreement between this model and experimental data at 5 and 7 Gev/c, but there

57 1000 800_P, 1\ 3.0 Gev/c * + + rr p K1 600 -.. THIS EXPERIMENT A...PRUSS et al -... REEDER & SARMA REGGE MODEL PREDICTION 400_ 200oo 100 80_ 60 40 I I I I.O.05..S.2.25.3 -t(Gev/c)2 Figure 20. The comparison of the rrp4KE cross section data with the Regge pole model

58 500 5.0 Gev/c T\+P t K+~ *... THIS EXPERIMENT a... PRUSS et al -... REEDER & SARMA I200 \REGGE MODEL PREDICTION b 50 20 I I, 0.05.10.15.20.25.30.35 -t (GeV/c) 2 Figure 21. The comparison of the nrrp-KE cross section data with the Regge pole model.

59 300, '-~ ~~~~7.0 GeV/c... THIS EXPERIMENT A... PRUSS et al - -... REEDER & SARMA REGGE MODEL PREDICTION 100 ' 80 60 40 20 \ 10 0.05.10.15.20.25.30.35 -t (Gev/c)2 Figure 22. The comparison of the Tp-*KE cross section data with the Regge pole model.

6o is large disagreement at 3 Gev/c. It should be mentioned that this model also has some limitations not apparent from Figures 20 through 22. The model wildly disagrees with experimental data for -t > 1.5 (Gev/c)2. C. Differential Cross Section for + + p * K+ + Y (1385): We also studied the reaction n + p + K + Y for which the exchanged trajectories in the t-channel are also K and K. But in this reaction the produced baryon, Y, belongs to the SU(3) decuplet while the Z in the reaction (5) belongs to the SU(3) octet. Figure 17 shows the results of this experiment on the + + * reaction iT + p 4 K + Y together with the previous measurements at larger angles.13 There is a good agreement between these two experiments. The remarkable feature of the reaction (6) is the turnover of the cross section in the forward direction, which is not seen in the reaction (5). Although the exchanged trajectories for both these reactions are the same, the amplitudes, slopes and the form of the cross sections are different. This turnover in the forward direction indicates that the cross section for the reaction (6) is strongly dominated by the spin flip amplitudes. The differential cross section measured for the reaction (6) at 3.726 and 8 Gev/c27 by other groups also show a

C61 turnover near t t tmin. Figuire 23 shows the results of this experiment compared to others. The turnover near zero degrees can be understood by the Stodolsky-Sakurai "p-photon analogy " hypothesis. To understand this analogy intuitively, consider the electroproduction of a single pion via a virtual photon exchanged (Figure 24a): e- +p- e + p +- (13) The overall matrix element for the reaction (13) is proportional to the transition matrix element at the baryon vertex, i.e., for the process (Figure 24b). Y + P A3/2 4 p + T (14) A multipole expansion of the transition matrix element,29'30 at the baryon vertex, has shown that the process (14) is dominated by the magnetic moment (Ml) transition,2853 which goes to zero at zero degrees. The experimental angular distribution of the photoproduction reaction (14) is in excellent agreement with that expected for a pure Ml transition.32- 35 Stodolsky and Sakurai suggest that the following processes (Figure 29c) +r + p * A3/2(1236) + rr (15) K+ + p A 3/2(1236) + K~ (16), for which the exchanged particle is a p(m=765,JP=l-) meson, are similar to the electroproduction of a sigle pion. They assume that the transition matrix element for the process (Figure 24d)

62 50IT ' I I I I I 'I ' I 50 5' o... BUTLER et al. 3.7 GeV/c _ - l *... THIS EXP....... 5.0 GeV/c... YINGet al..... 5.05 GeV/c x... ADERIOLZ et al 8.0 GeV/c T+p -- K+Y*(1385) 10 T 6- - 81; i 3A 2-,,,I I I,I,, I I I 0.20.40.60.80 1.0 -t (Gev/c)2 Figure 23. Comparison of this experiment with others on Y

~sLuo-ionpoJd aeqos-a; qo, suemITp ueueam. a *t~ aqn5,-, ++ c Id + E+ d 4- (9F)++ V 4- d + d +d +!d. ( II) /' + +V id +fd (0) + (d) V1 o+ d + Z/~V v d(+ ) oa d ~ t d 0 +d+0 " -

64 pi + p * A +(1236) - p + of (17) is proportional to the transition matrix elements for the photoproduction reaction (14). Because of this " p-photon analogy " it is natural to assume that the reactions (15) and (16) also go predominately via the magnetic moment (Ml). The reactions (15) and (16) show a turnover near the forward 36,37 direction,36'37 which supports the idea of " p-photon analogy ". Using the SU(3) symmetry which groups (A++,Y) (u K) and (p,K ) into the same SU(3) multiplets,3842we may speculate that the following processes: + p K + Y (18) K + p rr + Y (19) also go predominately via magnetic transition (Ml). The 43,27 reaction (19) also shows a turnover near zero degree. A Regge pole analysis is done by Renninger and Sarma45'46 to explain the isobar productions, A(1236) and Y (1385), cross sections. The assumptions in this model are similar to the case of the EE production, which is explained in the previous section. To explain the turnover in the forward direction, they have chosen the structure of the Regge residues to reflect the dominance of the magnetic dipole (Ml) transition between the nucleon and the isobar. * Figure 25 shows the predictions of this model for the KY production at 6 Gev/c compared with the data of the StonyBrook at 6 Gev/c and the data of this experiment at 5. Gev/c.

100 10 a + r-I 1pTr p K Y1 (1385) Tr+p - K+Y' (1385).....5.0 GeV/c THIS EXPERIMENT A.....5.05 GeV/c YING et al +.....6.0 GeV/c STONY BROOK -....6.0 GeV/c RENNINGER & SARMA REGGE MODEL PREDICTION ~.1.I A,, I.. I. 0.2.4.6.8 -t (GeV/c)2 Figure 25. The comparison of the rrp4KY cross section data with the Regge pole model.

66 As is shown in the Figure 25, this model explains the form of the cross section but its normalization is higher than this experiment. D. Determination of the Helicity Flip and Non-Flip Amplitude: In previous sections we concluded that the turnover of the cross section for the reaction rp 4 KY* is due to the dominance of the helicity flip amplitudes over the helicity non-flip amplitude. We also stated that there is no strong helicity flip contribution to the reaction rr p 4 K Z. We fitted the cross sections for the reactions (5) and (6) to the following function to find the contribution of the helicity flip and non-flip amplitudes in the cross section. dt = Anfl2 + t'L IAfl2 eBt (20) where Anf represents helicity non-flip and Af represents helicity flip amplitudes, t' = t - tmin and M is the mass It 12 of the proton. In equation (20) the term 1 IAdfi2 which is due to the double helicity flip amplitude ( a change of two units of the helicity, T1/2. -3/2) for the Y* production was neglected because t' was small. The results of the least squared fitting are summarized in Table IV. For comparison the data for the charge exchange reaction79 r p 4 n&n was similarly fitted to the equation (20). We integrated the terms in equation (20) corresponding to the helicity flip and non-flip amplitudes over the interval -tmin -t ~.4 (Gev/c) for better understanding

T --- —--— `-Z I-. — f~ ______ _________I rr +p K +Z U+p K ~Y!rr p rr +fl 5.0 Gev/C 7.OGev/c 5.0 Gev/c 14.83 Gev/c Anf B20.3 + 0.3 6 3.03 + 0.75 21.4 + 1.5 A 4o. o 20.0 A 0 ~...+ —,;0..u7- 0.. 0.0 35.0 40.0 35.67 + 5.33 192 + 20.0 9.4+0.8 1073 7 J JO1 12.0 +6 Af/ 00.4+1.23 f '/An~ 0.0 1.72 2. - 2.49 11.77 + 3.4 8.97 + 1.12 o. o08 j.5f019 +008-0.0 05 4.8+2.8 1.8+0.5 Tfnf ait Table IV. The results of the best least squares fit to the equation 20.

68 of the contributions of these two amplitudes to the cross section. The integrated cross sections corresponding to the flip and non-flip terms are shown by af and anf in the Table IV. As is shown in Table IV the ratio of o f/ /nf is consistent with zero for KE data. at 5 and 7 Gev/c. However, this ratio for KY* data is 4.8 ~ 2.8 and for r'~n is 1.8 ~.5. Therefore, the cross section for KY* production is dominated by the helicity flip amplitudes while KE production is dominated by the helicity non-flip amplitude.

APPENDIX I INTERFERENCE BETWEEN THE T-CHANNEL AND THE S-CHANNEL RESONANCE. The very forward peak of the cross section for the reaction T p t K E, at 3 Gev/c incident momenta, made us suspect that there probably is an s-channel effect interfering with t-channel. The total center-of-mass energy for the reaction rrp 4 Kz at 3 Gev/c incident pion momenta is 2.56 Gev/c. There are several P 11 resonances such as A(m = 2420 J 2 ) and A(m = 2850 P + J? ) which might decay to KE and contribute to the cross section. The following shows how the s-channel effect was calculated for the resonance A(2420). The scattering spin-flip and spin non-flip amplitudes resulting from a phase shift analysis are, f(e) = *JT [(c + ) ++ 1), a, ] t (a ) g( e,-) = K 2 I + 1) at ja] Ym (5) where K is the center-of-mass momenta of the particles in the initial state, YC(r ) are the spherical harmonics and at, ) and at, j_ are the partial wave scattering amplitudes for jo = ~ f 1/2 respectively. From the conservation of parity for the transition rp 4 A(2420) we obtain C = 5 and 69

70 j = t + 1/2. Therefore:,f( 2+ (l + 1) a, + 1/2 Y+ - 2- 1, + 1), + 1/2 C, We have = 2~,+l' t - m!) m imo YM(0,cp) = i ~, I m P% (cos e) e where m m (cos O) (m 2 + m 2 P (cos ) (1-x2) d t (x 1) ~~2 %! dxC ( where x = cos. From azimuthal symmetry of the scattering we can write CD = 0. The spherical harmonic functions for t = 5, m = 0 and m = 1 are Y = *I+ L- (63 cos5 0 - 70 cos3 e + 15 cos e) Y = (315 cos e - 210 cos2 e + 15) sin ] Y(5 -

71 The partial wave amplitude ae, A + 1/2 is m at, m + 1/2 er m - s- imP where m = 2420 Mev, r = 34.1 Mev and r is the width of the e r A resonance which is not known. r is the sum of all possible ri s. The central mass momentum, K, of the particles in the initial state is [s - (m + mP )] [- (m - mp)2] K = P Therefore the cross section is: b 2 d -t icD If(e) + ae2 e d t I2 dt iCP + Ig(e,p) + 2m- e2 c 2 p where pl amd cp2 are the phases between the corresponding tand s-channel scattering amplitudes. There are seven free parameters a, b, cp1, c, d, co2 and Fr to be determined from a least square fitting of the above cross section to the measured cross section.

APPENDIX II. THE HIGH VOLTAGE PULSER A fast rise time high voltage pulser with thyratron tubes was designed by Dr. Dave Rust at Argonne National Laboratory. Figure26 shows the schematic diagram for the power supply of the thyratron and interlock unit to start the thyratron. The EVENT signal after being amplified from -.5 volts to -6 volts was sent to an avalanche driver; the schematic diagram of avalanche driver is shown in Figure 27. The output voltage of the avalanche driver at the points (1) and (2) were about 350 volts. The reason for having two circuits for avalanching rather than one is to make the delay time shorter. The outputs of the avalanche driver, points (1) and (2), were connected to a ferrite core ( Figure 28) which combined the voltages and the resultant voltage was about 750 volts. This voltage was applied to one of the grids of the thyratron and the other grid was at a potential of 150 volts. A high voltage of about 6 kilovolts was applied to the anode of the thyratron through a diode. This thyratron pulser had a 50 nanoseconds rise time and a repetition rate of 300/second. One hundred volts was applied constantlyon the chambers as a clearing field. 72

I* WPsrst5TCo 5ir-j.-ov K2 t/d -—.- 3 s i! 4 3 4 II 301 s w ~{ws-low -. w _ _ _..___ _ 1O ~p' T -|,oos i f F i [ A I! >v! 9 O A RX..m sore - Ti TSI ) 1TS IARD 0t-os _. PA. 2)',0.= maIPsaL O- BAIE1 RsM tP AT REA. Figure 26. Thyratron pulser power supply.

0 t D;E~ NX l0c ~~ I >2 1 40A3*.0ot. R, I 4( 3)4 -— F(z) o sSC 5-g3 r_ _BI A ' r e2 la n Yiv r L).J%;) ALL 6-SI~STOIS Aft VL V.4.JS U.0LL A CI~eC&.u ug; ~~ ~ ~ ~~~~~L a~~~_) -r,4 Le.srOS OF THE T -9,219 *~ e~C.A( $SCOULD So~Sfoy.o -Ma tooV. ig.re 27. Avalanche driver.

$oESG' 22)I IOTT.VIt _... TAS ( 22w Uir; e-'~O t '1 0 ~~~~~~~~~~~~~~~~~t0 11'; 22 sow TUIL -'ro-"(D 1~~~~~~~~~~~~~~~~L. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~. S u b~~~~~~~V 4A C* F5~~~~~~~~~-Aar COa PYYC"4 C)? I 's~ i - 'q ' ~ r~ ~ ~C(1 )P~C ~ZI, )CP $ ~~ ~ ~ ~ ~ ~O i~ ot v I " '' v=. >~~~~~~~ (.eIxU -[ ---___.__.. 0 PI__ 150 ft~~~~~~~~~~~~~rc~~~~~~~~~~~~u~~~~cmur WLL I ALY.1I L~~ I WLANI H~~' '' / iSA**6S-TAajJA#A %C-W)OO IC Kv. DroDE A,r F- -t(-* TskiS C~Pwovt \L %swimAL t sCITM/'.~ - Figure 28. Thyratron power circuit. A~ 3o2A t65 \P~RI~OC)Figure 28. Thyratron power circuit. k"%I tA. iS- (%%EL

AF ~.-,''.DIX..: I NUCLEAR -..?ERACTION CORRECTION The rn;Aclear in-i r.a&ction correction depends on the total cross section aT. There are no measured cross sections (aT) of elementary particles on most of the nuclei that the material in our spectrometer consisted of. The only experimental data which exists on the aT for various nuclei are for pions and protons on a small number of nuclei 4649; cross sections for kaon on nuclei are almost non-existeant. However, there is extensive experimental information on the total cross section, -4,21 + _+ a, for i-, K-, p and p on protons The cross section, a, can be used to evaluate the total cross section on various nuclei by employing a theoretical model (an optical model). In the following, we give a, brief survey of the theoretical calculation and then use two models, uniform density and Wood-Saxon, to calculate the cross sections for various nuclei. We tested the validity of these models by comparing the results obtained from these calculations with the existing experimental data on the total cross section for pions and protons on various nuclei. At the end of this appendix we present a table of cross sections, based on these two models, for various nuclei. The scattering amplitude from a phase shift analysis is c0 f(e) = ) (2t + 1) ajPt (cos e) (III.1) 76

77 if spins of the particles are ignored. The partial wave scattering amplitudes, a,,,, in terms of the phase shifts are 2i(6, + i X,/2)_1 e = 2iK (111.2) where K is the center-of-mass momenta of the particles in the initial states. X /2 is the imaginary part of the phase shift which leads to the absorption and 6$ is the real part. 14 One calculates the integrated cross sections to be a(2 S+ 1) [1 - cos 26 e (III.3a) "Tota.1= T 2. L aabsorption = a = 2 / (2 + 1) [1 - e gelastic =o = K z ) (2 t+ 1) 1 - 2 cos 26 e + e K It (III. 3c) Let $ = bK where b is the impact parameter. For high energy scattering very large values of S can contribute to the cross section; therefore, the summation in equations (III.3) can be replaced by integrals over b:

78 ST hr mbdb ( 1 _- e~X(b )X ) (III.4a) <7 = 42 obdb (1 - e2X(b)) (III.4b) diffration d = ye = bdb (1 eX (b)) ( where it is assumed that 6t = O0 which means we have pure diffraction scattering. It is shown that a small value for 6 will not change the answer very much. It is now necessary to calculate X(b). X(b) is given in terms of the density of nuclear matter p(r) which is normalized so that; 2 = A jp(r) 4irr dr = A where A is the atomic number of the corresponding nucleus and r is the radial distance from the center of the nucleus. X(b) is given by the following relation:51 X(b) 2 -2 p(r) O (r b ) where a is the total cross section of the incident particle with proton. Therefore, it is necessary to know p(r) for calculating the cross sections (equations III.4). There have been many assumptions for the form of the nuclear potential p(r) to reproduce the experimental data. The

79 following are two of these assumptions for p(r). A. Square Well (Uniform density) p (r) - 3A for r < R 4r R3 p(r) = 0 for r > R where R is the radius of the nucleus. The integrals for the equations (III.4) can be calculated and the results are: -ocR T = 2R2 {1 -[1 (1+ a)e2 8e } (III.5a) (aR) =R2 {1- [1 - (1 + aR) eaR] } (III.5b) a OGR Ud =aT - aa (III.5c) where = 3aA rR3 B. Wood-Saxon Potential e +. This potential has reproduced the experimental data more

80 successfully than any other potential. To calculate the nuclear interaction correction for our experiment, we used the total cross sections (aT) obtained from this model. The value of p0 can be determined from the normalization of p(r) and from electron scattering we have -13 c = 1.08 A1/3 fermi (= 10 centimeter) Z =.53 fermi while the hadron-nucleus cross sections yield c = 1.13 A1/3 fermi The integrals in equations (III.4) can not be evaluated analytically for the Wood-Saxon potential, but they can be evaluated numerically. A Fortran program was written to calculate the cross sections for both the square-well and the Wood-Saxon potential. It also included an empirical formula for the absorption cross section which is based on the optical model.50 a = 44 A069 1 +.039 A-1/3 (a - 33) -.0009 A -1/3(~- 33)2 ] Table V shows the comparison between the cross section calculation from the Wood-Saxon rmodel and the experimental data.

81 Table V Comparison of Wood-Saxon Model With Experiment 23 Gev Proton Inelastic Data (Ashmore et al.) Material Data Ca ( = 40mb) Be 180~5 219.3 C 225~5 270.4 Al 400oo10 474.1 Cu 740~20 833.8 Sn 1221~26 1236.0 Pb 1750~30 1757.0 3 Gev + (Longo and Moyer) Material Data Calcu lation _a cd Ca ad (a = 33mb) Be 192~ 8 41.5~3.5 192.7 41.6 C 213~8 66.6~7 242.3 60.2 Al 428~15 160 ~14 435.8 157.1 Cu 790~41 445 ~60 784.7 38502 3 Gev p (Longo and Moyer) Material Data Calculation aa ad aa ad (~ = 44mb) Be 236~4 64. 82.4 231.9 62.4 C 260~6 107~6 284.6 88.2 Al 503~16 236~17 492.7 214.0 Cu 914~44 620~65 857.0 485.7

82 TableV (cont'd) 3.0Gev K~ (Abrams et al.) Material Inelastic Data a ( 17 mb) C 155~1.2 155.0 Cu 595~6 594.0 970 MeV r- (Cronin et al.) Material Data Calculation (a = 33 mb) Ga cd cd cd Be 197T9 76~15 194.7 41.6 C 252~13 78~21 242.3 60.2 Al 442~20 217~41 435.8 157.1 Cu 806~35 290~60 784.7 385.2

83 We extended our calculation for many elements and covered values of a which should be adequate for r-, K-, p, n and p. The abbreviations used in the Table VI are SIGBAR = a SIGA = aa SIGD = ad SIGT = a T

84 S1G..3^ = 17,0!~ C = 113 A/ F Table VI 1.13 A**I/;3 F 0.553 F RVI 1.30. F _ MATERIALA UNIFORI HODEL WILLIAMS. 1000-SAXON SIG& sIGr SIGTG SIGAI SIGA S18 SIGT HE 52,0 7.2 59.2 52,9 59.$ 4.2 63.2 LI 86.4 14,4 10,. 93,.2 97,2 9,9 107,.1 -BE 108,2 19.5 127. 181.. 20.9 144 13543 C 139, 8 27.7' 167.,5 1.53,2 154,7 21,7 17~,4 — N2 16.,. 2 33,3 193,4 175,5 176,2 26,9 203,1 o2 I '1,1 9,,0 21 9,.1 1 9 1. 1 97. 0 3.2, 3 229-,3 F 22 9,3 47,8 257,1 228,1 227,1 40,8 267,8 NE 28'8 50, 8 269,6 238",2 236.8 43,7 2803,5 AL. 283.5 72.1 355.6 305,9 322.2 64,6 366,7 CL. 362.3 1o0,6 462,9 386,6 -"f. 1 92,6 472, FE 524,8 166,3 691,1. 549,5 536,3 158,2 694,5 CU 586,1 193.2 779.3 610,0 594,0 184.9 778.9 SN 970,.8 381.7 1351.7 983,4 945,4 370.5 1315,9 W 1369, 9. 6O6.5 1975,6 1366,1 1298,5 5 86, 9 18'855 pS 15~6,4 6fI1 9.3 2195,6 j.497.2 1418.0 665.3 2783.3 U 1672,8 792-,3 2464, 1:6551 61, 3, 2 762,2 2325,4 SIGBAR.= 20,0 Ms C,1;3 A**1/3 F = 0,53J F RE = 1.30 F MATERfIAL UNIFOPM MODEL WILLIAMS WOOD-SAXON *i~~ eSIGA SIGD SIGI' SIGA SIGA SIOG SIGT HE 58,5 9,5 68,0 67,0 67,8 5,6 73,5 L1 96,5 18.8 8 115.3 11J,4 11..7 13,2 123, 8 BE 120, 5 25,4 145,9 136.9 137,1 189.56. C 154,9 35.7 7194,6 174,2 1.74,3 28.3 202,6 N2 177, 1. 42.8 21 9,8 197,5 1.97,8..34,9 232,7 02 — 198,6 50'2? 248,6 222,1 22', — 5.4. --- 1.8 262,3 F 23,1 611 291,2 252,7 253,2 52,4 305,6 _71- ~~ — -2- 4 7. (t4 5 6 63t 6 3 E (8 56 - 60 31 9-~2 b -r8~NE 2- 4 4 64. 8 305.2 263' 2...263,8 56.2 3-9-8 AL 379,8 91.4 471,2 333,7 334.2 61,9 416,l CL 393,. 126.5 520,,3 4174 417 167,4 - 116,4 533,8 FE 565.6 772 556 265 77 556 582,5 195,2 777,6 CO-U'~- ~ 632~, ~ 2-38,'9..8'68;~9, 647,9 643.1, 2.26,9 869 9,9 *13Z 4 462,6 1492, 5 _. 1,6 i0Ze.3 442,7 _ 1451.0 W 1441.3 723.9 2165,2 1421,3 13715. 688, A 2-'A59,' 5 pB 1582,.....81 _ 2471, 1 1554,9 1.49,8 775.7 2269,5....71'J' 1751,6 93b,6. 26 a'8,-2.-B- 1715,0 164 -, 8..3- ~,4 ---252-J,'5 -

85 SIGrrAR 22.0 MR C = 1.13 A**1/3 F Table VI__(cond. F.=.53 F Re 1,30F F.. MATERIAL IJNIFOPM MODEL WILLIAMS WOOO-SAXON _ $IGA SIGD SIGT SIGA SIGA SIGD SGlOT HE 62,5 11.2 73. 7 5 7 7 3,5 6,7 80~.2 LI 102i6 21.9 124.5 121.1 119,2 15,5 134,6 BE 127,8 29.4 157,3 148,6 147,1 22.1 169,3 C 163,9 41.2 205,2 187.0 186,4 32,9 219,3 N2 187,1 49,3 236,4 211.2 211,1 40,5 251,6 02 209.6 57.6 267.1 234-4 234,9 -...;8-...283,2 F 242.,3 70,1 312,4 267,9 269,1 60,4 329,4 NE 253,2 74 3 327,3 278,8 28 O,1 64,4 344 6 AL 325.0 (4, 4 429,3 351.0 353,4 93,7 447.0 - L 1 —1-,4 8 14-3-, —3 — 55-5-75 7 43,6-.-6 439,4 132,22 571.7 __E 588.4 21.32.8 821,2.608, 609,3 219,2 82'8,5.....-Cu-...........654 -,4........2658' 6.... 923,0........... 67,.4..........67i,-3......254-, 0 - 925, 3 -SN 1062,1 51i3,7 1575,8 1059,9 1043.6 487,5 1531.1 w 1i...479,1....796, 3 2275.3 4556 114&t1,' 4 8 7 49,1.2 i 6 -Z.8 PB 1621,4 898,4 2519,8 1591,7 1535,5 841.8 2377,2 U -179275 '2-74673. 7 -3-i783633 -,'5' SIGBAR 24,0 MR C 1.13 A**1/3 F 0,= 53 F RO = 1,30 F MATERIAL UNIFORM MODEL WILLIAMS WOOD-SAXON SIGA S I GO S I GT SI'4 SIGA SIGD SIGT.HE 6.66,3 12,8. 79, 1 83,9 79, 0 7,8 86,7 LI 1.,.3 25.. 133,44 131. 127 17,3 17,9 9 145,2 BE 134,6 33.6 168.2 159,6 156,7 25,5 182.2 C 172.1 46.0 219,1 199.1 19 7.8 37,7 235.5 N2 196,1 56.0 252.1 224.0 223.6.46,3 269.9 02 219.5 65.2....284,7 247,9 248.4 55,. 303,4 F 253,3 79,2 332,6 262,3 283,9 68.5 352.4.NE 264,4..3.9 348,3 293.4..295,3 73.0 368.3 AL 338,5 117.3 455,8 367.2 371, 0 105,4 476,4 CL 427,6 163.9 588.5 454,6 459,6 147.9 607,5 _ FE 6,68.2 258.5 866,7 629.1 6353,4 242,6 876,0 CU 675,4 297.5 973.0 693,5 696.7 2820,1 976,8 SN 10659.2 562.2 1651,4 1687,5 12174,7 529,7 1604,4 w 151~,3 863.8 2374.1 1467,8 1446,9 805,2 2?52,1 PB 165j3,8 972.1 2625,8 1624.3 1571,8 9~?,? 2473.9 u 1826,'-.11- 5.3 2931,3.1738. 6 172' ' ]'A.-~-'...

86 SIGiAR 26.0 MP C 1,13 A-*1/3 F 7. = (,53 F 0H= 1.30 F Table VI (cont'd).I_,30. F MATERIAl. UINIFOR MOILOEL WL LI IAMS4 WOOD-SAXON SIGA SIGO SIG T SIGA SIGA SIGD SIGT __ME 69,8 14.6 84,4 91,6 84,3 8,9 93,2 LI 113t, 28.3 141,9 14:,.6 135.1. 2,4 15 55 BE 140, 9 37,8 178,7 169,8 165,9 28,9 1943,8 C 179,7 52, 6 232.,3 21?, 5 2. 8,7 42,6 251,3 N2 204,4 62,7 267,1 236,1 235,4 52,1 287,5 "-02... 228.5 72.9-301.,3 ~26~., 5 261,1 61', - 322,9 F 263,3 88,3 351.6 295,7 297,7 76,6 374,4 N-E 274.,6 93-, 3,.- 37.1 39,5.81,6 391,2 AL 350.6 130,1 480.8 382.5 387,3 1:17.1 504.5 CL 441,7 177,7 619,3 471,5 478,0 163,3 641,3 - SE 625,5 283,4 908,9 648,8 655,2 265.,2 92.,4 CU 69307 325.5 1~19, 2 714,2 719,5 3 95-3 1024,9 SN 1.1.112 2 6c8.I 1720. 3 1113, 4 102.4 l0 569,1 1671,5 W 1 536.64 926.5 24 2 9 1518, 1477 8-,0 856-,6 2334,6 p E 1680,6 1 4 ', 2720,8 1655,9 16'23, 8 957,3 2561, 0 * U 18~3,7-? i7.6 33.3.8.7 1739 1797 23 u 8' —7 '-2'g3J 3r6' SIGBAR = 28.0 MB C = 1,13 Ac"1/3 F 0 5;3 F RO 1, 0 F MATERIAL UNIFORW MODEL WILLIAMS WOOD_.-SAXON SIGA SIGD SIcT SIGA SIGA SIGD SIGT HE 73,1 16,4 89,5 98,8 89,4 10,2 99,6 LI 118.5 31.5 150.0 149.3 142,6 22,9 165,5 BE 146,6 e42.1 1.8__ 179.4 174,6 32,5 207.0 C 186,6 5 8,4 245,0 221,2 2J. 8,9 4 7 6 266,5 N2 212,0 _ 6 9 4 281, 4 247,3 246,6.58,0, 304,6 02.......2 36,6..,6.:-...3 2 72-2.2' 3... 273,~ -8 '....4 6 1,'6 F 272,3 97,4 3(9,7 3 J08,2 31.,6 _ 84,8 __ 395,5 NE 283.9 1oi3, i. 3E6,9 319,8 322,8 90,3 413,0 AL 361., 5 1J.42 8 54.,3 396,7 492,4 128,8 531. 2 CL 454,2 194.1 648,2 487,2 495,0 178,4 673,4 __. FE..64,6 347, 4 948, 0 667,2 675,1 287.,0 962,1 CU 7~ 79,7 3 5 2'.3 1 06 1,9 9 733.6 74'.3 3 29, 5.1.0 6 9 8 SN 1131,n - 651.2 17n3, 1 1 t37,5 1127.2 6`5,9 1733,1 W 1558.3 98;4,5 25/2.8 1546,1 15 5,7 923,9 2439,5 P_ _ 1723,1 11c2.P 20~5, 9 165, 3 1632,3 1~07,5 2639,3 U 1876,8 i~2 417.6. 31,24,4 185L2,6 1783.3~ i j,33 4J —2 j97i

87 SI3BAR 30,- MB C 1.13 A*'1/3 F 0.53 Fr ___%I~ =1 F~ ~Table VI (cont'd) MATERIAL U NIFORH M.* EL WILLAMS WOOD-SAXON! SIGA SIGG SIGT SIGA SIGA Sl1O SIGT HE 76,3 18,2 9.4,5 15.5 94,4 11,4 105.8 L. 1 23, 34.9 157.9 157.5 1 49, 8 25,6 175,4 BE J.52., 46.4 1 98.4 18,.3 182,9. 36,1 219.0 C 192,9 64,2 257',1 2, 23. 28.6 52,6 281.2 ' N2 218,9 76,1 2950, 257,7 257,0 64, 321.8 — '02'....244,i 88.2 332,3 283 '3 -84. 75.5 359.7 F 28., 5 1C6.4 386.9 319,8 322.8 93,0 415,8 NE 292,3 112,5 404.7 331,6 3354i 98,9 4'34,1 AL 371.? 155.2 526,4 409.8 416.5 140,2 556.7 CL - - 4465.2 21,1 675.3 51i, 51.7 193.2 703,8 FE 653,8 33. 5 984.4 684,3 693.2 308,0 1001,2 CU 72395 378.7 11515 751,5 759.2 352,6 1111.8 SN 1148, 5 691.6 1840.1 1159,8 1149.6 640,3 1789,9 W 1576,7 1,38." 2614.7 1572.2. 1533.6 947.1 2477,7 PB 1721.9 1160.4 2882,3 1712.6 1657,9 1053,4 2711.3 U 1896,0 139.7 3- 25.8 1881.2.18-.8 11-2'2-,1 2991.8 SIGBAR 32.0 MD C 1,13 A*'1/3 F 0,53 F R: _ 1,30 F MATERIAL UNIFOFM YODEL WILLIAMS WOOD-SAXON SIGA sI G1O SIGT SIGA SIGA SIGD SIGT HE 79.2 29.,1 99,3 111,6 99,3 12,7 112,. L ' 1' —27, 3 38,2 165,5 165,0 156,7 28, 3 18'5-, ___E 156,9 50. 2,:7.6 196.5 1980.8 39,7 230, 6 C 198.7 699 268,6 24,1 237 577 295,5 -- _N2 225,2 82,8 2 378.0 267,3 267.0.70,0 336,9.02..25,8 g95.8 346,6 293,3 29 4,7....-82, 4 3'7 7,-1 F 287,8 115.3 4;:3,1 330.6 334.1 101,2 435,3 NE 299,8 121;,P 21.6 342.-6..34-6,8 107,5 4 5-4' '2 AL 379.9 167,4 547,3 422.7 429,6 151,5 581,1 --- Cb~~~~~~~~~~~~~~~~~~~~ _ CL 475.1 225.6 77~.7515.3 25,2 2'7,6 73?,7 F.E ___ 665,4 352.7 1181 771t.1 7.9,9 328.0 1"0389, CU 735,7 4.'2.5 1138,2.768,'.V.. 776-5 374,61 151 sN 1162,9 729,4 61892,3 J. 182 4 117,0 672,3 1342,3 U........9.....2..,3n.. 13.6674.. e, 9 13 1. II 1[ 592.3-"i~;7. J~~ 2679';:.... '59'6.'3.. 1553';2...986,8' '2543-. P8 77. 21,.. 2951.~ 1737,7 16,31.2!~53277.451 U' 19,31,-;. -7 —79-'-,18.812, 6.l

88 SIGBA? = 33.0 M-B C 1.13 A*1j./3 F i. =r 0 53 F fR = 1,30 F_ Table VI (cont'd) MATERIAL UlNI F Or1M t nODELL W I LIAMS WOOO- S XC O, _ SlGA SIGIO SIGT SIGA SIGA S GO S IG HE 80,6 21. 2 11.6' 114 5 1..6 13.4.115 0.LI 1..129,3 3. 399. 16.9,2 63,5 1'. - 0 29,7 189,7 BE 159.2 52. 9 212,1 22',4 194.7 41.6 236.3 C 201,4 72. 7 274,2 244,4.242,-3 60,2 3-2.2S N2 228.2 86.1 314,3 271,8 271.7 72,9 344,7 02 254 9.5 --— 353,5 298,1 299 85-[ 385, — F 291,3 119.6 41C, 9 335,6 339.6 1I5.2 444,8 N' 32'3.4 126, 4 429.7 34 77 3523 11.7 464.0 AL 384. 7 173.3 557,3 427.7 435,8 157,.1 592.9 CL 4179 6 233. 2 712. 8 521,6 532.,-2146 744 6.6 FE 670,7 363. 1034 1 707,5 717. 8 337,7 1055, C LI 7...741. 2 414.3 115 55 75..7757 784.7 385, 2 1 i69 98 SN 11.69,3 747,4 1916.7 1i92.1 1179.5 687,5 1867.0 Wi 1599,-2 11 111'.24 2.79.6 16J7.6 15S3,-7 1.05, 4 2569. 2 PB 1744,9 1237.8 29'2.7 1749,5 1692,2. 11 4,. 286,. 9 U1919,4 13'2-.8 - s-1~2,.2 1922.0 1845, 124"7- -3-91,9 SI G3AR. 35,0 MB C = 13 A*:1/3 F Z 0.53 F RO'= 1.30 F MATERIAL. U NIFORrM hOODEL W I LL I AS WOOD-SAXON SI SIGT SA SGIG SIGT S IGA SGA SID S I G HE 83,3 22,9 1i6,2 119,9 106,3 14,8 121,0 L i 133, 1. 4,3 176,3 17, 1 166,5 32 t5 199, BE - 163,6 57.2 223,8 227,6 20 2.1 45.3 247.4 C 2.6,5 -78,4 285., 25.3 25, 8 65,3 316,1 N2 233,7 92.65 326.3 28,.2 250.9.78,9 359,8 02 259, 9 1 6. 9 366,8 326,9 3'9, 5 92, 6 402.1 F 297,7 12P, 1. 425,9 344,9 3520, 113.3 463.2 NE 329,9 135.4 445.3 357, 2 362.9 12, 1 4863,1 AL 391.4 1_ 5.? 576.4 43,3 447.6 168,S 615.6 C t 4 8 88, 24! 735 9 5 3,S 545,0 2 28, 3 773 4 FE 68w:, 4 384,2 1~064,4 721.2 732,6 356,5 1089.1 CU 751,2 437.0 11883.2 790.2 81,2) 405,6 1225.6 SN t82, 8 71,' 4 1962,2 12J `3. 1197,4 71. 6,3 1913,7 1611,6 ( 11.53 2765 3 162', 6 1583.6 1 40, 3 2623 9 Pa 17J57,4 1253.9 334,1.3 1771,5 1712.,4 11.51,5 2863,9.U..'1932,.1 1A?." 2 33742'.i9'43-,'2 186..'i a6 '5"...2-85",-5..31'5l.,5

CZ.::4 NO..- i'n;C L"-:,,' ':. -.~ '." V- V- NXr '~ (_ I 1 I K o,I ' I 'I, -- c~~~r:Cr ~~~~~IS~~ CI~~~~~ ' I\IWI'W f ts, u,% o., r~~~~, i,a jf.- - - oV — I',~.r.,o~"~.~:,V-4 '~- M' -- CN ~ 0. NV fl II) V c0 -4LN L%O IA IZ V-4, UT- 4 P9;c XI~ M ~ N0 'Hl '0 " cc) "04 C.- 'fl.C n Nc:LOv 'H' %4''.")c, ')! "9 '~~L N-~ C\ O I i'W 0 0 W W a,.W..... ~ 4o~~~~~~~~~~~~ ~ I c.. ':.:.i,.. '.t ' ~-l~ C" Nr, N t'I NJ *') ")E) r'3 N 1rr'9, j 6t c~ r:;:N '4r r ~- Ii CM - v co - f qq Ln (l' C\t 0I C C' I) r'.. d CA N C C r-) V- r%. o C)% C\4.c rll_ '1 4r, r.. ~ r)f>.: r%. 0;Nr C C 2:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-~:,o o,;. o, jh O~ o- ~c~c,,o f I C:), C! ',-4 c-C N -O O'2 O'JA N CT C V4:C\ "a iN4hX cc~~~~~~~~~~~~~~~~~~~C v-fC. vOC' m *c~~;~ ~~ h OI ~i ~~j41 C\'~ O1 i4c~ v *vl~~~~~~~~~~~~ i, AiiC - C.C..! OD C\Y 0I O.'O 01 tl- CU PO -C..; M' 0 CD M0 ~ LAIG LA ('VN(' LC' N '32N I WN. ' I -W' W.W 1~~~~~~~-4 - - - ' k-w Cs,; C'. 0,. lx~ 0% ct 10:v: Ln (n %O:I, P-.- C~ 1-1 1 lit" (V laC T~ cC~- 1~;n'L 'H i- ' C'J~ 'i ('.tEI i I'H'Hu;<u c~ i"' H)) I C US V-4'HVI \1 I < h C!v # 'O N J ~ ~ C'.C O T ') 0' i-(d\ O'? C \ 'O r '1 '~. C.'rj - ~h,.L'~:~ '"0 l,-t 'OL'~, 'C,. 3C"",,-4I.r,~ N., -t N, O, CJ ~ '),,00, L, " ) N I'- A,-~ N".I 'H, i-'. I1 — I I;~9 O ~iI(cir~, u*Ii r, Icr z cul co O K CL; C CL j % V m r I % Cy 1! rt N v -, C,o( CO i E~~~~~~~~~~~i;~~~~~3 OI it" ~~~~~~~~~~~~~~I 'i, I -I C 3 I ~~~~~~~~~~~~~~~~~~~~~~~~I,i O WW WW,4 o\ ~3 &l c I_; C ~ s M L.^. ri rl 0?"-. re) N L Cr C-N: -V V 'rO In I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- CV \.t n r3 M, M % W W - IW r >W W Gl ~ ~ ~ ~ ~ ~ ~ ~ ~ l~ C'JN I '.J D'C -4. CO ~ ~ ~ ~ ~ ~ ~ ~~, O,,C% -,ir-~ I-:~-, C,.~ ~~ Z,,, ~-4C III-J; C.:: I, '.~o ( D I C \: M c r - C~~~~~~ ' P"' ~- 0 C.: i Nn r ZS. V! \, r I W r, I,GIf; h c J %O - V' %.%r %. Nr O im re.):la M PO No Ln 10, U V-i W..* -N I, in% CO Cv, r: VU% JCM ' tr% C-; j.... C\ NJ.. 3 - I U~~~~~~~~~~~~~~~~~~W ~ ~ ~ ~ ~. W, W,:0 0W W W W j 3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ iI,1 I '-~~~- ~~ftr, LL 01,- n 'o; n.. '. coc, Ch, Ci NC) W jCO; V- C\J r"m W ' CI i -ii ~G (V ~:P ~ rn I C % vI C f oA.1 =7'-j CO I U CD LA- 12~ -4 C.> (n, CL. =O x-J M; u:P-" C) L,'. k! t-ct i U LL C), 9) Z C5 ~:c3 ~0j ~ r QO; C~!r t~. ~~ y P~11h~ ~ \G I ~V ~i' ~-~~~~~~~~ r) i\O ~~~~~~~~~~~~~~~~~~~~~~~ j rl Qr Oc C~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:~~~~~3 Ch 1~~~~~~~~~~~~~~~~V ~~~~~~~~O I~Cf~~~~~~~~~~~~ ' 1,,,~~':: r t)It '~-:t-''.,. i~ 3> t I~ ~~ ~ ~ IV)

90.$1~BAR = 41l,~ ~< C ____ 1.13 A*1/3 F EI -- rJ5 F F = g 1. 3'0 F Table VI (cont'd) MATERIAL UNI FOMMP D;EL __ I.L.LIAMS WOOD-SAO!"9 SIGA SIGO SIGT SIGA SIGA SI6D SIGT hE't: 089,3.._27.,7...117.0~_ 131,. 117,.3 18.3 135,7 LI 41,4 51,6 193,3 S18,6 181.7 39,6 221,3 *BE 173, 1 67., 241.8 222.44 219,3 54,8 274.1. C 217.Y6 92.3 329,98 26,8 27,4 78, 348,5 N2 245,6 1r.'8,5 354.1 297,6 3 1,8 93,8 395,6 02 272.5 124,8 3973 325,1 331.5 l9,5 441,8 F _ 3.1... 3 9t,1 9 I9 46,.2 36 4.4 373.5 1,32., 506.4 NE 323.8 157.? 480,8 3/7,. 386,9 140,7 527,5 AL 4O7,. 212,6 619,6 462.,3 474,2 194,2 668,4 CL, 5.5,1 282,5 77.66 5577 5740 260,8 834.8 FE 6 9699,9 43... 4 1131, 2 749,8 765.2 399,8 1165., CU 77 1,.3 4f8.7 126~, 1 82., 1 833,8 452,4 1286.1 SN 1223,5 856,4 2059,9 1245,5 1236,6 780,9 2016.6 w 163 1247 28 7 1672,3 1626,9 1116,1 2743,. PB 1781. 5 1382, 7 3164.,2 1817.1. 1757,0 1238,6 2987,6 U 1 956,5 I 546,7 35r;3,2 199Z.,9 1912,8 1368,1 3283,2 Si AGBAR. 42,0 MH C = 1.13 A**1/3 F:Z = 053 F Re = 1,38 F MATERIAL UNIFORM MODEL WILLIAMS WOOD-SAXON SICA SIGO SIGT SIGA SIGA SIGD ST HE 91,4 29.6 121,1 134,6 121,5 19.8 141.4 LI 14.3 —....54,;9 ' —1 991...-93,'.. 87,4.42,5. 229,9 BE 176,5 72,2 248,5 227,2 225,7 58.6 284,3 C 22,4 97.7 319,9 274. 27/,7 83,2 363.8 N2 249,7 11.4.7 364.3 3;3,2 329,5 99,6 409,1...02....276, 8 1.i31." 4.... 8 5 3 '9 339,6 116,1 455,6 F 315,9 156.9 472.8 37",6 382.1 148.,5 522, 6 NE 328,5 165.2 493,7 3.3,3 395,6.148,6 544-;2 AL 412,2 223, A 635,2 467.3 483,7 204,2 687,9 CL 5Jr,,8 295.3 8;6, 1 565,5 543 853 FE 706,2 448.6 1154 8 75.8 9 7768 415,7 1192,5 CU 777,B 57,.5 12' 5.3 829,7 845.8 469,4.13152.S...... 121i,6 2,.. 2,93,4 1257,4 125,5 82,6 2253,1 W 1642,8 2 79, 3 2922.2 16:6,2 1642,23 11. 42,5 278~ 7 -Pe 1789, C 14I1.4 3'5, 4 183;1,5 1772,8 1255, 2 3A3, 8 U 1964,'/"15'. 2 56.. 1 2;,1 6','119- t.;?3 — 1396,6.....3 325'-0'

91 $1G AR r 4, EttI -.. N 1.,30 ^.F'..........'-le - t —:...(o.n-t —tfl-}..........fik} E R1A L_ _ l &k _ Q r..1-.. _ t J,-.E. A!:L5....... t/QQ t)n-S. XQ.J SIGA SIG) SIGT SIGA SIGA S l(G: SIGT.. HE.5..........315........1'25,......13...., 6 2 __.3......_...3. 21...147.,.. LI 147,1 59,2 2;5, 3 196,7 192.9 45,4 238,3.. B.EL. 7 _9._6 li.. 25L,_231,. _2.2_, 9_ 6.2. _4 29. 3. C 224,9 12 9 327, 8 2738,6 284,6 88 2 372.8...N2 253., 4.r__. 12,..37 4,.,1_ 37,.9 7 3 1 6,.8 _1 5..4 _422,2_ 02 280,8 1358.3 419 1 335.9 347 3 122 5 469 8.._... _...... 4.._7., 8,.2....4.8., 0. 53...2.. N E;332, 1773 2 5.6 3E8 e.7 4'33,9 156 4 56,3 ___AL. 6 5? _3_3.__6_......-.-., _ 3 4,_?_7, 7 214_. 7.....7_,_. CL 5:15 9 37. 6 823, 5 572 1 59'4.1 2E84,8 878,9 F..E......7118..464,_9117_, 8.:.706,7.787 _,7..430,.8 121', 6 CU 783,6 525,1 136'!A8 837,8 857, 0 485,7 1342,7.....N...S,..... 1.21 6. 9..... 97I"3..2 _ 124,2 1267....1263.,.5...5..823,8.... 2087, 2 W 1649,3 1.3 88, $ 2958 1. 1693,.j 1656,7 11 66, 9 2823,6 P> Q7..1,9.5_5_.4.A.t 2. 2_1__A.7 7___12., _3 3. 7..L, __ U 1970,6 1614 4 355 0, 2031.9,1 19.43,7 1422,9 3365,6 SIGBAR = 46.0 Ha - __C -t 13.h_.L3 f.__ * _ a0.53 F 8~ = '. t35 F1 MAIER.1 AL___ - IJ.ERL LEL__ LLS..._O.o_- SA. X O.N SIGA SIGO SIGT SIGA SIGA SIGO SIGT...... H 9_..9 5,._....__.3,,5.....__.12,....1., I. 2....29, 6...2 29 1......5 2 LI 149,7 61.4 211,1. 199.7 198,2 48,4 246 6.BEf 1 2 *LE?1 _ 2 A- L ta6 2.4 3,6.Zf_ _ 7 _b_? __3 _ 4 C 228,2 18. 1 336.3 282,3 291,2 93,2 384,4...N...2 256,9.126 5.....3,. 383.311 8 _ 323 8.i 1... 35, Co2 2284,4 144,8 429,3 34'' 354 6 128,9 4835 5 F..... _323,9. 1.7.2. 495,9 33 2 397 9 55 3 553. NE 336.7 181, 51'7.7 395, 1 411,7 164., 575.7 ___AL._A_ 42.1!, 2 2.22.2,. _2....___22 4 2,_7 CL 52'8,5 319.3 839.9 577.6 6C3,3 296,. 899,5.FE 71 9 48 C,',? 4 3 445,33 29611243,9. FE. - 716,9 4.8.. I.1197,.3 _7 13 i. 798,. _.44 5,3 _.; 124 j 3 CU 788.8 541, 133, 6.944,6 867,6 6 5, 1 1363,7 SN......1222.... 9 2152,.....1 276. 1275,7.. 843,6 2119,3. w 1655,? 1335, 299.8 1787.9 167.2 11.89,6 28 9 B.._1__ i s.. 1,2__145,4_ 32 76, 7_ ~5/-.3 1 1lA147 1 _. 3,4 U 1976,3; i643.8? 3622.2 2 29.g '19:gst..%~4z 4 -,,.,

H" wV i~~~~~r,..cco o r-i r-. -IcvP o C-rUV) 1)~~~~~ ~ Ln L i O\ f o" No, or v, V- \0.c 0. Oo V 1 o(1 r ma-.i & ' -"1 ('N ~ ~ "~'"', "q" IrL, \. r'Pi C, C CO,-"l ",. ' m, I M;\- -j....~ C -r-. a ', '~~~~~~~~~~~~~- v -4.~\~J C\: M''t r, nN I~'j ',7' 1,,4: V`" UN UN,,O I"'OC'J' -I C". - C\. T, ~I OI~~~ 1 0fd OC~~k'clc 1rlv r -.n o i! ~ I '~ ~ ~ '~ ~ ~ ~c,,-,~ ~ u~ ~ ~ ~.,~~~~~~~~~~~~~~~~~~~~j o'- '-''0 LC\~~~~~~~~'0 t~~~~~~ CM v, r'J r'~~~~~~~~~~~~~~~~~ r~~~~ ~~~ o'. o4 -iC~ I Ic rJ T( CV V r-; M CU rl ' Ct- CM,i c'C - C' O.l j' rt Cr %o 'Pt r; E~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C \ rJ (1 M trc n M n cO N %o - V-, V4 M- O Ln 'I 4 Q..:I I i:I 4 J iln ini % o u P2 r0 > c Lj -qf~jri r- I~ ' r- t-, ), v -4 o h~ -; co i~~~~~~~~u~ H I C r-.-f t4 ~-i 'C 1 ct' ~r-d 0' r3 ( r- cY) ~C V \ I~i It LA4 r-4Nc\H~) '3C r; i) CJv)) (ZIJ ) C -. C\;,C) K '7"0~j~iCM CJCM UIiOT4~0C~r~ I\~ c\JxC.) Crz c Ci c r- c&,,- cCc (' ~~~~~ '7I~~~~~) CM ~~~~~~fO' O~~~~~ C\J~~~~~v If' r'~~~~~~~~~ w-4C. ~~~~%OcocoC\ 1- Vi \, vsz"n -- L -i -1 i i r: ~ ~~~I ~~~ clIN CV. r; L Iu Vf. -1 li Cj C jC.-Di C, v in C\ co IO;~i~r - 19\ CC', yr O I~Ci~ ti ~~~~~~~~~~~~~~~~~~~~i ~~~~~~~~~~~~~~i P3~~~~~~~~~~~~r- r - r,. NO O, V-121 1O c` C h P 3 t % ~~~~~~~~~~~~~~~~~c'!~ CM cu.t. C-, n v F2) co Cj r- rII C.- I -rr' I C), W,; C, C LCI..~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~T I \ N, lWC' I i E- r cV') c-, c!r C0'-(\ifW I- % vl r- * ~ ~., ~,?.. ' (-I), ~ o~ ~!~ ~:~~,, ~: L~1' -.T C~jt. O\ r +II t~r u~ rr n7: Cr~ I~ In L i -0 ) co — 1~~~~~~~~-. "IT C cn CD -i NO f: r3, C\ C~~~~j I &.-v *- v~-I- I~1II vo -,; 'H1 C\. Z7V C.-1~ f'o) C> U I".\ C> '0 r, C(~ V) V-4 IC v C L' 611-1) C\. -— ~ n T-V Lr~ r —v I LA.I rl (\ n 4 '-4%' INW IN' CV., -....n..%. i P~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. III C'JC,, (? mU,, L, 5 Le I* I* C5 C-) Oi~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l' CD: C'. r': cL' -. ("\,0, <:,I - Cp-1 C\ cr- C".'-e.; ~,,, t~ ~-i C~ ~ t~ r/ L~5 Pif-:?L -C a\ r4: N ~~~~~~~~ r) IY3: O iC~~~~~~~~~~ ~~n V\ 4 V4 Vi V i v:LrCr C) aJ c~.N > %i cciY-i c u r\i y, -c wi~~~~~~~~~~~~~~~~~~~WC ~L.i LLLICcI r P.- r'"J- ON LfvN'."'4 is.rr zaL'r)"; N I~"O"'cC '~" r r-J 0-, c. 1 c: e. C.) Cfco' cCi4 1 -.H Lr\ r,,z 'c ':0 W) r.4\ M C' 0. 1-..... M ': t "j L 1 L rr r) ni co 0' Lf~~~~~!:,:r, c..~,,~j~ Li, ~i d Zu'p~, CWJ AI M —, "N o': M LA3 x -j L) z C) - - -) ' C......... F rci ri~~~~~~~ tI re t~~~~~~ rl r3 t~~~~~~-~~ ~f i +-1~~~~~~~ ~~U (V C~~~~~ r) r: Vi in C~~~~~~~~~IL ccu 7C. i &-.M ) L C. ( '~~r. t; II~~~~~~~~~~~~~~ ~ ~ ~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_ i t!~I i~/14U wc _ 1 i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1J~~~~~~~ 't,c u u U ',,D., — U 3~O: j ir L~ Oh.: t) ~ —.' L~, C3~ ~ ~ ~ ~ ~ ~ ~ ~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~N cr r- r- 4' C3t tr, C. LL ~~i '~ O~- eU iO,~. ~.~ Oi in ~ ~~ _c V i'

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