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TRIUMF
Mathie, Edward Lawrence
The differential cross sections for production of positive pions by bombarding carbon with 400, 450 and 500 MeV protons and copper with 450 and 500 MeV protons have been measured. This data was taken at pion production angles of 60°, 100°, and 150° with respect to the incident proton beam. The results are compared to theoretical calculations and to similar work at other proton energies. The earlier results of Lillethun at 450 MeV should be renormalized by a factor of approximately 0.3. As proton energy increases from 400 to 730 Mev the differential cross sections for a particular energy pion increase monotonically.
TRIUMf EPO LOW ENERG't PI:JN PRODUCT:i:ON BY PRO'l':JNS WI'rH INCIDENT ErfERGIES FROM lf-00 TO 500 MeV by EDWA.RD LAiJHENCE HATHIE B.Sc., Univer:;;ity 'Jf Victoria, 19?1+ A THEdIS SlIBMI'r:CED L'f PAH.~IAL-FUiJFILLME."iT OF THE HE1~TJI3 .. EMENTS FOR THE DI~G.REE OF MJ\.S'rER OF SCIENCE in Ghe deparcmant of' Physics Wa aceept thi :3 ti-ies L:; as conf-Jr::i1.ng to t~1.e required standard (, {i;) .E:DWA.RD LAWRgNC:2: MA'rJ:IE, 1 ';}7-S Uui·v•a:-sity of Victori,3. May 1976 All rights re.served. This thesis may not be reprodueed in whole or in part, by ml:.neograph o.r other r11eans, without the · perwisslo~ of the author. - ii -A3STRAC'I'., Superviso r : Professor G.A.Beer The differen t ial cross seetions f en• production of positive pions by bombard:lng carbon. with l+oo, 450 and 500 MeV protons and copper with 450 and 500 MeV protons have be:3n measured. This data was taken at pion produetion 1 ,, OO 1 -''OO d 1 50,:J ,.r'i t:h .. t '-} .; ; i t a'1g . es oi. b , ..., , an l .,...__ respeev o i_, 1e .... ne ._: en, proton beam , The resu l ts are conpared t~ theoretical calculations 3.nd to similar work at o the!' p1·0 to!l en e rgies. The :3arlier results of Lillethun at 450 McV shouli. be renormalized by a factor of approximately 0.3. As proton energy increases from l+OO to 730 lfoV the differenti a l c::-oss se :~tions f:.ir 6. rnrticular energy pion i ~1e::-ease m•)~l-:)to !1i :~ally. 7- ii;_ -ABS~..C:E{AC·T • • • • • • • • • • • • • • • • • • • • • . • . • • • • • • • • • • • • • • • • • • • • • ii L I:3T !JJ:i' ·TABLES.. . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v LIST O.Ei' l?IGUR.F.:S •••••••••••••••••••••••••••••••••••••• vi ACK.i\JO~fl~E~G-EMENTS • ••.....••.......•.•...••.•..••....•. ,,iii C:HAPrER ·1 CHAPrEH 2 INTRon·uc: rr,J1f ... . ......................... . !\. .L ~ S\ .LY1J.!jl ~1l i....,1.tl!'i ..L 1.JJ:!, 1111 ••••••••••••••••••• EJ1rn·,ur ;,,r•·, , T.,,AT TE''' U-J,TTQTTT.1 2.1 Pion Detection . ...........•........ 1 3 3 2.3 Data Acquis i tion Sys t e~ ............ 13 2.5 Caltbration of the Monitor Telescope 23 CHAPTER 3 CALCULATION 0£i' CROSS SECTIONS ............. 30 3-1 Differential Cross Sections ..•..... 30 3.2 Pion Detection Efficiency ......•... 33 3. 3 Pion De::!ay Sorrec tion.. . . . . . . . . . . . . . 31+ 3.4 3. 4.1 3 .. 4-.2 3. 5 3. 6 3 , 7 C,n,re1~tinns f ,:,r Nu.clear Effects .... 36 Nuclear Absorp bion a 11d. Inelastlc Scattering "························ 36 Nuc!.ear Elastic Scattering ..••...... 37 C-:)ul,) tn:.> M~lt j_plo Seat tering . . . . . . . . 38 D:L,cussl.on or Unc·~rtai!ltias ........ 33 Sa.mp.le C atlc 11J_ 9. t i 1.Jr1 ., • • • • • • • • • • • • • • • • 4-1 CHAPTER l+ ANALYSIS OF TWO BODY MEASUREMENTS ••••••••• 43 l+. 1 Calc ,1la t :Lnn of Differential G-ro.s s l. ::;' Secti•) ll , ., ..................... · · · · · ""t.,, 1+.1 . 1 Two Body Kinematics and Related Facte>r·s .... . ............... ......... 45 4.1.2 Telescope · Efr .. icicnc~y ............... 47 - iv -4-. 2 Ph 13nomcnological Differen~t:i.l Cross Sections ..................... 55 CHAPrEi~ 5 DIF.B1EHEN'.;:IAL CROSS i3EC'rIONS FOH CAR.BON ... f\.IID C! 1J PP Eli.. . . . . . . . . . . . . . . . . . • • . . . . . • . . . . . . 58 5 58 .1 Experimental Results .............. . 5.2 Discussion of Results .............. 68 CHAPrEa 6 -SUHMAJ:Y: AUD CONCLUSIONS ••••••••••••••••••• 78 ItEFEl\l~i'T(: ~;3 ., •••••••••••••••••••••••••••••••••••••••• • 79 A?PE1'EHX A DA':2A ACQUISI'.rION PROGH..41"1. • • • • • • • • • • • • • • • • • 81 APPENDL{ B CALCULATION OF INCIDENT PROTON FLUX ••••••• 86 - y -LLS·r t)F TABLES 2.1 'rypical Energy Loss, 9.nd Time of Flight for muon, pro ·con and pion., .....•. _. . . . . . . • . • . • • • . . . . . • 5 2. 2 Range Telescope Dimens.ions. . . . . . . . . . . . . . • . . . • . • . 14 2.3 Copper Degrader Dime:nsi'.)ns and Telescope Energy Bites ........................................... 15 2.4 Ji:nonsions of t.he Mon.it :):- Counters •.....•...••.• 20 2.5 Su.i11111ary of NaI Crystal Efficiency Measurements •• 27 2.6 Swmnary of Actj_vation Measurements .........•.... 29 3 .1 1rarget Paramete:!:'3 ... .............•••....•....... 31 3.2 Values of Correction Factors .............••...•. 39 4.1 Energy and }foment1.l.Il Straggle .............•.....• 52 4.2 '+.3 5., 1 5.2 5.3 Pion Detection Eft"icianci ,9s..................... .51+ Differential Gross Section for reaction p(p,1Y)D. 57 Dif eerential Cross Sections for 500 l-1eV prot::ms cJ.rl CarbVl"l~ ...................................... 59 Differential Cross Sections for 1.~50 HeV pr0ton.s ,J11 C arbo11.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Differ~ntial Cross Sections fn, i+OO ~1eV protDns 011 Carbo11~ ........................................ 61 Dif eerential Cross Sections f ,)r 5CY.) >1eV pr .J cons ,::>n Cop~per .••.•........•..•....••........ . . . . . • 62 5.5 Differential Cro3s Sections for 450 MeV protons cJ!l Cop:pe-r·. . • • . . . . • . . . . . . . . . . . • . . . • • . . . • . . . . • • • . . 63 - vi -LIST OF .?IGURES Figure 2 .1 Sch 13rn.a. tic D:ia.gram ~):' the Rang -s Teles~opa.... . . • . . • . 4 2.2 Two D:imensional Hist -:>gram From. a STQP.:3 .r1n......... 7 2. 3 Two ::):L-nensional Histogram From :1.:.1. EVSNTS Run........ 8 2. 4 One D.imens ional Histogram:=.; From a s·roPS 8.un. . • . • • • • 9 2.5 One D.imensi -Jnal Histograms Fro-;.11 an EVEN'.rS HmL ••••• 10 2. 6 D:iagram or th~:i TRIUMF Proton Area. • • • • • • • • • • • • • • • • • 1 .2 2.7 2.8 2.9 Schematic Schematic Schema ti ·~ Diagram. Diagrai;.1 D:ia.gram. of thi3 of the of tre Copper Degrade1~ Transport. 16 Range Telescope Electroni -~s 17 Monito-r• Telasc()pe . ........ 19 2.10 Schematic Diagrar.1 8f the Monlto:r Telascope Elect-ru111c s . .......... ·. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.11 Graph of 11c production cross sections ..•.......... 24 .2. 12 Semj_log Graph of the area of th 13 0. 51 MeV gam"'.1a peak as a fw1ctiJn of Measuring Time •••.•..•..••••• 26 3.1 Orientation of Target .•••..•... ; ...•..•.....••..•.. 32 4.1 Obse:rv-ed Ang·1la.r D:lstribu:ion o.f P i::ms Prod:..1.cen ft'o Jn (;H9 I'arget., .................................•. 41~ ,_ 4.2 Schematj_c :8iagra;n :)f the reaction: p(p,-tt)D ......... 46 l+. 3 Cu·::---;.res to damons tr ate efficiency o:' telescope. . . . . . 49 l~.l+ Calcalated Angular Distributi0n of Pions Produced 5. 1 5.2 5,3 J \ 5.+ ~ln the t1eac ti,)r1. -~ p ( p ,,rr) D. . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Differential Cros .s iSecti,:ms for Carbon , . . .. . . . . . . . . 64 Differential Gross Sections f::,r Garbo:.:1.. .... . . . . . . . . 65 D:iff'er .311. t ial (~ro~:13 Gectior13 for Copp8 r. . . . . . . . . . . •.• 66 D:lff e-r,3n~ial ·:ross Secti::ms f ·:)l" Gopper ••. . . . . . . . . . . 6'7 5. 5 D:ifferential Cross Sections fo:- 32 and 53 MeV pi:ms produced at 100° from '.::arb::m by p.rotons with energy between ltOO and 730 MeV ............................. 69 5.6 5 ,,g - vii -D:ifferential ~ross seetions f:)r pi,)ns Drodu :ced at 60° ·by p1·otons with f3nergy betwet1:'.'l. ft00 and 730 r1ev. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Present results co~u~red with theoretical ra3ults for pi,.)!lS produced ;it 15()0 by 500 MeV protons ..... 72 Present results comparej with theoretical results f :>r pi ,.)!lS produced at 1 50° by l+50 "tfoV pr.:> to :as. • . . . 73 Present results compared with theoretical results for pions produced '1 t 100° ·by 500 HeV proto!is. . . . . 7l+ 5. 10 Pre3:3n t r9 ,s:.1.l ts ·~-:::>!trn~1.:red with t :·1em."eti ,~al .rssu.:... ts for pions produced it 100° ·by 1t50 MeV pro tons. . . . . 75 5. 1 ·1 Present re Jul ts compared with theo-ra tic al results for pions p1•odw.!,~d at soo by 500 HeV protons ....•. . 76 5. 1 2 Present -results coI1pa.r r~d with theoc- ·atical rasu~- ts fo1" pi .'.)ns p1•0d-1ced at 60° ·by 1+50 HeV protons ...... 77 A.1 Flowchart for the Dat-=i. Aquisitlon Progr:i:n .•.•••••. 82 B. 1 Flowchart for the · rm..1.sh1e INT8rl. . . . . • . . . . • . . • . . . • • 88 - viii -The au-sh.or wot1ld -.i..L,{e t:, t l1ank Dr. G .A.Be£~r for ~ssist=1.!1C9 du ,:-l-11.g 197:+ and ·1175, 1.nd D:rs. 1.P.Robe .rtson and G.R.Mason f ,-:,r their s!.lpa!'vis ion during the bulk :.1f the pi ,J!l proc..u.etion experiment. The autho1.• w~ul:i also lik:e to thank Drs. D .A .Bry.,na:n, A.Olin and J.S.Vincent fo:r their a.sststance :,,rd pa~j_anc9 throughou~ the exper:t:nent. At all times the beam physicists at TRim1P worked hard ·t;o imp:ro,,e the quality of th~ be:c1.m? ::1.owevar pa:rtieuiar thanks are d:w D,• E W 31 .3.nJ.1,.·rt: >i"·:.> f',...,.. :-1; :--::i -:.f't·or .. · t .... °"J.·"rJ-.11 -jo - •. • ..,_ \,,, ·'--~- . • - - •J - - -•. \J- .., V ,I >.I :t.J """ '-' six different pro~on enarg!es du~ing a single night shift . For 1.,ead.t:!.lg prel imi:.1ary d::."af ts of th I~ th,3s ls a:..1.d o !:'fering mm1y valuabla eom.::.n.a:n-~s, the au t .':1or is i:..1.debted t o Drs.R.M.Pearee, G.W.Bushnell and C . E ,.Pi c:.!i :)tto . Financial suppo1·t fr0 1:i. t;ha Universj_ t~r of Victo1•ia and CHAPTER _ 1_ INTRODUCTION Pion production cross sections are imporGant for several reasons. The differential cross sections may be used to choose the angle at which a secondary chann,al in a meson factory is located in order to maximize , the flux of a specific energy range of pions. Estimates of these figures have been made on the basis o~ higher e.n,ergy data for use in designing Tii.Iffi,fi-i' m,eson ~hann ,els a.."1.d ata at TRIIB{8' energies is of imrn.-ediate interest to evaluate thoe oper:ition of these chan ;,H~ls and th ,e de.sign of new channels. Pion producti~n measurements provide a tesG of nuclear pion production models. Beder and Bendix (1971) have requested large angle d ,s. ta for this purpose. Measu:'.'ements hava been madG by James (1975) at proton enf~rgy 580 MeV and by Cochran et al ( 1972) at 730 11eV for a wide va!'iety in targets and a w:id0 ra.age in the angles at which the pion is emitted. Hirt et al (1969) have measu:-ed pion produ c tion by 600 MeV protons at angles 0.8° and 21 • 5° with r e3pec t to th e pro ton 'Jeam. Earl i.er ri1.easurements were made by Lillethu t1 ( 1962) at 450 MeV, by Meshkovskii et al (195 .g) at 660 MeV, a.."1.d by Haddock et al (19 -Sl+) at 725 MeV. The latter two e.xperime .n.ts were primarily concerned with high energy pions. Th,3 purpo s e of this experiment was to measure 2.ow energy positi v e pi on production differential cross sections at large angles wi th respect t;o an ineid.ent proton beam. - 2 -The measurements were intended to supplement those for proton energies 5.30 and 730 MeV for carbon and copper n ;1clei, with data betwee!l l+oo and 500 Me1l. Of partici.llar interest was a measm:-eme.nt 01' the cross sections at 450 MeV, where Lillethun' s data has been q;_i,estioned by Hi rt et al ( 1969), Beder and B•and:lx ( 1 971), ~nd James ( 1975). The experi:nental teehniq_t1e is described :Ln Chapter 2 . . Chapter 3 is a surunary of the calculations of differential cross sei~tions, d2o-/dT,r di), . An important calibration and check of the calculations was done by measuring pions produced in the two body reaction,p(p,1r)O . This meas-u:::-emen t and comparison with pre~rio ·J.s results is discussed in Chapter 4. The cross sections for nu~lear pion prod-uetion from carbon and copper are summarized and compared with similar cases and theoretical calc u lations in Chapter 5. Concluding rem :trkd a.nd a summary of this thesis are found in Chapter 6. - 3 -EXPKtD:.fE..~TAL T ~Cifil_I QTJ-3: 2.1 Pion Detgg_:tion To measure d2u/dT,rd.{lfor pions the experimon~al method must allow separation of different en,3rgy pions at each produ ·:!tion angle. A range telescope, shown in Fig.2.1, ,:!a..'1 be used to select particles of a given energy by placing the appropriate amount or absorber mater.ial between the source and the stopping cou:1.:er nuJ.nber s4 . The logic c:>in 1:!id9nee signal for a particle stopping in 1'.!ounter 84 is 1·2·34·5 which is def in,3d to be a "3'r0P". The symbol 5 means no signal observed in counter s5. For a particular thickness of absor'ber several types of particlcs with different en ,argies may be stopped. To d:istJ!'lguisn between tl:11.~ differen~ types of particles, analog signals representing the time of flight between two counters and the :3nergy lost in a third counter are digitized and reeorded in two di:nens.ional his to grams. An 13xample o~ the di.ff eran s mean stopping energies, anergy losses and times of flight in the range telescope used is given in Table 2.1. Fro11 this example it is clear that protons can be separated from pions and muons, however time of flight and energy loss alone are not s:.1.ff icient to .separate pi.:ms and uu:::>ns, and additional ti!!l.ing r9straL-i t s based o.\l the !la t:.i.ral decays of the ,r+ c3.nd JL+ ar e invoked as de3cribed below. The pion to muon deeay ,-r/-t,l+u/J,, has a mean lifetime S2 S3 S4 S5 s. DA DB De 0.6m-'\J 19m ----~~~~~~02 ·m Fig.2.1 Schematic diagram of the range telescope showing target,counters and copper absorbers. I . + I TABLE 2.1 TYPICAL MEAN STOPPING ENERGIES, ENERGY LOSS IN S3, AND TIME OF FLIGHT BETWEEN S1 and S2 STOPPING PARTICLE ENERGY LOSS TIME OF PARTICLE ENERGY IN S3 FLIGHT ( MeV) (MeV) (ns) I \Jl. I muon 69.20 5.89 7.81 • 76 .13 6.55 8.17 pion proton 15 9. 8 14 .61 12 .0 - 6 -of T,r: 2 6.0nS. The decay mllon has a kin1.~tic energy of 4-.1 MeV whe:i the pion decays at rest, which is in general too small for th,3 muon to e.sca.pe the stopping counter and be d0te~ted in an adjacent coun.ter. A l+.1 MeV muon can travel :1.pproxi.na tely 1 • 6 m::1 L'l the counter + + -material. The m!lon dec9.y,JJ,._.8 + lie+ llf' , has a mean lifetime of Tf' = 2 .2 0 JI-S In order t~-:> separate stopped pions from mllons in the telescope a signal corresponding to the pion decay in the stopping counter, s4, is requit'ed within a 100 ns period :following a STOP signal. Th~1s a stopped pion is ind:Lcated by the l::>gic eoincidence - -signal 3-4·5 during a 100 ns gate following the STOP signal which is ·defined to be an "EVENT". . . The anticoin-cidence signals on 1~ow1-:e:rs s3 and s5 el lmL'1ate other part-icles traversing the telescope after -che S,TOP signal. The prob9.bility that a pion will be detected within this 100 ns gate is •1r ai1d will be discussed in section 3. 2. Fig.2.2 aJ1d Fig.2.3 are c~xamplcs of histograms fror:i {i. s;rOPS and a.n .EV~NTS run respectj_vely. Fig. 2. 4- and Fig. 2. 5 are projections of these histogram,s onto the time o::' flight and energy loss axes for the samG two rLlns. Negative pions undergo atomic capture at a rate much hight3r than their dacay ra-~e, henc!e they could not be idcmt-ified by the mothod desc~ibed above and negative pion prod-uction cross sections could not be calculated. / -- ------ -- ·--- ·-·-·· ·- -· - ·--· ----- - -£.-- --------- ··-. ··· -- ---· ·- - -- ··-· I )( I I I X _I _ I I I V I I t -- I ·- ' X I I T t X I ~ ! .. t : I X T I I I -· X . I t I T X I l T - -. -·- -I X I T I I X __ I . 1 .. I I 1 I X I I I _I _ X t I T IBS . 1 1 1 1 1 3 1 1 2 1 Fig. 2 . 2 Two di rnenslonal histogram fl' om a s·roPS run. This particc1larrexarnple is fo:- 32 MeV pions produeed a. t 1 50::,, fro,n 8a rbon by 500 MeV protons. The number system used in these figures is base thirty, such that the number 311 is written 1ox30-t-11l<1: .AB ., 2 5 4 2 5 3 2 2 1 4 '3 1 1 1 2 3 1 1 1 2 _ _ .3 5 5 6 . 1 1 3 B 3 B 4 2 2 238463 1 1 3 4 9 9 A 6 l ,11 #'1 ~7Ar-7, -1 2 8 E H 7 2 1 l .. 2 1 3 G L C 7 5 3 1 1 1 ·1 1 1 2 1 1 3 9 M K A 2 4 1 • 2 . 2 9 F H F 9 2 2 1 _ ·-· 1 . 1 ---·-· ·-· -··· .i_ __ 1 --· . -1 3 5 C M19 n C 4 l 1 1 1 2 3 e Elll"- r:> .J 9 2 1 2 2 1 1 2 5 SPlAlDl'>K 4 6 1 1 1 1 1 -,. -,, A1t,1<=111fl a , , , . , . . 1 2 6 C MlSlPlO K 5 2 3 3 1 3 1 5 P1G2L221C r:J 6 5 1 2 1 1 3 1 A M1D292S2511 6 6 2 1 1 1 ---1 -- 2 - 6 . Gl 0354431 lR 8 . 4 4 1 2 - 2 -- ··- · - 1 - -- - -- - -- ---- -- - -1 p Al32L3K40?C T R 6 3 1 l 1 1 3 4 E2':l415T3,15 R 9 5 2 2 1 2 1 3 D1P5H5')111H () 4 3 2 2 1 1 l A1 0 '• 7r.; 1"1 11 c; 0 q fl .,. , . 2 2 P2H40:!1)1C l 5 . 3 4 ? - ___ _ l ... ? . . - .1 l . . . l . . . .. ..... t. ___ _ l 2 l A 2 :3 l i t l 1- · 2 1 G24322fl O .Jf<J 4 3 /\ i sr22 ·6·2m ·1 2 3 ------------ --· ·- ··- - ----- - ----- -- -2 .. 1... Cl O J 9 7 5 5 7 1 3 1 ... .. ···-· - · -- ------ -- - · - -- -1.. 2811.53355 2 2 1 2 2 4 3 5 '.'3 5 2 3 l 1 3 . n-:>µ. 2 2 l 3 2 5 2 2 l 6 4 2 2 l 2 1 ? , .. , fl ., , "' .. ., ,:. fl , , 2 2 5 4 3 6 4 6 3 4 4 4 l l l 1 3 2 t j ~· i ; 5 3 2 3 4 3 1 E~'E"0 Y 5 1 6 6 4 2 2 3 4 2 1 3 ---~ -~ -'--:_?' ' _____ 1 s·- -2 . 1 _ 1. 2 A 6 G I B G 7 . 8 2 3 1 1 .. .. ..... -- -. ... . LO$S 4 2 A E H F J D 9 7 2 4 1 1 2 1 6 8 E G Q G F M l A. 7 2 1 l 1 1 LIMiTS 1 1 5 3 6 9 Jl6 r> Pl7 K F 4 5 2 l ' ? ? ? "'r:1<s H '\ 1 q n1 1 "'"' b .... , "> 1 1 2 5 0 a I T R N D C A. 3 1 2 l 1 1 2 5 B 9 K F J F L D 5 4 1 l l 1 2 9 8 F F D H M C 7 4 3 2 1 l . --- - - . 1 . . 1 3 3 9 6 F j K L . D G B 3 3 3 . 2 1 .. ··- --- .. , 1 3 4 5 6 A K H s N L 8 2 4 3 2 2 1 2 3 5 4 9 M T13 LL 7 4 5 1 l 1 4 l 4 4 4 A. 4 C 9 9 7 3 2 1 ? .. .. , ? .. fl c; , :> .. , , , ·-l 1 3 2 l 2 1' 1 1 1 , 1 I , , , 1 l 2 1 1 l '-' l 1 -----· ·- --·--- -· --- ·--- --' ~ ,-,ME of FLIGHT LI C\1 iTS 1 -1 1 1 2 2 1 1 _1. 2 1 2 1 4 5 4 3 1 1 1 1 2 2 1 1 - -·- .. ,. - -- . - ... . .. -····-- ·- · ··-· I I X I I 1 X ___ l I __ , I 1 1 I I . -)( T . I -t )( I I - -I I X T I - - I - I .. X ··--I I I ' X I I I -·- -- ---- -···--· · I ··-l X I ' I I X I -I I I y I I I .I. .. . _ X l T I ·- · ...,._ I - I --------- -- ----- ----- - -- -- ------- - -- -- - ----- - --- -- -- -I X I ··-- ·- - ..... ·-·---.. - .. ·-··-··-- ..... - -- ·- ·-- -------------·-· I -- - I I X I I I X Fig . 2.3 Two dimensional histogram from an EVENTS ru.~. This particular example is for 32 MeV pions produced at 150°,from carbon by 500 MeV protons. I ! X -- ·I . I I I I I I -1-- - ---- - --- -- - --- - - ----- -- - --- --x I I 1 ·- - --- -- --- ------------ -- ·- --· . --------- --- --------- ---- --- --1 --1 I I I ! I _____ 1 X I I _j =--- --- -= I I X -··- ----· -·· - -- ---- --- --- - - ---- - -- ------- -I X I _ __ 1 _ I I X - ------------ - _! _________ ___ ______ __ ·1·---12 ----··· - I I 1 1 2 1 1 I I ___ 11 X I i --------- - _ __ .EH~B_G.~-- ----l-.OSS .1. 1 L \1¥1 iTS I I X ·· -I I I I X :f I I ,, 1 1 1 1 , 2 , 1 l 2 2 1 2 1 1 1 , 2 1 1 l l 1 1 l 2 4 1. 4 . 4 2 5 1 4 5 2 5 . 3 lJ. 5 1 1 2 1 I I . . ·······-------- -.LI---·-- - ------- ------ - --- -- ·- X ·-·· 1 l ... l l l , 1 5 2 1 2 4 l l 2 1 3 2 3 3 2 4 1 6 . 5 5 4 2 2 . 2 6 8 4 3 3 f3 7 1 1 7 D . 8 fl 'I G 6 1 2 6 Fl A 5 D 3 2 1 1 0 Q B Cl -~ z !:l 3 3 7 D D 8 9 3 2 2 2 5 A 4 3 3 8 l l 1 4 3 1 3 1 l ··-- .2 .3 . 1 .2 . 3 2 __ l l 1 I 1T I I I ' X I I - --- - r __ .. -· - . ·•·· ----- ----- ----- -- - -- ! 2 1 1 2 I 1 ' I I )( -- ---- ----- -- ·- _ ___ __ ____ ! __ _ \. I I I 1!.. I I ! - · I X - - ~------ ----- ---- ---- --------------- - - .I - -I I I IEQ ilME of J:LIGHT .... i X I I 0 (I) ... z ::, 0 u LL. 0 a:: hi m ::, z r Cl) t-z :, 0 u II. 0 a: Ill m :e ::, z 600 400 200 0 10 20 ENERGY 800 600 400 200 - 9 -p 30 LOSS IN p '! .,,,., fl, 40 50 60 s3 .< CHAN~EL NO.) ~u1creas1ng energy increasing time 0 _ ___,m _______________ ----,1.___ ___ _ 10 20 30 40 50 60 TIME OF FLIGMT BET\"/EEN S1 AND S2 . (CHANNEL NO.) Fig.2.4 One dimensional histograms of energy loss in counter s3 and Time ~f Flight between counters s1 and s2 for a STOPo run. . u, ._ z ::> 0 0 LL · o a: w CD :E ::) z V, t-z ::> 0 0 LL 0 0::: ul al => z - 10 -1T 60 40 20 increasing energy - ~ 20 30 40 50 60 ENERGY LOSS IN S3 ( CHANNEL NO.) 60 40 20 increasing time 20 30 40 50 60 T_lt~E OF FLIGHT fJETVIE~N ~1- AND1 S2 Fig.2.5 One dimensional histograms of energy loss in counter s3 and Time of ~light between counters s1 and s2 for _ a~ EVENTS _run._ _ _ - _ _ _ _ ______ _ - 11 -2. 2 CQ1J.11:ter. Teles cones and Ele_c..t,r:.,Q_l1l~ The experiment was perrormed at tha proton target a..."li scattering stand,P'r1 , in the external proton line IVb at TRIUMli', as shoW~'l in Fig. 2. 6. The range telescope eonsisted of five NE,021 plastic scintillators coupled with lueite ligh t pipes to photo-? multiplier bubes·-. Counter s1 was posi tio1rnd as clDse as possible to the target. Tim remainder J.f.' the telescope was positioned at the back of a mobile boom giving a reasonable time of flight distance betwaen s1 an.d s_2 • The area of counter s1 was kept small in order that the counter shou l d not become saturated. Sa~uration of counters occurs when particles are arriving at such a rat;:3 that the signals 0 1,e.rlap ;:,r that sufficient cu:::-rent to amplify the signals in thB photor:rultipliar c3.Ilnot be supplied. The areas of counters s3, s4 , and a5 were chosen sueh that all particles passing throQgh the telescope could not miss coun~e:::-s5 giving a false STOP signal. The solid angle of the telescope was set by. counter s 2 • For so11e moasurements it was advan~ageous ( se ,3 section 4.1) to replace ,~ou.nter s2 with a smaller :1.rea counter, which has been labelled counter "X ", to reduce the solid a.."1.gle of the telescope. The dimen-sion of this counter and th,~ other telesco:pe d :Lrnens ions 1. Manufactured "by Nuclea r Enterprise s 2. Manufact,1red !)Y TI.CA, tube model 3575 - 12 -C:----------t TARGET~ PTI PROTO~o MONITOR -------48M6 CYCLOTRON VAULT RANGE TELESCOPE ON BOOM MONITOR TELESCOPE HE LI U r~1 ION I Z AT I O N CHAt\1BER . Fig.2.6 Diagram of the external proton line IVb at TRIUMF showing position of one of the u~.of ,A. remote controlled b~om,proton beam moni~or location, , monitor telescope, and helium ionization chambar. - 13 -are given in Table 2.2. A rem.Dte eontrol dGvice was built t o change the amount of copper degrader in the telescope. The dimensions of degraders available and thP. correspondi:'lg range in energy of particles stopped in the telescope is given in Table 2.3. The position of degrad0rs DA, DB and De are shown j_n Fig. 2. 1 • These energies were calculated ·:rsing range energy tables (Barkas and Berger 1964-). Fig.2.7 is a sch13mat:f.c d:lagram. 'Jf the degrader transpo.rt. A schematic diagram of the electronics used w'ith the range telescope is show.a in Fig.2.8 . The tj_me of flisht me1.su:rement was done with a Time to Amplitude Conv9rter · (TAC)1 utili~ing s2 as a star~ signal and a del9.yed ;.11 as th1'3 stop s.ignal. The TAC outp~t ? was d:igi ttz0d~ a....'1d stored a.s one vari3.ble of a two dim-sional histogram :ln a two dim.ansional pulse height analyzer. 3 The s3 signal was split into two parts. One part was utilized in. the digital logic to dete:::-mi:..1e .if there was a stopped parti::l,s, and the ·'Jthe:- part fed thr:)ugh a linear gate :,1.nd streteher :1..nd th,3nee to an Anal::,g to Digital Converter (ADC)2 to be used a.s the second irariable of the two d:l:.nenslorn1.l ~'l.istogram :L'l the pulse height analyzer. An - -EV"~NT was recorded if a 3.4.5 w:i.s observed du1~ing a 100 ns gate which was generated 22 ns after the end of the 1. Ortec model 4-37A TAC 2. Nuclear Data model G.EN II ADC 3. Nuclear Data model 24-00 TABLE 2.2 RANGE TELE SCOPE DIMENSIONS COUNTER DIMENSIONS COUNTER SPACING counter S 1 3.80cm•3.80cm1<0.32cm target to 51 64.7cm S2 8 .86 8.86 0.32 s, to s2 186. I _., + I S3 , 15.2 15.2 1.27 52 to s3 13.0 S4 11.4 11.4 0.63 53 to 54 4.43 S5 12.7 12.7 0.63 S4 to S5 1.27 II x" 2.54 2.54 0.32 s1 to II X" 167.2 TABLE 2.3 COPPER DEGRADER DIMENSIONS AND CORRESPONDIN G ENERGY BITES DEGRADER DEGRADER DEGRADER STOPPED .,,- ENERGY STOPPED 7r DA Cu De Cu De Cu ENERGY BITE ENERGY ENERGY BITE (cm) (cm) (cm) - not including target- -with OJ89 g/cm-2 C-(MeV) (MeV) (MeV) (MeV) no degraders 21.75 3.65 22.69 3.54 0 .32 31.26 2.97 3 2.0 0 2.93 0.95 0 .32 52.81 224 53.35 2.22 2.2 2 0.32 75.68 1.8 8 76. 13 1.8 8 2.2 2 1.59 0.32 101.24 _ 1.72 10 1.65 1.72 _., \J\ 0 BEAM DIRECTION REVERSIBLE MOTOR COPPER ON BEARINGS COPPER DE GRADERS RA NGE T ELESCOPE +- SUPPORT STRUCTURE Fig. 2.7 Schem~tic diagram of the copper degrader transport. Each pair of degraders are mounted on bearings and are moved under the control of a reversible 110 volt motor. Positions of the degraders are indicated by a series of microswi t .ches. __. O'-. DIS CR IM IN ATOR S 1.2 CAtv1A C _ I rDrrr< ) ;:::::n 1~·3-~-s s,~ DELAY ,c 1·2 STOP TAC KEl D discriminator c:> CA..\1.AC scaler o,coincidence XADC s2 SPUTTE s "~ 3 S4 S5 LINEAR AMP GATE Fig. 2.8 Schematic diagram of the range telescope electronics. Y ADC START TAC IOOns GATE II II STOP 11EVENT 11 _.. -...J - 18 -S'.EOP pulse. The monitor telescope consisted of three plastic scintillation counters pa1':-na: en tly positioned to detact scattet>ed particlGs fro:;n a thin aluni:rnm :'oil at monitor l0cation 4BM6 shown in Fig.2.6. A diagram of the monitor telescope is given in Fig.2.9. A 1 .25 c~ copper absorber between counte-r 112 and counter M3 imp1•oved the definition of a logic I:J.o:.:iitor pulse, 1 ·2 · 3 , by set ting a lower limit for energy of scattered particles. The di~ensi~ns of the monitor counters are presented in Tablo 2.)+. A schematic diagram Jf the electronics for the :n~nitor telescopa is rv given in Fis.2.10. The symbol 1 means a delayed counter M1 signal. Each experimantal run consi.stad of ,1, :neasu.rement for a particular L1.cident proton ern~rgy, -pi,)!l production angle, pion energy, and target. A CAMAC1 data acquisition system ') using a NOVA 1220 minicomputer::... ·..ras used to record the data during each run. Single cou .. ntar 1--::ites, numbers of :3'.rOPS and EVENTS, !Ilo:ni tor telascopa counts a::1d :'.'andora counts, ion ch.am-be-r c,.1rrent i:ategra tion counts, and li v-etime were recor:ied in the computer f,J .r each r1.in. In add:ition to this information experiment parameters f~r each run, such as target thick-1 • Modular Inst-ru .. --nenta tion System, U .S .AEC Report TID-25875 2. Data General Corporation ALU~v11NUM FOIL ~11 M3 k"' PROTON BEAM DIRECTION 1 ~SCATTERED PARTICLES /coPPE R ABSORBER Fig. 2.9 Schematic diagram of the three element monitor telescope showing scattering foil, cou.nter3 and copper degrader. ....... '° TABLE 2. 4 DIMENSIONS OF THE MONITOR COUNTERS COUNTER M1 2.54 cmx2.54 cmJC0.32cm COUNTER M2 5.07c m "5.07cm><0.32cm COUNTE R . M3 12.5 cm x 12 .5cm • 0.64cm f\) 0 M1 M2 M 3 DISCRIMINATOR CAl\1AC SCALERS ,.., 1·2·,.,. ., ,a. I i:J I I 1 :::D=( J _4' , • 1·2·3 Fig.2.10 Schematic diagram of the monitor telescope electronics. sur~, of RANDOrv1S f\j - 22 -ness, and material, stopped pion energy, incident proton energy, monitor calibration ., and pion prodllctj_on angle , were read :in';o the compL1ter for a prelim in ary analysis at the end o::' each run.. A listing and guide to the data acquisition computer program is given in Append:ix A. The analogue information .in th,3 two dime!lsional histograms stored in the two di 1uensional pulse height analyzer ·11as tr an.sf er:red to magnc9tic tap e at the cor.lplet-ion of each run. 2.4 Beam MonitQrin,g_ The three element monitor telescope has been described in section 2.2. Calibration of the monitor teles cope is discussed in section 2.5. In order to demonstrate that this monitoring scheme was linear over a wide range of ineidant proton beam intensities, a series of measurements of monitor count rate was made. This count rate was compared ·:;o the rate measu :red with a helium ionizH.t:lon chamber (Stetz : 975) located in the pro ·~on beam about 1 m downstream o:' th ,3 monitors. Measurements by the University of Alberta group indicated that the ion chamber was linear over the range of currents used daring this test. The statistic9.l uneertainty due the ntunbers of counts in each rw1 was typically 1 • 5.i and the standard deviation in random corrected monitor counts was (Dlnly O. 6-'1. Ion chamber co1.1r1ts were recorded throughout the experiment and. provided a check on all monitor calibrations. - 23 -Duri:..1g a 100 µ.s period following a s·roP pulse the discriminators of the monitor c-::rJ.nter.s were shut off S·:J that no monitor counts would be recorde d while the range tel,3s cope was inactive. 2.5 Calibration of the MonitQ.r Tel0scou§ The monitor telescope was calibrated absolutely by an activation techniq11<:L Carbon targets with areal density 0.344 g/cm.·2 or 0.858 g/cm 2 were activated for a short time with a beam intensity about the same range as that u.sed throughout the experiment. The activated foils wer9 placed between two alum.1num foils .so that posltrons from. the decay lie ( r.,+) II 8 . . /J . would promptly ann1h1la te . The foils were placed adjacent to a NaI scintillation counter wllich was used to observe thi:~ 0.51 MeV arrr1ihilation gamma rays. Repeated 200 second pulse height spectra were recorded on tape for .several hours after th,3 activation. Th•a number 12 II of incident protons was calculated from the known C(p,pn} C cross sections and the nu.,"D.ber of 11c nuclei produced which was calculated from the number of annih i lation gamma rays observed. Fig.2.11 is a graph of 11c production cross sections ( Cumming 1963 ). Details of tho calculation are given Appendix B. In order to cher~k the method of recording pulse height spectra and backgrollnd subtraction in the ASPEC comp.1ter 55 50 45 ....... .D - 24- -12C(p11pn)11C PRODUCTION CROSS SECTIONS 40 ....... u =~ 35 b 30 25 20 ________ L_ I I L 100 200 300 400 500 600 700 INCIDENT PROTON ENERGY ( MeV) . -· -- --- - n - - ---- - -Fig.2.11 Graph of C production cross sections based on a review by Cumnings (1963) - 25 -code, the areas of the O. 51 l-'ieV ea!IE'Ja peaks for a series of spectra have been plotte o. ag :.i inst time in Fig.2.12. From the slope of this curv 9 th ,2 half life for II C ( fJ+) 118 was calculated to be ( 20.3 S:Q.I) min. ,in ex ·~::;lJe,nt agreement with (20.39 i 0.06) min. {Ajzenberg-Selove 1968). Th/3 effic1-an.cy of the NaI crystal was found by measuring the O. 51 :1av gamma ray produced by the decay positrons from a c~libratad 22Na source 1 in the reaction 22Na(,8"') 22 Ne with the source :tn the same position as the activated c::1.rbon fo-Lls. Table 2.s is a SUIDllary of the NaI crystal efficienc y meas ·J.,':Jments. N( t) is the activity of the cal:iora ~e:4. 22Ha source corrected for the date of each m0asu :reme:1.: 11s ing a hal t"LU 'e for the decay of '•12.: 2. 602 yr. (A~·1spa~l1 1965) . The product of efficiency and solid a.1.gle f,-)!' the NaI cou.n.ter is given by: _ ( 0 .51 Me V y co u n t rate ) ----------------~+ 2(Ec+1PN(tl t where the ac ti vi ty at tim3 t, N ( t) , :1!?.:3 been multi plied by a factor to correct for the decay by electron capture. The average ratio of electron captu:re decay s to positron decays is 0.1044 ( Williams 1964, Leutz 1964, Vereshchagin 1968). 1.l'{ew England Nuclear,calibrated on September 17,1973 -lO • 0 z en 1-z => 0 u 1cq 5 0.1 130 - 26 -135 140 145 150 155 Tl~1E OF RUN (x3. 40 min.) Fig.2.12 Semilog graph of the area of the 0.51 MeV annihilation gamma ray pe ak,with backgroand subtraction, as a fun~t i on of th8 time of each observation. 16 TABLE 2.5 SUMMARY of N al CRYSTAL EFF ICIE NCY MEASUREMENTS MEASUREMENT DATE 22 No SOURCE 0.51 MeV 0.51 MeV E.0. IDENTITY ACTIVITY N (t) y RAY y RAY (I0- 2sr) (yrs) ( I0 4 cts/s) COUNTS COUNT RATE calibro tion 1973.70 4.66 TRX2 197 5 .29 3.0 5 8514 425.7 0.771 I\) ---J TRX5 197 !5 .30 3. 05 41640 416.4 0.757 TRX9 19 75. 52 2..87 3 94004 '394.0 0.758 TRXIOa 1975 .54 2.86 394 531 394.5 0.765 TRXI0b 1975 ~54 2.86 3932 86 ~93.3 0.762 TRXIOc 1975 .54 2.86 39230 4 392...~ 0.760 TRXI I 197 5 .56 2.84 77940 389.7 0.758 TRXl4 1975.71 2.73 73814 369.1 0.747 TRXl6 1975.72 2..73 75371 376.9 0.763 - 28 -The ratio of beta decays to to ·~al decays is: 13+ - 1.000 = 0.905 -EC+ /3.,. 0.1044+ 1.000 Table 2.6 is a summary of th,3 activation measurements performed du.ring the experiment. The monitor c0unters after April used improved. photomultiplier t1.1bes for higher rates. Other variations in the monitor calibrations reflect small .changes in monitor geometry between runs. For those runs when the ion •:!hamber was available, an ion chamber e,1rrent gain was calculated for comparison with p-p scattering measurements made by Kitching et al ( 1975) . The calcala ted gains were in good agreement an.d provided an. independent check on the absolute beam monitoring calibration. TABLE 2.6 SUMMARY OF ACTIVATIONS FOR MONITOR CALIBRATIONS ACTIVATION PROTON PROTON MONITOR PROTONS PER IDENTIFICATION Et4ERGY CURRENT RATE MONITOR COUNT (MeV) uo10p1s> (cts/s) TRLY (22/3/75) 500 3.94 4. 63 -101 8. 51 · 105 1RX6 (24/4/ 75) 500 2.98 3.31·10 4 9.00 -105 f\) '° TRX7 ( 4'7/75) 500 4.12 6.12 · 103 6. 73·10 6 TRX 9 ( 11/7/75) 500 2..56 3.90-10 3 6 .56·10 6 TRXII (26/7175) 500 2.76 3.98· I0 3 6. 94· 1<>6 TRX2. ( 15/4/75) 450 1.45 l.55· 104 9.55· I o5 TRX 18 ( 2/10/75) 450 2.49 3.26· 103 7.63· 106 TRX 16 ( 18/9/75) 40 0 1.42 1.40· 103 I 0.2 · 1<>6 - 30 -3 1 D 'f" L' 1 C r, L' . J_ 1 e-ren .,J _a ..... __ IQ§.§. .... 9 .. ~.:::! ·..,lill.lli The cross s,zctions were calculated using the equation: d2u dTmJSl -- ( 3.1) where _: N'JT is the number of evants detected by the range telescope. These ara siiply the stopped particles with a pion decay dGtected. f11 -is t~e correcti::m for · proton contamj_n.ation as found from the two dim en sional histo-grams. This correction eli:ni .. 1ates fal.39 EVENT s:Lgna_ls generated by a stopped prot::,!:1 and a pion which had previously stopped b1.lt took longer than 100 ns to decay . . Nt is the nu:nb,er of target a toms per unit area. Tabla 3. 1 contains a list of Nt fo.r the targets used i:i ";he experimant. a is the t'3.rget angle as shm•m i:1 Fie.3-1. Np is the number of protons incident on the target as determined by the projuct of the n1unber of monitor couI1ts for that r'ln and the mo::1i tor calibr:l.ti,Jn for tl1at si.3ries of runs. n is the geomatrical solid angle of the pi,)n rang ,3 telescope. The solid angle w~.s deter:nined by the counter in the s2 position. The no:-mal telescope had a solid ar1gle of .(1~25 !0.QI) fOSr. and the teL:iscope ',vith t:-ie "X" counter had a solid angle of ( 1.19 t 0.01) · I 0- 1 msr. - 31 -TABLE 3.1 TARGET PARAMETERS IDENTIFCATION OF TARGET (mnemonic) U.of A. Carbon (UACA) UVIC Carbon (UVCA) UVIC Cu11A11 (VCUA) AREAL DENSITY Nt (g/cm2) tatoms/µb) 0.20 1.01·10-a 0.37 8 I. 9I· I0-8 0.591 5.61·10-9 UVIC Cu "THIN" (THCU) 0.149 l.43·10-9 U.o f A. CH2 (UA CH) ·o.Ia9 8.14 · I0-9 . UVIC CH2 (UVCH) 0.147 6.32· I0-9 all target nreds = 5•5cm 2 - 32 -NORMAL to TARGET .,,,,. ,,, ,,, ,, .,,,,. ,,'a PROTON BEAM Fig. 3.1 Orientation of target showing definition of target angle. · - 33 -as given by ·cn8 Mon~Q Carlo pr0 5raa Rl~VMOC (Kitching 1971) ~1ich included the effect of pions orieinating throughout the t:1.rget. fl. T -.r is the errnrgy a.cceptance; of the pion range telescope as d L,cussed in section 2. 2. _E.,,. _is the pLm dotection efficiency which is si,nply t~1e r:itio of pions d-atectad to the nurfJel' o:e pions stopped in com1ter s4 . <=0 is the pr.Jbability that a pion will :iot suffer 11uclea1' :1.bsorpt1on or inelastic s,~attering in .E traver~ing the telascopa. , el is the pro~ability that a pion will not be 16st becauss of m1claar elastic scattering. ·.e m is the probn.bili ty that a pion '.vill not be lost beca.usa tE of m:.i:!. tipla C,::>i~L)n) S:!a t taring. d is the pr ,Jbabili ty that a pion will :.1.ot docay i:..1. t:.1e telascopa befo-re it stops in counter Si+· The estim::ition of the efficiency factors E7r thr,.Jug:1 Em are di:;c·J.s:3ed in t;:ie followL1.g sections. 3. 2 Pion.J2eteetion Eff ici2n~ The pr.:>babil i.ty that a pion will decay dur:L'lg a . . ( I 00 t I) ns pe:-iod beginni ·.1g ·c 22.0 0.5) ns af tar stoppi~g in counter s4 is given 122*1 e.,,. = ( exp (-t/T,r) } T-rr 22.0t.5 dt -- ( 0.41tO.OI) The pio11 lif-atim8 is '1l: 25.Q3!Q.Q2 nS (Chaloupka 1974). The probability t'.:1at mLwn will decay in t:-.e s::Ha.0 - 34 -gate is gi'!e::1 by: dt = 0.04 . The muon l"ifGti11e i c; 't'µ. = 219 9 .4 ns (Particle Dat!l Group 19711-). If all the m:.10!·13 w:nieh co ;1ld decay within the gate were coun~ed as a.n. EVE:NI' a corractton w.:>uld be re-quired, :iowev,~r t,iere is a m-.1eh larger :1.11ount of kinetic energy nvail~bla to t~e electr~ns from muon decay ~1an to the mUO!'lS from pion decay, he::1c,;3 t:1e majority of the muon dacays a.r~ veto9d by t:1e 3·t:··5 , req'.li reri .. ~m t. The val".1e.s of e.,,. -1..1.Sed W,:.1.s based. 0!1 a,:!t 1al ·nea3:.irs-ments at .SH.EL anll oerkeloy (Ja.0.03 197l+), whi..:!h L1.d1.~ated E,r=0.3920.01 in agreem ,J:1t with the abpve calculated probabil.i ty. A cor1"ec tion f Jr the numb Gr J.f pi,J!l.3 wi:li:!h decay in the telas~ope bsfora bai~g datactad as pion ev3nts has bee11 incl, _l'.ie:i :Ln the cros ;3 3ectio:ns. Th l s cor rac tion W3.S calculated fr ·Jl!.I.: ,0 ~d = (exp(-tlTddt = exp(-Th-v> ) -r,r - T -W'nere T is given by: _ T = I ti+ l: ts , - 35 -The t. ars the flight times i:1 the i th air dr.ift of the J. telescope c1..1d. ar.a gi v .::m by; · 1/2 ti = Ii ( I - ,8.2) fjic :i- · 1 · · ' 1 t· f' t' · th d · ft i /J 1· s i: ·-" A me P.,., w .. ier3 1 is -cne _ang n o~ 11e 1. r1 am / i _, ... _ c, ...... velocity i::i t~at dri~t d~?ided by ~he speed of light,c. The second t,3rm L1 tJ1e ,expr-es :3ion for T is t::ie stoppl.ag timG i.:1 where Mo is tbe pion r3.st ~a.ass' Pssc and Ps2C ara the initial. .~11.d final '._nean v ,31,::>ci ti0s L'l t ,31.Jsc :Jpe elem8nt s; p is the density of telGS{.!ope el:3rnant s; a:1d dT /dx is tbe r:i.te of energy loss per w1it araal density for plans i~ telescope el3ma~t s. The t for each ~elascone s -with the r:i.ng ,e in /3 separated i!1:o twe<rty P'il' Gs. The v:1lL1e 3 of the pion decay correc tionE dare s'.ln·1a::-ized i..11 ·rablc 3. 2. - 36 -The probability that piou s were not detected due to nuclear inelastic scattering or absorption, and nuclear elastic scatteri!1g ara d:. =3c·t1.s e d i n se -~tions 3 .4 .1 a n d J . i+.2 . The ft',::..c c ion of st op pin g p :t,J.r1s ·whj_ch ini ~j_all y ha d. t ) ,:1 · i · 1 e-.-, .... 7 y , . .., ~1-.,.,.: 1 c 11 r1'- :.,-. 0 ·b,, -' _ -, ',·7'1·11·c 1.1 1·ntAr"'cted 11 gn a1 ~..,!:,. c !::, ,, ,_, ,..,:.) tJ .L : l . 1,(:,. . •J )+ CA. ,, - · .• :., Ilificant; :~Jr :./ 1.L:3 g~om.et :!'y ;) f t e l e s ~:)pe (Ja >:Ile :3 '1975) . 3 4 1 N 1 => "" ,· .. , '· -· · r · ·-· . .:i I · · 1 · ·i· • ,... S t t :::>l"'-', r. -,, :. -. t · · r ,~ · •• 1UC.,.. •-.1.r auS ·,) 1. pL,10.l ,3.l l . .1. n e .)AS . .,1,"" · cq,__, -_ _ _..__,ill JOr:.,,,,l,,,l ,) .. b CQ is t~e p.l'obabil:i ty that a pi r.m W:l.S £1:'.) t de t ,3C ted d·2e to t l1e effects c:>f mlcl~a:- a b3 )rp l.;i.)n or nucl~ar in-elastic scattering . This probabi -Lity i s gi~en by: :r,,. .. Ea = exp ( - No 0"0 dT ) · A o dT/dx ,r i"' . A • -·1-,, · ' ;,r , ,_ -~..-. " i"" ~: '"' +- · .: ,.. • rrht .,:, where 1~0 ·=> vog:11. .!J s H ,lUl .Jl. ... , ..:'io .:, ..,:'.l,,,, a..,·::>ffiJ_..., we1 0 OJ. the material, CTa is t:-:1e total rsac tion c ross ,.met ion f()r .. nuclear absorpcion and :L1e1 ,1sttc s ,.!atte r ing, ~n.d dT /dx is the rate of 3nergy loss par 1~tlt areal density for pl 8ns. The i :'.lt13gr'ltion w~:1s p;arform •.:J .'i. n i.1,-:n;;Jri 1.:!al l y 11s L1g Simps ,.:m' s . . r)f era nd dT / dx wer(; stored tn the in ta gra t1o .a p :..'C>g:.. ,'l i.ol as -1. ftL."lC ti::rn :lf ~C 9.nd t :1e m;:1.tar:tal. Th e t'Jtal reaction - 37 -cross sections were taken from a compilation of available data in the pion energy range less than 300 MeV ( James 1 975) . The computed valwrn of Ea for each stopped pion energy are given in Table 3.2. 3.4.2 Ny.clear Elastic Sc 3 ttering Cor1~ections Eel is the probabil tty that a pion was no ·: detected due to th 13 effect of nuclear ela.s tic sea ttering. This probability is given by: •e1 = I - a ( 1- Es) where a is the fraction of elastically scattered parti-cles ¥hich miss counter s4 and E'S is the probability that a pion was not elastically scattered. ES was cal-culated ·by the same method as Ea using the equation: •s = exp ( -No / T.,,. 8cr0 dT ) A O dT/dx where 8 is the observ·ed ratio of the total nuclear elastic scattering cross s13ction, ere, to(Ta . 8 was taken to be 0. 6 ':t O. 1 ( Kessler a11d Lederman 1 954, Dzhelepov et al 1957, Koltun 1969, and Binon et al 1970 ). For this telescope geometry a has been estimated to be O. 2 :t O. 1 ( J amas 1 975) . The computed values of Es and Eel are given in Table 3. 2 - 38 -As a cha~gai particle travel3 t~r0~gh the r~uge tel.es·:!:Jpe i i.s .1•3pea tad:y scA. tt:)J'.'Jd fl;{ 1)u3 Coulo:nb 8..E7::1oc (Kitching 1 ·;)71 ) is a Monte Carlo p t·og::.•.'.l:~ whtc'.1 will Cou .. l,ynb ·,1u1 tlpla s,:!a t te ring is .. Ti·1~_'l" 'l"T ·1· '"' ,._ - - . i .,:, cope count:ar Si+' when multiple s,".!a.t te i'.'lng w1s cal -.:mla ted. The val-aos :)f•m a.re give :1. i.n Table 3.'.2. of f t .. . ·t 1 l" i . o. ne varia) 03 r .l :'>CUS:39 : J.n r -~la ti7e, va.r:r ::.ng f rqm run to r ·.v.1 or. between different pion TABLE 3.2 VALUES OF CORRECT ION FACTORS STOPPED Tr Tr DECAY NUCLEAR NU CLEAR ELASTIC COULOMB ENERGY CORRECTlON ABSORPTION SCATTERING SCATTERING (MeV) Ed Ea Es .. , Em 22.69 0.533 0 .993 0.9 96 0 .999 0.701 *0.0 05 ::1:0.001 ~0.001 =0.001 zQ.012 L,.J '° I 32 .00 0.606 0.980 0. 988 0.998 0. 833 *0.006 :1:-0.0 2 =*0.002 •0.001 *0.015 53.34 0.685 0.92 8 0.95 6 0.991 0.725 *0.007 *0.007 *0.007 •0 .004 ~0.017 76.13 0.734 0.844 0.903 0 .981 0 .100 •0.007 "*0014 *0. 015 •0.O10 •O.014 IOI. 65 0.772 0.735 o. 831 0.966 0-747 *0.008 •0.021 *0.025 •0 .017 410.014 - l+<) -energies. Other uneertainties are absolute and are comm.on to all the measurements. The m-:1.jo1" relative uncertainties arise fror:i. counting statistics in N.,,.and f 7 which vary between 2 and 5:i. At some forward ,s.ngle measu::-ements the values of f7 were taken from higher s ta tis tics runs with the samo produ~ti ::m angle and pion ene-egy. The uncerta:i.nty in .';arget angle was to.1° and was consid0red :insignif:icant. Th•a absorbe:::- and counter thick .. 11.esses a ... rid d:L.rnensions were well kn.own henca L111certainties i.n.6T11 were consiiered about 1}&, iue mainly the Ut1(!9rtaL1tiGs of the range energy l'.JSS tables and the lower 1e~1el bias on the discriminator for cou.nter s4 . The uncertainties inEdware esti ·~ated to be about 1%, 9.lso d:tl.e the ~.1ncertaintias .i:1 tb.e ra-i.1g?. energy loss c.q,l~UL3.tions, whi(!h set the i:ategration limits. The ,1ncertail1ties i:a Ea and Eel •rary betwee:::1 1 3.nd .2% fo:r inc::::-easl11g pion energy and are dm~ the esti:>na.ted 10% uneertainty ina- 0 . The uncertainties quoted :ln E mare sta tistj_cal only arising from the nmnber of rays in the Monte Carlo program which were accepted into counter s4 . The largest absolute uncertainty ar i ses frm:i the monitor calibration.. This ?lo uneertainty .is do.t:1:.1.ated by the estimated. 5,:ti uncertainty in ~he 1 \~ proauction total c:r-oss sections. The measuring unce:rtainties in Nt were approK-imately 0.1% and hence were neglected. The 3% uncertainty in E-,, is a result of the measurements of pi:::m detection efficiency. Th,3 uncertainty in solid. angle.(), is less than - 41 -0. 5%. The effect of the slightly distri but ed .:iource was checked by comparing the sol i.d. a ... YJ.gl e f r om -~he REVl10C calculation with the geome t:r i.c a l cal culq, tio.::1.. :-Jo signif-icant d:i.fferences were obsar v-ed . 3.7 Samnle Calculat.1Q11 The differential ~r oss section for 32. 0 MGV positive pions produced at an angle of 150°, fro m carbon i s calculated in this section. The inci:len r, pro t on ,3nergy t' ·::>r t his case w::1.s 500 ~eV. The histogra.:.o. f o:- an adjacent s·roPS rw1., shown in Fig.2.2, gave time of fli .ght and ener gy l:)SS lim i.ts for use in the EVEN:' S r1.111, histogram shown i n Fig.2.3, to find f-r = 0.99•0.02 . Fron t h ~ mollito r calibration for that series of runs and the number of.' mon itor counts for that run, N was fou :'ld to be: . p .. . . . ... . Np=(9.0:!:0.6l·I0 5 protons (9.807·10 6 )monitor monitor counts counts = (8.8 -~1012} protons The other pa.ram.eters for this r un arr~ listed bs .lov. N1r = 53 8 t 23 ~.,,. = 0. 39 :!:0.01 Nt =(1.01 tO.Ol}·I0- 8 atoms/µ.b a =(20.<;)1 0.1)0 . Ed = 0.606 :1:Q.006 .{l · =(1.25 :tO.Ol)·I0- 3 sr ~Tr= (2.93!:0.03) MeV Ea = (0. 98 :!: 0. 0 I ) Ee, = I. O O :!: o. of Em : ( 0.83!: 0.02) - l.+2 -;-;s lng equa tbn 3. 1, the di :.:,ferent1;'.tl :!ros::, s ·e:)tton f .)r this case is: 2 d a- = (7 99 2 0 76) p.b/MeV·sr dT1rd.O . . The unc8rtainty qlloted i::.1cl·J.d13s .1.ll 3.DS;)l ·J.te a!ld rel3.tive 'J.ncertainties c.iscussed :L'l saction 3. 6. - 4-3 -ANi\LYSI3 OF TWO BOJ2._Y 11&\SUREMENT~ The :mo::1itor calibration, ·3nargy bit e s, :i.nd. pion d.Gtectio:a efficiency of ~he telescopa were checked by a measurement of do-/d.0. for the reaction p(p;r)D, for several pion ern~rgies for w:i.1i,~h the c:-oss section has been independently estimated using energy dependent fits to the total cro.:,s section.. At each of t.he L'lcident pro to!l I • C 5 energies ·+OO, 1+JO 9.:nd 00 MeV, production aY1gles were selected ~1.ich prodaced pions energy h:ttes of the tel -ascop:a. rhe kin~::i.attcs :Jf this c3.l ·~!llation are considarsd sectton 4.1.1. Not all of the stop9ed pion e:iergies C;:nld. be meas:ired at each of th 1.3 incide:it proton ene:rgies beeause of the physical lim :·.tations of the sc3.tte:ri11g chamber. To ensure that the nax:im:~rn. p:i_ J!l yield was bei:ig detected f'.)r :i. p .:1.rticular pion telascopa energy, m a.ng:1lar distri·bution w:is me;1.surad a':)o·:.1.t the cal ,::mlated pr•oduction angle. This method was used ra th•.:!r than varying the primary p1·oton energy in small steps be(!'3.;.1s3 changing the angla was fa.star than t,1crementlng the pr:J t,Jn en :3.rgy. An ang ,.1lar distri:mtio~1 foJ~ t11e t'.!ase of p.lons produced by 1+5CJ MeV proto!ls i~ t~e vici~ity 0f 82° has been plotted in Fig.4.1. Thi:=i figu:-e clearly shows a background co:ntri'butio!l from tne carhJn wi1ich is present in the CH? ta.rg:'3t as well as ttt ,_ lower angles fro:!l. the reaction p(p,p,,,n. ,.._ ... Cl) 50 40 ' .0 30 20 - 44 -- ------ --- - - - -0 carbon background · 0 0 Q ____________________ _ 78 80 82 9,4 86 81r (degrees) Fig.4-.1 Observed angular distrih:ition of pions produced by bombarding a CH2 target with 4-50 MeV protons. - 45 -4-.1 CalQul_.~1.on of Di ·fferentlal Cross Sections 4-.1 .1 Twq__B-9..d_y Kinem ,1.ti -~3 an d Relatild Fact ,:n·s _ The Monte Carlo progra ,n REVMOC noi-·mal ly would be used to .• .. -model the range telescDpe. In REVMOC pi ,.1:ns are assu..r:iod to be c:.".'eated randomly with.in t he t9.rget and exit the target mlt::'::>r.:nly Jn all. dir3~tions with momentum chosen ft'o;n within a giv3n ra..."lge. In or-ier to specifically model the tel,9S•:!ope for pions prod:iced i.n ~h,3 reaction P ( P, 11") D the RE\TM:OC prog n.r.11 w·:1.s ::n.,xllf ied a:~1d renamed HEVKIN. The inc id en t pi:·ot-:.)n b':lam was not assuo.ed -ce> be I!lonoGnergetic and the incident energy for each proton was calculated on G~1.,3 bas is of its energy loss ~p co the rando rn.J.y ehosen poL1.t of interactl()!l in the t::1.:eget. The pion pr:Jd.U,:!tion angles wera ch.:,s311 r'.:l.ndo:Jtly wit;:1in .:1, sp·3c if ied rang r~, !ind aach pio11 ~rie1'gy ,ns c.1lcul.s .ted f )r the _ particuJ_.ar proton e~ergy and pion prod:ic~ion a~gla. A schematic diagram of t~'1e react i~n is showt1. in Fig. 4-. 2. p + = p + D 1T p1 p p2 ( 4.1 ) I where Pp2 is the f'our momentum o:f the proton at rest in the l:3.b frar..ie. From ~q. '+.1 it is obviotlS t:1at: P.D2 =(P .,_ p - p )2 pa p2 7T (4.2) and hence a rel .9.tion between the pion pr0duction - 46 -D P----• p .,,. Fig.4.2 Schematic diagram of the reaction p(p,1'f)D - 47 -angle a.vid p :bn ene r gy , pc .Jt,) /1 energ y a:1d t:1.e masses of the particles can be found. In part i cula r : cos 8-r =t (M2c4 - 2Mpc2 (Tp-T1r+Mpc2-M.,,.c2 ) +2(TpT,r +TpM1rc2 + T1rMpc2 +Mp M-rc4 ))a(,i+ 2 Mpc2 Tpf12 1 (ri + 2M1r~T.,,. )- 112 ( 4. 3 ) where Equa tlon 1+. 3 W3.S i :1verted ~:.i1 RE'/KIN to g:1.. re the pion 'ri·.-, 0 j ,... "'.,, P. .... ,:,y r.,,. . l'~ ... . :. • ..., •,J . • - -..: . .L-'. ,:,, ' i 11 j- ,:,,-.·,u C':' ,)P +-'•1~~ p ·' ') r1 p ·., ., '1-i.l·"' t ]0 ') ll ' •• ·' _ _ ,_ - ... > ' .•• ;,,,,.t - .L , - ; J .. •.JU \,,,, . .. ... ang l 3, 81r . The pion's el1er.-gy l oss i n t ::1e target from. the point of interaction o~ t to entry into the · te l es cope was cal-culated .. Fr :::>1;1, t hi s p:):L11t cH1 the pl' ogra.r..a ass~"led normal RKi/MOC mod8ll i.ng and ~~l,~uJ.ated rn';Ll tiple scattering of particles accepted into co ~ 1~er s4 , N(Q), as a function of initial pion D'l·.Jmantum out of the target. The usa of ~(Q) in the calculation of the efficiancy of detecting t :·1e pions :ls dU,cussed :in t h e fJllJwing s3c cion. 4. 1 . 2 Tela3cope Ef:f ici ,3ncv f:>r Pions .frQ..l!l._pJ~ 11'") DTo determine the munber of pions which stop i:i counter s4, the rnr:nbe:r of pions 1.-vi.1i,~h fell ins i de t h e energy bit e - 48 ·-including the energy straggle of the beam was calc,1lated. The ene!'gy straggle is simply the fluetuation in Hnergy loss for a give:i path length. The range straggle is the fluctuation j_n· path length fo.r a givea enH-:-.5y loss and for these l•)sses the straggle is assumed ·:;o be a gauss ian distribution . If the average incident beam energy, Tb, is the average stopped p.i,.)n •:mergy,T,r, as shown i· ,'l Fig.4.3, the efficiency of the tales;:!ope is gi11en by: (To+~ T/2)/crs E : J ql(y) dy ( 4.4) (Tb-~T/2)/cr, where -112 <l>(y) = ( 2,r er,) exp (-y 2/ 2) 0'"5 is the root fil·.93.Il square en13rgy straggle, and~T :ls the tel ·ascopa energy bite. From the definition of the e:r-ror function equation 4.1+ may be written: « = erf (!\ T /(2 · 2112 )) If the aver .':l.ge beam en.ergy is different fro;:n the me-s.n telascope stopped pion energy, the telescope's energy bite is no - 49 -.6.T ·~------.• _...:::;;. ____ _.,_l.--11 ...... ,r ________ T l Ti I I b T1r~T ·-2 Fig.4.3 Curves which approximately represent the distributions of pions in energy wh•:m: (upper curve) thP, average incident beam energy Th eq~als the average stopped pion energy, Trr; and ( rower curve) when Tb* T11'. Ll~is the Energy bite of the Telescope. . . . . - 50 ·-] 1) 11,:-r '" 1" <! ;r -,, 'fl"''-,.. .•L'' "'-,...,_..._ 11 ·i; \·.;., r.> b ::. "i" ,:, 'l'°' -~ ::-'{ 'Tl · , _ V"'""' -.1 ·"' _ _ .,~. _ .;i.w ... 1:.A \. .,•J.- , - ::.\. r.u, ..,,.., .., ·· -=>- -, ..• b 7i'1·',7 4 ~- I ·-, t-·,·1~ .~ ........ ~.'.> F ·1p ,:,+' f' 1· , ... ~ ,::,-... ,, • .,. ··J-f' '- '.·1P l- -,1 ,:,,-, ,-.,)D·" .L ' • • ..;;;Je "J. •. • • . .., . -, ...,,."1.:::>....., ,., • .:.,. .. ·, .:.. _. -.J~ ·...,, .. L·-.• V , , . v .. _, 1>::. . -- J ) .. .,,. ,. ·-U • . . :Ls 5 I.,rr~:1 1JJ: Tiers T11'.lu8 E(T,,.-Tb)= J CZ>(y)dy + J ¢>(y) dy (Tr-.1T/2)/o- 1 Tb/o-, (TT+~T/2 )/er, + f c;I>(y)dy T1r/o-, Makl ... 1g 1-:;··1e (!ha.11fp i~1 v:iri,1blss X=y-Tb ,gr.r3s: /J., (T,,.-Tb)/o-8 •<Tr-Tb)= J<%>Cx)dx + f cZ>(x)dx (T1r-Tb-6T/2)/o-5 0 . ( T 1r -Tb+ fl T / 2) / o-5 + J <Z> (x) dx (T,r-Tb)lo-s + _L(T,r-Tb+AT/2) erf ( T1r-Tb+AT/2) 2 ITir-Tb + liT/21 2112 a-5 - 51 -The val trn3 ·Jf °g f:>r v:1 1• i, J ,1S ,!l·.:::1.~1 te L~s-:!ope st·) ppad p'Lon ene:rgll~S ha-.r·3 b 8r :3ll. e a l. :!Ll l 1!.:;~i (Ho hG:-ts,m 1 ')76) tlC t i ,J!l N (8) Ii! J N ( p) E ( p > d p (4.5) In 0 .-,-,1_ l(.1_r +.:, (~."'_ ..... ·, -~,.ll __ ,·-::if-:p a 1- ·L~·-·r .:··)· 1 ·:-~ )' l N (8) 1·t ,, re,~ - V - ,_., - ;a. - - - · . • .:, :J .. L i :.... ., J_I • ';• ' • J .. .:.,..::, ' l-,: r f , ·-r.., '::l ,,ld ·'l" 'T r-.., ., :- H' 4 cJ ,-, tlC.. ,,J_,) .l 11, l~ -'- -J a~ '- '"'•, ct.L-Hl ,,_, -'-"<l. • ) 1 ·::>1. t·-.. .,, ·".1· •rc, ,-'l ·i.·1 -:rl ,:, ci"'ld ::,rr~ ~- 1,._,·i-,:, li'l l+ , · ... , ~ 1. .!.. ..:.~t.. -.l r.:. t,-- -· q ,.: • .. v ,-:-..1.l.~ ;.;i,.v·~ W l . •) + . ,-. ·1 -. -.· , , ._ ·'.'> ,.:i ·i ,, .~ ! - I"' -~ ·. ·, ., .t.. • r r • ,. : - ·, F ·" 7 4 1+ vYP.1--a._ •JQ. l.- - -L •- ,l~ ·..:, l (_ I . .:, 'J • L _,) -_._•,1. .) .1 ]_,:, -:.icl 01 1T_l .J.!.1 l !:, •• - • At th,~ ang_l -~. 8 = 8 peak ' C!·:-n:·1·espond.i .1.g t J the maxt ,a•.m :,: ;·•T']_ : ·1 ;r ··->·:• -"{( -n 'i J -4. ·- • - • - ,.;:;!,./ ,"' ,J 1.l~l ~' " r> Si .,_'.: 1--· . .. - - . + ·-~J_:1d :L'.1.g t ·,19 ,affGcts of Cou:'.om."'.:.l m.tltj_ple sca.ttar:L.1.g . The ~al•.:!ulatad 'n.1 ·-1e:, :)f •, cor 1•e ;:3p ·:md 1 .. ag t -J 83.::! :1 r v.1 ar <J l:i :::;tzn l l.1 n:'abl3 1+ . 2. The -;_ral;W of •r WJ.3 :i:wt ':!J'l '~L!'llty ':;".-1e fact that 1Jite of tlrn teles :~ope and t :1·3 pior1 en,3:!.'gy bea m sp .:;:•ead, TABLE 4.1 R.M.S. ENERGY AND MOMENTUM STRAGGLE MEAN STOPPED PION ENERGY - (MeV) T11" 52.0 75.0 102.0 ROOT MEAN SQUARE MEAN STOPPED ENERGY STRAGGLE PION MOMENTUM CT I (MeV) p (MeV/c) 1T 0.93 131.0 I. 32 163.0 1.78 197.0 (all values of cr5 calculated for copper } ROOT MEAN SQUARE MOMENTUM STRAGGLE er, (MeV/c) 1.35 1.72 2.17 I \J'1 [\) ........ Cl) +-·-C: ::, >-'-C .... ·-.c ._ CJ .,_._ 2000 1600 1200 800 400 78 - 53 -80 82 84 8-,,. (deg re es) 86 Fig.4.4 Calculated angular distribution of pions produced by 450 MeV proto ~1s in the rea~tion p(p,1r)D. TABLE 4 .2 PION DETECTION EFFICIENCIES FROM THE REACTIO N p{ p,1r)D MEASUREMENT STOPPED PION ENERGY EFFICIENCY I_DENTIFI CATION ( MeV) Er \J\. +· REVKIN04 52 0.605 i: 0.012 02 ·52 0 .674 '.t. 0.034 05 75 0.445±0.045 06 102 0 .312 :t:Q.034 08 52 0. 5 82 tQ .012 09 52 0.57 6 :t 0.012 (uncertainties stati st ica I in natur e) - 55 -4.1. 3 Calculation of dcr/d"1rrom th ,9 mea.sured d2cr/dT.,,d.O, The differential cross section dtr/d.0, was calculated from the observed distributions by first using equation 3.1 giving thi3 relative yield versus production angle into the energy bite, /). T 1r , of the telesc::>pe and second evaluating the equation: ( >io6' (Y - C) 0.5 t::.T.,,. •r where Y is th 1.3 peak valu,3 of the observed distribution, C is the carbon backgro ·..1.nd at the central angle, f::t.T-,, is the appropriate en,9rgy bite of the telescope, and « r has been discussed in section. 4. 1 . 2. The factor of 0.5 is required becallse the CH2 molecule has two hydrogen atoms. The values of dcr/d.Q for each measurement are given in Table 4.3. 4-.2 Phenomenological Differential Cross Sections The center of mass differential cross sections are given in terms of the total cross secti~n ~y { do- ) -dil cm-cry {A+ 2n I 8 cos vcm ·41r(A+-+-) 3 5 +Bcos 48 ) · cm - 56 -A= 0.31t0.04 B = 0.03t 0.2 ffl._. C. ·rhe fitti.ng p:1.r.=i.r,1,a·';3:r,-s, baS-3 ·1. O!l a .re ee:nt; •'.!Oli'1pl la.t ·-J.• r1 ""'\"f ..:i., .1-a rso ·:,J 'l =>"l"' .a-1·1,:l Me"'>'":l; :>iT 1 (9'7 ()\ :.>r ,::,• Q_ 1.j . • '..lr.4\., .. \ , . --<-- . -·J~ •• . , .:,.) .. 4., , (. I ::.. ~• A1 =(0.186i0.010) mb A2 = (0.93t 0.06) mb A3 = (-0.07t 0.03) mb The d ~ffarential cros~ 3e~tian wer9 tranafor~ad tJ the lab ainties in these calculated cross sections have been made by adding the uncertainties of the fitting coefficients in quadrature. TABLE 4.3 DIFFERENTIAL CROSS SECTION dcr/d.Q FOR THE REACTION p ( p ,-,,.) D MEASUREMENT STOPPED-,, PION ANGLE INCIDENT dcr/d.Q IDENTIFICATION ENERGY PROTON ENERGY <µ. b/,r} (MeV) 8.,,. (M eV) EXPERIMENT THEORY REVKIN04 52 97.0 500 127.2! 4.3 116 :t 12 \Jl. --..,J I 02 52 96.0 500 120.0:1:6.7 116 12 05 75 78.5 50 0 127 % 18 112¼11 06 102 64.0 500 ugz 16 107 * 11 08 52 82.0 450 76.3•3.8 78.8*7.9 09 52 64.0 400 49.9• 2.5 46.1 *I.I - 58 -C!i:i~_pT~R 5 DIFFEREN'rIAL c:aoss 8EC;rIONS "Ei'OR :~_A:.9.BON ANJ COPPER The differential cross sections fo r carbon are presented in ~ables 5 . 1, 5.2 a.~d 5.3. Graphs of the differential cross sections against pion energy for carbon are given in Fig. 5 .1 with the pion prodw"!tion angle as a paramater, and in Fig. 5. 2 with th ,3 pro ton en,3rgy as a parameter. Each differential cross .seeti on is a:1. average of all the runs at that proton •anergy and production angle throughout the experiment. For example the differenti al cross section for 53 MeV pions p.rod:.1.ced at an angle of ·, 00° by 500 MeV protons on ,~arbo :a, W3.3 observed to be: ( 1 0 • 6 * 0 • 3 jJ,b/Me V • s r , ( 1 0 • 4 -i O • 3) J', b/Me V • s r, ( 11 . 2 * o.4)/1-b/MeV•sr, 9.!ld (10.6*0.3)µ.b/MeV-s:- dm~ing three d:lfferent shifts of the axper:.ment . These four values were averaged to gi v·a ( 10. 7* 0. 2) /1-b/McV. sr. The agree-ment of these independent measurements is an indication of the int;ernal consistancy of the e~::perinent";al proceedu:res used. The differenti~l cr~ss sections for copper are pre-sented :ln Tables 5.4 and 5.5. Graphs of the differential cross sections against pion energy for copper are given in Fig.5.3 with the pion production angle as a parameter, and in Fig.5.4 with th ,e proton energy as a parameter. TABLE 5.1 DIFFERENTIAL CROSS SECT IONS FOR PIONS PRODUCED BY 500 MeV PROTONS INCIDENT ON CARBON PION ENERGY 2 d a-/ dT,r d.Q ( p.b/MeV·sr) (MeV) Br =60o Br= I 00° 8.,,,.i 150° 22.7 6.96*02 .2 - . 7.86*0.17 32.0 7.12•023 8.91•Q.18 { 8.05•023 53.4 9.08•0.29 101 1 • 0.18 8.30* 0.24 76.1 9.41 *0.26 7. 7 3•0.19 3.83*0.13 101.7 8.44*0.3 8 3.91•0. 10 1.38 *0. 07 \Jl. '° I TABLE 5.2 DIFFERENTIAL CROSS SECTIONS FOR PIONS PRODUCED BY 450 MeV PROTONS INCIDENT ON CARBON PION ENERGY 2 d u/dT-,,. dfi ( µ.b/MeV·sr) (MeV) B.,,..=60° 8,,-r100° 811*= 15 0° 22.7 4.45~0.16 4.14~0.19 6.62 -t: 0.21 32.0 4.93~.14 7.28=0.14 7.27* 023 53.4 7.25 :t:Q.15 7. 3 :3 :k 0.18 5.51 *0.17 76 .I 6.29*0.21 4.51 *0.14 2.49* 0.12 101.7 5.49 :1:0.11 228 *-0.10 0.11:1:0.01 °" 0 I TABLE 5.3 DIFFERENTIAL CROSS SECTIO NS FOR PIONS PRODUCED BY 400 MeV PROTONS INCIDENT ON CARBON PION ENERGY (MeV) 22.7 32.0 53.4 76.1 101.7 d2a-/ dT.,,. dSl ( ,.,, b / MeV· sr) 8.,,-+= 60° 8,rr= I000 87 4-= 150° 4.79* 0.16 3.65:1:Q.II • 4.75:t.0.12 (T,36.0MeV) 5.49*0.18 CT,,= 56.4 MeV) 5 .17 :a; 0.16 (T,r = 78. 7 MeV) 3.60"*0.14 ( Tr= 104.0 MeV) 5.31 z. 0.16 3.28*0.15 1.2 9 *0.05 4. 68:1: 0.17 5.2 5 *-0.16 3.49~ 0.12 1.46 "* 0.07 0.43~0.04 •due extra material in range telescope during these runs 0\ -\, TABLE 5.4 DIFFERENTIAL CROS-S SECTIONS FOR PIONS PRODUCED BY 500 MeV PROTONS INCIDENT ON COPPER PION ENERGY d2a-/dTvdfi (,.,_ b/ MeV· sr) (MeV) 8,,-+ =60° 8,,-.= I 00° 8,r= 150° 22.7 17.0-J:0.4 21.5*0.7 20.Ss0.6 32.0 21.5¼0.7 26.1 ~o.6 26.7 "-*-0.9 53.4 26.0 :1: 0.8 29.4:J:0.7 25.1*08 76.1 21. 9 :1: 0.7 19. 6 =0.7 11.0~0.7 101.7 18.1 z0.6 9. 9 "*=0.4 4.6*-0.5 I\) • TABLE 5.5 DIFFERENTIAL CROSS SECTIONS FOR PIONS PRODUCED BY 450 MeV PROTONS INCIDENT ON COPPER PION ENERGY la-/dT1r d.Q C,..b/ MeV·sr) (MeV) 8 ,rt = 6 0 ° B.,,..= 100° s,,...: 150° 22. ·7 13.3 :t 0.6 I2.5-z0 .6 I5.I* 0.7 32.0 15.6 *0.6 17.6•0.8 20.1~0.9 53.4 16.2* 0.7 18.3 • 0.8 17 .7• 1.2 76.1 12 .7 :1: 0.6 9 .2 * 0.6 8.1 • 0.9 I 01.7 10.7*0.6 4 .6 :! 0.5 2.5 =0.4 °' w - :S4 -CARBON 8-rr =60° 5 o---, .. o---------o--Tp=500 b __ a ___ _ ---- -c--,,,,,,,. ----~-A------..... _ A ..._ °' a a ,~---- ··L.1-............ , Tp =450 " ,A -----~-Tp=400 , 0'-----:11!!!:"'21r'---- -----------40 60 80 5 5 ·0 ~-. . . T-r(~.1eV) 100 ~o~ CARBON 81r=I00° . / a"',,--., c 0 LJ / ' / / ', . I A-- --- - ---~- ...... N.. -LJ. -... ,a ---,:r-- ......... ........ __ o ...... Tp=500 I ...... .. ~....._....._ 20 40 60 T1r+ (MeV) , ...... - ... -.....a_..._ Tp=450 ---~-- Tp=400 80 100 a---o-_,,_,,-,-a - O-- ...... ,.,,,,. 'a CARBON 8v=l50° ~ ---~-----' -- ... , '--- ... ' ... ........ Fig. 5 .1 20 ~....... ........ ....... 'C ........... '--... Tp=500 ------:::: :-1p=450 40 60 TTT+ (MeV) 80 100 Tp=400 Differential Cross sections for pions produced by 400,450 and 500 MeV protons bombarding Carbon. The0three plots are for pions produced at angles 60, 100°, and 150°. L.ines on these a.vid fol lo·,ring cur ·;;e s dravm to guide the- eye. - 65 -CARBON Tp =500 M eV -'-u, . 10 5 . > o----:~-- ~--~~- ~ ~- --- -c, 20 40 60 80 :i T1r+ ( t\1eV) 100° 150° 10 AR C BON Tp=45 0 MeV ---- . . 1::,.--IY---..;_;;.o --- ,.1/ / ....... 'll ~ o . ,.-a 5 / 0 '.6., ........ , -----0- 9 -60° """ __......... , ', a' .,,. -"O ', ..... ' ' a!: ' ... 6 ......... ... ' -a--...... ' ... --- .6--Nb Q----::-=-----:-:::-'~-~~-----=---"O 20 40 60 · 80 100 T1r+ (~1 eV) 100° ·150° I 10 CARBON Tp= 400 MeV 5 0 0- .-=.ir-, :: _;;:,C..Q ....... 0-----.,,,.,,,.-,, ~...... ...... , ti /0 '6... ....... a 0---..... 8-,,.= 60 ° I ,.., ... ........ ...... ....._ ....... 6... - a- - 100° ----- -6 ... - 150° 20 40 60 80 I 0 T,r+ ( ~"1eV) Fig. 5.2 Differe!ltia6 cros~ sectioBs for pions produced · at angles 60 , 1 00 .3...rid 150 • The three plots are · for pions produced from 400, 450 ani 500 MeV protons incident on carbon. · 2 10 - ,)6 -COPPER 81r=6QO a /· . ~ 0-;:> /---a-- - -a.. -- ......._ · :J'p=500 /la· ........ a ..... · I ........_ -- CJ-450 T1r• · MeV . 0 '- __ 2_0 ____ 4_o __ s_o _______ a_o __ 1_0_0_: en 30 ~o COPPER· 81r= 100° / =l 20 I ,,,,--·"'"' 0 ......-20 10 /a a, Tp=500 ·I ' Tp=450 /a "-' / a, o, ' ........ a_ COPPER /a-,, / 'a p Tp=450 '-, I ' o ' a, Brr= 150° ' T1r+(MeV) ""---. ...a __ o '--- ·;_::. 2:..:::0~_4.:..;:0:.,___..,:6..=0 _ 8;::;..0.:;..__ __ Fig. 5.3 .Differential cross sections for pions produced by 450 and 500 MeV protons bombarding copp er. rhe three , pl ots are for pi ons produced at ; angles 60°, 100 =1.nd 1 50°. - 67 -30 COPPER Tp=500 f\1eV 20 20 40 60 80 100 T ,r+ < r~1 e v > COPPER Tp=450 MeV 20 10 0 -Srr=60° o--------------------20 40 -so 80 100 Tv+ ( MeV) Fig. 5.4 Differen~ial gross sestions for pions produced at angles 60 ,100 :llld 150. The two plots are for pions produced from l+50 a...'1d 500 MeV protons on copper • . . · . . 100° 150° . . 68 ·-Several general trends in the plo~s of differential cross sections against pion energy have been observed. For any particalar in ,~ident proton en,~rgy th,3 differential cross section peak is observed at lower pioa energies for larger production angles. For bo~h carbon and copper these peaks were more pron,:n1nced at larger production angles. For any particular pion produc~tion angle th9 c~1r\res have inc:-easing peak valu,~s fo:- increasing incijent proton energies. This trend is better demonstrated i~ Fig.5.5. In o::der to spe ,~ifically i.:1vestigate ' the pi::m production from carbon as a function of incident proton energy o bse .r~rn. tions of 32 and 53 MeV pi ,:ms were made at a single productj_:m angle for six proton energies between 400 and 500 MeV. These meas:ire!!l:;.!nts were taken in a single nigh~ shif~ utilizing _TRim~~'s var~able pro~on energy capability. The ion chamber, no-:malized to a 450 MeV activation, w:iS used as the relative beam !!l<'>ni tor fo-: this series of rtms. Also plotted i_1 Fig. 5. 5 a:-e the cross sections measured by James ( 197'5) a.--id Cochran et al ( 1972). The diffe~ential cross sections !or pions produced at 60° fron this experiment are shown in Fig.5.6 to be corisistant with those o:' James (1975), md Cochran et al (1972). The shapes of these curves a:-e similar, with the magnitude of the c:-oss section increasing with increasing i:..1cident proton energy. These results di sagree in magnitude '"t: ,n > G) :E ' .c :t. .__. "0 ._ Nb . "C - E.9 -15 BERKELEY 10 ·2 #° TRIUMF Tv= 32 MeV 5 rl 9.,,. = 100° / 0 350 450 550 650 750 Tp Crt.eV) 20 15 T1f=53 MeV 10 0 8-,,.= 100° ofi~TRIUMF 5 7 0----------------------350 450 550 ·sso 750 Tp (~"1 eV) . Fig. 5.5 Differential cross s3ctions fo~ 32 and 53 MeV. pio:n.s produced !it 100 from carbon as a 'function of proton energy between 350 and 700 MeV. 30 20 10 0 - 70 -CARBON 81r=60° CHICAGO Tp=450 MeV . l ------l--l__..,-~--y aERK~i:.Ev-- ,,"! . Tp =730MeV .......... J:,, n Ix 1· .. ,, - - ':I. - - - ;a;. "1"A. ·-. ~,..... i- ~---sREL580MeV "\ ·,. ~1•:::=• 0 "TRIUMF 500MeV ~" {,,• ~• --- • ----...........• TRIU:v1F 450 ~1eV , ? . •'-TRIUMF 400 MeV 50 roo T1r+ (MeV) 150 .. . . - . . .. Fig.,.6 n16rerential cross sections for pions produced at 60 by bombarding carbon with 4oo,4,o,.,oo,580 and 730 MeV protons. ..-- 71 -with those of Lillethu.n (1962), which .are a factor of ~pproximately 3.6 too large. There is also general agreement between the differenti~l cross sections ~aasured L~ this experi:nent and theoretical values calcul9.ted by Beder (1975). These" classical absorptive gas model" (Beder an:i Bendix 1971) calculated cross sections for carbon and copper are comp~red with the present experimental results L~ Fig.5.7 to Fig.5.12. Typically the calculated differential cr oss secti -:>ns have peak magnitudes within 20; of the measured val:ies. In the cases of pions p1•oduced at 60° from 500 MeV incident proton3 and pions prod ·i.1.ced at 60° from l+50 MeV 1nci1ent proto~s the measured cross sections had ?eak values at lower pion ene~gies than the calculated val:ies. The only free parameter 0:f this modal is the nor;na.lization of the free NN~NN''ff'matrix element which was fit to available Unfort11.~ately it is not possible to calculate total cross sections with only the results of this experi:me:it. It has been s:1own, ,"l::>tably by Hi rt et al ( 1969) prot ,:m anergies, ~l1.at a slgnifica..'1t fraction of pions are produced. at f orwar ,j angle3 hence a...'1 integration ov-a'!! s0lid angle must i:iclude data from t:1at ragi~n . 30 25 ' / 5 - 72 -___ EXPERl~1ENTAL -BEDER CALCULATION I I ' a a----... / ' . ' / C I ' -- '6 -,,o \ \ \ \ \ \ \ \ 81r= 150° Tp = 500 MeV \ \ \ \ \ \ COPPER \ \ ' ' ' ' b, o ',CARBON ....... 'o ..... Q ....... _________________ _ 0 20 40 60 80 100 Tr+ (MeV) · rig. 5.7-Present experimental dif6erential cross sections for pions produced s.t 150 by bo::nbarding carbon and copper with 500 MeV protons compared with calculated results.· · 25 5 - 73 -___ EXPEFtlr\1ENT - BEDER CALCULATION a-..._ / ' I ' , / a I \ I \ a ;- o- ....._ ,o ........ , o, \ \ ' \ 9.,, = 150° Tp = 450 MeV COPPER \ \ \ a \ ' ' ' ' CARBON', 0 ' ' ' ' b, ...... --o-0~--...,....,----------------·-----------o 20 40 so a,o roo . . . T1r+( MeV) Fig. 5.8 Present experimental difberential cross sections for pions produced at 150 by bombarding carbon arid copper with 4-50 MeV protons compared with . calcalated results. · · 30 I ,a 25 I I I C I I 5 - 74 - __ EXPERIMENT - BEDER CALCULATION ,,,,,. c, / , 81r=I00° / \ Tp = 500 MeV \ \ ' ' ' \ \ \ D \ \ \ \ \ COPPER \ \ 'o ' ' ' ' ' b, ', CARBON 'o ,....._ o ___________________ _ 0 20 40 60 80 r.,,. . . < MeV > 100 Fig • . 5-9 Present -experimental differential cross sections , for pions produced at 100 .by bombarding carbon · and copper 1.vi th 500 MeV pro tons compared with calculated results. . . .. • ----I. • 25 :>20 Q) :E ' . .a :l.. 15 5 - 75 ---- EXPERIMENT - BEDER CALCULATION - .... ,,. 'D / ' ,Cl I \ I \ I \ I \ I \ a \ I \ I ', I p I I , . a, er / B,,.=I00° Tp=450 MeV \ \ ' ' ' ' '-a_ 0---------------------20 . 40 T,,. 60 (MeV) ao 100 Fig.5.10 Present experim9nta] . results for pions ·produced at 100 by bombarding carbon and copper with 450 MeV protons compared with calculated results. 30 25 20 5 a/ I I I I I - 76 -___ EXPERIMENT --BEDER CALCULATION ~---,, / ' / \ I \ 81r=6Q O Tp= 500 MeV I ' p a, I ' / ,,o .,,,,,. .,,,,,,. "- - ---0-.--,...J - - -o-_ CARBON 0-------- - -----·------o 20 40 60 80 100 r.,,+ <.Me v ) Fig. 5.11 Preient experimental d~ffe r ential cross sections for pions produced at 60 by bombarding carbo n and cop;ier 'ili th 500 Y1eV pro tons compared wi th · calculated res ults . • 25 5 - 77 ---- EXPERIMENT - BEDER CALCULATION 81r = 60° Tp=450 MeV 0----------------------20 . 40 T,r 60 CMeVl 80 100 Fig.5.12 Present experiment al dif 6erentia l cross sections for pions produced at 60 by bomba ~ding ca rbon and copper with 450 MeV protons compared with calculated . results. - 78 -CHAPTER 6 SIB1iMARY AN:J CONCLUSIONS Positive pion production cross sections have been measured for lmv energy pions ( 20 - 100 MeV ) from proton bombardment of carbon and copper. These m0asure-ments have been made for incident proton energies between 400 and 500 MeV at a11gles of 60°, 100° and 1 50° between the pion and incident proton .directions. As proton energy increases froI'.l 1+00 to 700 MeV the differen t ial cross sections increase monotonically. Previous results (Lillethun 1962) at 450 MeV should be renormalized by a factor of approximately 0.3. After this renormalization, the forward angle data could 'be combine d with the present data a..11d a total cross section calculated by integration or d2o-/dT7Td.O,. Comparison of the results with calculations from the classical absorptive gas model is quite favorable , with 0 the exception of pions produced at 60 by 500 MeV protons and at 60° by 1+50 MeV pro tons. , ' - 79 -REFERENCES Ajzenbarg-Selove,F. and Lauritsen,T. 1968. Nucl.Phys.A114,22 Anspach,S.C. et al 1965. Natl.Bur.Stand.,Misc.Publ.260-9 Axen,D. et al 1976. Nucl.Phys. A2£,387 Barkas,W.H. and Berger,M.J. 1964. Report NASA SP-3013 Beder,D.S. 1975. Private connQnication. Beder,D.S. and Bendix,P. 1971. Nucl.Phys.B26,597 Binon,F. et al 1970. Nucl.Phys.fil'7..,168 Chaloupka,V. et al 1974. Phys.Lett.'3'0B Cochran,D.R.F. et al 1972. Phys.Rev.D6,3085 Cumming,J.B. 1963. Ann .. Rev.Nucl.Sci.1.3,,261 Dzhelepov, V. P. et al 1957. Soviet Phys. JE'rP. 4,864 Gurd,D.P. 1971. TRIUMli' internal report Ti:U-DN-71-1+0 Had:iock,R.P., Zeller,M., and Crowe, K.M. 196i+; University o.f California at Los .A.ngelGs -Report UCLA-MPG 64-2 Hirt, W. et al 1969. Europea..11. Organization for Nuclear Research Report CEaN 69-24 James,P.W. 1974. Private comi~unication. James,P.W. 1975. PhD dissertation at th,e University of Victoria Kessler,J.O. and Lederman,L.M. 1954. Phys.Rev . .2.'±,689 Kitching,P. 1971. TRIIBvfi? internal repor t TRI-71-2 Kitching,P. 1975. Private corn.1m1nicatio11. Koltun,D.S. 1969. Adva,.-,1g_~ in Nuelear Physics 3.,7·1 Leutz,H. and Wenninger,H. 1967. Nucl.Phys.!2,1,55 Lillethu.n,E. 1962. Phys.Rev . .12.3.,665 Mesh.."!{n-rskii,A.G., Shalamov.2.t·I., and Shabm1ov, V.A. 1958. Soviet Phys. JE~P • ..1'.:t,987 - 80 -' Moliere,G. 1959. Z.Physik.126,318 Olin,A. 1975. Private com::ru.n icati::m. Robertson,L.P. 1976. Private COJ'll.L11"J.r1ication. Spuller, J a."'ld M:easday, D .F . preprint of 'On th~"llli.'l~ mductiQl.l. of pioM :in_p_(_p_;!!)D' submitted to Phys.Rev.D. Stetz,A.W. 1975. Private commu.11.ication. Williams,A. 1964. Nucl.Phys . iZ,,324 Vereschagin,A.N. et al 1968 . Isz.Al{ad.Nauk .J/4,623 - 8·1 -APPENDLC A DA'r{\ ACQJIISITION PROJif.iA.];1 The data ,9.cqt1istion program served to I'9Cot'd a.11 scalars. A prelim1.nary cal ,:rnlation of cross section was performed for each run, The program was written in TnIU~fF 3ASIC (Gur cl 97-i) w.nic:1 i,3 t l1e no .r.-:-11,9.::_ BASIS l;=mg-llag.a plus a series or a.sse:nbl ·ar lang1i-:1.ga :E.thro~ti :·13s f :) r CALL sta tem8:nt. A sj_rnpl:'i. tied flow ch :-1rt for the prog.r::i::n is given in Fig.A.1. A copy of the program :1.s reprodllced Froa statements 7 to 960 is the control section of the mabi0~ such ~s r~t idsntification, ~~rgat p1ra~etsrs, proton and pi :)!l e,1ergies and pion pl' ·'.)Ju.c tion angle. Once di. r.ect ,ad to do so in. the control section, the program raa:i all the infor:;nati0n in the CAMAC units ·by executing statements 1100 to 1210. The user would then decide to execute stat ;a-me.n ts 2000 t; ,.) 3099, -:!:1.lculating a preliminary crosa section and obt-1ining hard cop/ of all CAM.AC infoT·raation, or.- ~o exe~uta statamants 5000 to 0 o ., .-, · ·•hJ' "''1 ,., .... 'Ll, ·i 7 • .:_ nJ. _,_ [ ,. ..J • .J_I _ cl·aar ~11 CAl1A~ uni ts .!.n p.rep3,ration f -Jr t;:i1e :1ex1~ r ·l.!1. 8,a~ events stop9 - 82 -target thicf,ness protons fuonitor clear a ll cross sect ions sc alt!rs, rates Fig. A.I FLO\VCHART FOR DATA ACQUISITION PRO~iRAM - 83 -. ~-~! - >:r:~·f it) _~fJ ·~, °'1 :..: i.: JL,'t 7 ~' 9 ,·~t~,/ ,:E. i: ?? D -~iL·.S I ') ·J · .. I f ~I ,-_,;:.') L t'I .'-11': CT..J )C :-( 2P. · v: c l 7 5 ·iO .. F f ::~o .. ~I :- CC . 7, J J £( 1 · .-': , I · \i f 50 .--',d\}i' . "fO •, C,i_.J_, .;_;;_i )•:,-:ii'Il ) ·.TS l';'.J~:;<;£: : 1 F'() :t {E S ~ \lT) 0 FO:·: \ii)" 60 . 1<·~1 '.J{ "~· ;;·!' £',:.~:i (~i::-:f i>nc ,·,\il<:Ss Pi ~i'O' ~S/ ,-::IC 1::01y:i·:~\j, T5="; . 6 1 ,I \i? (: f .1' 5 . 65 :'·. s,:·r, f G=? .·J) lQ ,i~, I ··:, f') \}! i'O --~ QO U 'U' 69 fJ ."i I 'Ji' "" 70 . ? rd 'l'i' " S E'i' T:,=F- ,:·,o l'Ct\1:;,;/ ·'.l"J ·d t'O,·: Ci)U \!f"; . 75 I \if='Uf '1'6 . 99 ::2\1 100 iiS / 1{) i< ? :~ I ,; f 1,09 1 1 0 ,; FO:-. . ? I ;:-:i QQ,JCl! O\T" ~~00 i:,~--I \Jf "l W \J 'JO. l' 1) G :·>i' '-i•J, 2 ,·:O \JO \lE \iE'::'·. GY,? 1 E\JE, ~.G Y" 801 I~F01 V9jV7, J 5,~6 . H02 ? _.; I ,n 803 .P ii! '-lT "~, -.:,; 'JGL E, 'f ,~; , GE'l t\ \i CH .... E, EVF -rr S= 1 o ,-:. s ro PS==~" 804 I~~ u r V~,V4,V3 ' · s325 900 · 911 913 981 928 C)~~ 5 930 931 ~-:f,:.1 ? i:· I ,rr ;:i:I ir ? .d ·.Ji "il() '{()• i . ':. /.\S!T 'fl) I \lt' :n· ;..:l -, ?,, .I \T1 ' , I - , 1 1 ! c· 0 ., n ·1 1 .., ..., t' ! • ' : i 1 l 'J I . ,! I. i=; . . I ,Ji' "qo.t r:,:1 : __ \; i' l' C) I \J,<H :..11 93;~ ? ,: ! '-Yi' ~;i33 . IF !; 1 = l o·o f') ·> YV) · 9L.\O • :.;:·:I'H "DO 'i°')i_i . ,":,:!' ;-;,_, .~ .. '.~ .. -:· ,~ ·.1!) c. ;o :::.. :;=.;.::-scYr-o,;": 9:1 l I -..y ; ; · : f : l 9:'.!:2 · ! ;.;- . 1 = 1 ('Cl i"0 ?. ·) 1Y) C'•/..; 3 r : · ! •,l l . 9:;:1 - -ll" ;JJ 1 1 1 0 11 i 1 1-1-~5 1130 11~5 (~() ;,1 . ,>()() ;. :· I '-li' ".SC~L;:;;t - .. ~ l'.IDO J 1' r '.l: . '11= 1 l'() Li F'()' ~l= n f ,") 3 C ,_, LL 1 , ) , '1 1 , '.'. 1 , :) , n 1 , E 1. ! J F~ f' C C · l l , I'.'. 1 J =• T) 1 Tii" · f:~ 11 i _: 0 ·:: . : I ,) i: \l 1 , C C \i 1 , ·: 1 , r:: C \:. l , 1 J , Gr. 11 1 , ? J , C r. · 1 1 , ? j 11 f l S 115!) 11::jS , 1160 11()5 . 11 71) ··,i: : f . H L? t' ' i 1 = 8 GO!'O 18 ,),) COLL 1·, 0, 1 1,~1, O, Dl,El Lf T %:='Jl+ J.--iT <~1/ :'.1) T...,'t::f.".l;~=~l-( \J~-'-ll) ,:~ i; - 84 -' fl70 LEi-~~=~l-C~ ~ ~~l)~ 1175 U:.i.' Dli=Cf ,i:c_>,6- ::n ·. 117 ,5' \lF::.r ~ 1 , , 11 -'::o • FO"{ '!~= 3 fO 5 11 /"~ S 1 1 l'' iJ 'f ;; __ :. j., 'T ~_.:.. \J2, C [ \'f·~, ... ()J,CC -1~, 1 J, CC --1~, 1 0 0 t: i ! ··H " f ; '.11) () ti' S C Cl C .I\ : ·: , , E 6 D ) " U?,,")S . . _t f f . iY-!=(:~ I i, tJ] 1:?U0 ? . I \ ]f 11 . : .. ~~T., fl \·,,::. ";i)2/' A :) H :n 7 ·,<, I 'J 1 18 ,J~} t:' d 'Ji' l?.10 .G01:1 q3 ,·1 2 :Jl)i) LE: f S '-:-==C [ 1, :_, J fKi:J 1 · t. r,: f s 7 = c c . 1 , 1 :i 21),)2 "~003 L .• ;:r r..,~.f :; •! = G C- 1 , :·~ J ,.:_;()=(; [ 1, ~J ~n (l<i ~-:._ r 1.r f ,, _ .1...,, :·::••: :.)() ., ,. -:.'·-·r 1, -r~-: -:,~ , , ; , .. :3 ;...;() .1 , J 8 C)').,) 81):::~ :.:>,):3i) 8()/.li_l . ~1)/.\] }~QllLJ . 201;5 20LU:, :?,1~i: 7 ··-· __ !),_:)::' 9 .. - .2()S1) ::~· I :· J · r 11 .') f ·J .- s ti : i ; " ::_. v :~ · \J i :.> " ; ;; 7 t. ':. i' : , '.J = C C '' · , n J T_.'i:i' .·:,1= .. i ?- .\ 1-: ·1 L ·:: , . : 1 a:: C C i'. , 1 J L i:: f ! ! :o, 0. t . 1 r-. I_, E; f · ·,: ·:i, = C C :3 , (1 J L ::>· · "· 3 = C C :'3 , 1 J L·!·: l v Lt =C C 3, :~ J T_~F-t' \~5= ' ... l -· ·::2,- ,JJ-'ti''. \ Lr.-: f · 1~=:~ :;; .-.·: 5 !., (': f •. 7=S7/ ·: :-j ,.., :. ~. I ·.i !' " ·. ?:~ ,1 l_. ·. · () \l I r ,~r ." ; ~\r ; " ··/ l " ; .'." 1 ' . :.?. J, Cr. -1~~ , ~;. : I ·u " . 1 < 1 > 11 ; ., ·-::: ; " . • 1 < i·: ) " ; -.,. 3 ; 11 ·, 1 < 3 ) " ; -r 4 3] 2tJ51 ·2052 I:, : ! 'ji' 11 ·:_;1,') F'.:; / './O\il.:i ,'.); . ".: .. ,-:.:" r.:;,;E \JfS/ ·v"/)\i!'i'O ;: ";?.? P053 2·oc,o 807:) 2C73 . ;?.()90 2100 1: i 1 3DOO 30()8 P /~ I :_·~ r " L. f 1..~ I c " ; -.. ,-'~ ; " s !.~ ~.-~ " ; ,vr 7. J ! \1 J' " ( ~:; f ) l)" ; : ; CJ ; " < 1 ) -~ 3 h '" 5" ; :· 1 ;-. I :-rf II ,,:;) ,JI.,: r:.. . : " ; _.; 5 / ',• 7 ; " ·,; () \) I I C" ; .•,15 I '.r ? : I 't r " 1 ~" ; c c · Lt , :1 ; " s 1 3 11; c c 11, 3 J LS I' :i s==CC ~, OJ _:._. I ,t1' "C:JI ·JC _; t) ·1·:;: .~ "' ;:; ,, I \: 1 " 1 . ::! 11 ,; ':.; .: i ; 11 1 , . ( ~ ) L;; f I _l= I 'Jf Cl.i?. / l +J) L~i GC 3J= . no0~ss "; :~s 3 0 0 :3 ___ l,1 F !' (; C ~)]:: . • ()() ('l :<,;.: I G C 7 J = • C' :) '.) 5 31)1V 1 •. r_, !' · 3GrJ $ 3•)01S 301 t1 · · 30:.:;o J_.:i_:'i,' L Y L' J..r-: I' .~ r. l ,) J = • ,'J ;"IO ! I 1 0 r;·c .:; J = • .-, ,·:, u :; n :3 -J \ = :. 7 :'.: C ·1 '3 < .; /; / 5 7 • 3 ) / G C I 1 J , r 1 t . ~ . '· - 85 -3()L~O. 30:50 30~0 t.r.:i' Dl=f;5/CC I• , OJ ::: t,:1,::fr ,,:: 1.r, ~:-1 ,·:, l· . : I '.J f " :_:, ~ (\ ',i C :. i. \J f ' ' ; I) 1 ,; " - ··.;.~ 11 i ': : T. \Jf 5 :)f),J 5() 1 .J :·."._.-, ·r.::-\r., YI · ..... iF cr _ ,._Jc~~ \i·1f i_<:ts . ·:·.:,;Jr-':~-~! .. :·: · 1<·1~:c;;.-:: _ .. ;: , .i.\1 £ 11 ,-, ~~'.\f,fl \·'.'.'. Ci_/ .1(;:.i"· I '.) cr_,;-,·c, ;,·n" . co· • .:; ··-~~,.:;.} _\F' I) t i \ l}. = 1 l O It FO:i. ~1= 0 f,) 3 , · :j:)l:?. \11) () () 9(301 ·900Ll . 90()S C~LL 1, ,) , .·.Jl, _.'.:q, 2,1X! ,Vl ~F'.,:. I' t.\ 1 Q()Jr.:., :.;E.:. r \J 1 Ci(l '.) 7 G '.) L' () ,:., /\ :·) 9;·,,-:, C1lU _. ·1, '.), 3, :c 1, '.~,}):-'-:, ;~1 ():y,9 . ·.! ,~.-. f t'.\ 1 ( )! ') 1 :) . !~-~·; i \l !' " ~-~ C ·:" f_/! \ '· • . :) C T_. :1:1> .. : ;:::'·} II ()')}.1 .- .: j· ; ~· -;;·11 1_~:J r n ,·; t;, , • ') 9 9 -.J :,;:,m . . : ,~--·-'· •. ·. ·--~ ' . : 'z- ... , . : .-- .. - 86 -AP!?E!if:)l;{ -~ The 1 2,-. ( ·p n, ·l) ·j ] i""' ,., \ ' t.J~ .J acti-;ra t1•J!l t9chniq ·te has °'.)0::m s :1mJn'-'l.l'l:~o:i by Jame i~ ( 1975), who damonstrated t }·1at the b ... ,.. pl' ,_) l~ .·0L.'.1CJ.0 ,.:i_ n:'t: •."'. Yl ,".· 12 .., T"' .: ·1 .• ., ·b· ' q -,, .:i • .• f:' .... ,_,ii _",~ num Eh Ji: o,J1J,:, _1_ ~,.# _, '" _., .• 0.1._ 1 .• 1 _:)mJ.-.• · .. d . .::.10 .,._ I= R A To T 2E!), per 1-exp{).To) 1-exp(-).T) 1 ·1 w.1·1e ·.r. A iR 1· S i:_1-·t(=! C de C ' .. "' .,'-' "" ,_ . .:, ·m,:." ,~ '' "' ·:, .:i ' l _. '- ]0 ·m •• rn .., _ - _ :::1. ... •:.t.V~ L ·.~ ·-.'\.,·) ·4J..""q· ,: v t, ... t:., .J. ' En is the efficiency s.ud. solid anglG pl'•:)duct A is the i :'1verse of t:1e mean. l:i f etiin8 'Jf the 11,.., d,~,.ay V -v• ' ( B. I) ., ') P 1. S +-hr-, U' lfil})"'.., ,....,.. I '-C Il'tr• 1 :::.; ·ne ·r '1 r1~ ·f-: "r=-a O.eo 1-~·1e v . V . \. ,._ ;_,j. ·.I..!. .. ~·--!--. .t" .. ... , .. " :':1 • • 'v~ L 1,.,_ tar _..,. . .,-1.. e,t_, i,' :Lr~~ the 12c ( p, p:.:1) l l G 1963) a,..--'-i·11n·'··l,)'l , ..... .. )"' ·"' ·;•,;io.,·'-1"r)r1 /nu,..1r1-' ·1·"]' V l.., . :-;. L, .J .. ·~ ·'- _, J.. ~") _,;., "' \., l.1 . ''- \, ., !..\ .I. . I ..;:, :..:> The ASP EC ( 01 :i.n 1 975) pr ,Jg .ram .1.11 9. gen~1r!ll utility program for utilizing dat3 storad on oagnetic t~pe by the puJ.:=,2 ~eight analJ~9I'. to t:1aad .,__ ..l.i.'19 11 C de 1JaJ spectra an:i cal,J :1J.:1 te . th~ in:!ident p t•o to .a flux :is lng the subT.'1) •1 tins rw:r;~!if w'!:llch is desc ribe:i below. peak pe.r unl~ ttm0 (ARSAV), F.tnd the time at wh5.,~h the - 87 -spectr;1m was recorded with raspe-:! t to t·:ie begi21nj_ 1g of the b::w,i'.)3. rdr.ae::rr. (T) • rhe p!' :Jg !'.'a::i .req'..l.i.raJ Y,"l.Lws 1J f A , TO, .. n , p -~:id (T :!:') r. each C-~l ,::.1.la t -Lori. Ti't' (j-;il "ii' i~. 2. 11 , t:ie v.9.lues -)f (T :HS 30. fJ * 1 . 5 ::nb, J 1 • 7 :t: 1. 6mb, :X.li J,~.6~1..S m.b .f.o.1' proton energies 500,1.1-50 1."'ld. l+oo l\feV F0r bomb-1.rdL..!.lJ t;imss lass t:r1an fiv-e mln..1.tes, .3qua.-~ion B.1 has baen written: BEAM= I= R T. 2ill pu exp().( T-To)) I~ exp(-X To) (B.2) In the s·i1b .r?::>U ~ine Il'J"Ti:N, tb.e pl'·Jgi"ar.J. eiri.lUa ted equa ti::m B. 2 for each of a ussr spe .. ~ifi•ad saries rJf spe:.!tr:1. and averaged. them for a fi..'13.1 va.lu9. The se~i~s of spac t:r-~ warG c}1os,3 1 which involved intenstt1e'3 ,Jf 1 "i..~ deca.ys ")f the S:Vl9 ::n:;,g:l.:lt .l:ie ') ') a 3 tl·1a int ,:i1B ty :1f ·--'-:rra d.-3c:1:ys ~.,:li-::~1 Wi'Jr-9 ·:.1s'J:i to dat.9rmtne A simplified flowcha~t of INTEN is gtvan in Fig.B.1 and \ - 88 -INTEN IR I, IR2 STOP N _ I_Q_op_:_l:_LRLl_Rg_ ____ _ fimeon T CT= AR=CT· I I bet. ween exp(~-:-T0 Af'iSAV I I 10.1-1 -:r 1-- -- ==== I I I t AR I I I ASUitl = I I . ASU~v1 + I A.R _j L _______ ----t BEAl\1 FIG. 8.1 FLOVICHART FOR ROUTINE INTEN . - 89 -lNTEN SUBROUTINE INTEN C8MMCN /SAVAq/ IRUN,IT IM~,fTI ME (2 00),A RSAV(200 ) ,AERSAV( 2 00) ASU~=O AVAR=O REAC(5,2) TAU,TO,TS,SIG~ A, ATNC , EP S I .7. F'JF:'.,1AT(' MEAN LIFE . ',El4 e 4, ' ACTIVA T ION CRCSS SECTION ',El4 e4/ 1' TARGET DENSITY •,E1 4e 4 ,' DETE CTOR EF FICIENC Y',E1 4e 4/ 2' LFNGT~ nF ~C~A~RC~EN T ', F1 0o2,'ST ART OF COUNTING 1 ,Fl0e 2) 2 F O R'-1 .AT ( 6 ": 1 0 • 2 ) WRITE(6,7) TAU,SIG~A,ATNO, EP Sl,TO ,TS WRITf. (6,5) 5 FOR~AT(' RUN ' •' AREA '•' ERROR ') 1cc PEAD(5,1) IR1,IR2 .l . F ,J RM AT ( 2 15 )_ IF (IRleLToO) ~ETURN IF=(f.Tl~1P.( lRl-1 )eLToCo l ) E T I ME ( IRl- l ) =T S DO 200 l=IRl,P:~2 T=(ETlfJ':( 1)+1=:TI~E( I-1) )/2o CT=~XP((T-TO)/TAU) AR=CT*ARSAV(I) ARE=CT>iiAERSAV(I) 'ti R IT f: ( 6 , 6 J . I , A r~ , -~RE.. 6 FQRMA:(l5,2E15o4) CS=lo/A~RSt>.V( 1)**2 ASL~=ASU~+CT*CS*ARSAV(I) 200 AVAP=I\VAR+CS 1CCC AAV=ASUM/AVAR AER=SQ~T(lo/AVAR) WRIT>: (6,3) AAV,AER 3 FOPMAT( '. "'1[1\N ARE A .... =. .. ~,F.1 .5 o~ , -~ _ _±.::..!_t._t;:_t..§..ill _ CS=SIGMA*ATNO*(l-~XP( - TO/TAU) ) CS=CS*2*EPS I BfM-1=~AV/CS :: R"1fR= AER/CS 8E4WN=REAM*1o60?E-10 WRITF(6,4) nEAM,B~E~,BEAMN 4 FORMAT(' OEAM INTENSITY=' El4o4,'+-',E14o4,' PROTONS/SEC =•• 1 F10o3,' NA') GO TC 100 END Surname: MA.THIE ----------------------Given Names: --=E=D'=t"11=lR=D~L=A=W=I ... IB="' N,..,=vE=---Place of Birth: ___ K_R_i,_O. Wl_iA___,_, _B R_I_T_I_S_H_C_O_L ll_.fB I_A __ _ Date of Birth: Augus t 24, 1952 Educational Institutions Attended, with Dates of Entering and Leaving: UlUVE.RS ITY Oli' vrc:·roB.IA. 1970 to 1976 Degrees, Diplomas, Etc., Awarded, with Dates and Names of Institutions: B.Sc. (Honours) 1974 UNIVERSI'I'Y OF VICTORIA Honours and Awards: Governn10nt of British Columbia Scholarships 1970/71, 1 971 / 1 972, 1 972/ 1 973, and 1 973/ 1 974 University of Victoria Graduate Scholarships 1974/1975, and 1975/1976 PARTIAL COFiHIGH'.C LIGENSE I hereby grant the right to lend my thesis ( the title of which is shown below) to users of the University of Victoria Library, and to make single copies only for s'.lch users or in response to a request from the library of ar1y other university, or similar institution, on its behalf or for one of its users. I fu~ther agree that permission for extensive copying of this thesis for scholarly purposes may be granted by me or a member of the University designated by me. It is under-stood that copying or publication of this thesis for financial gain shall not be allowad without my written permission. LOW ENERGY PION PRODUCTION BY PRO'rorrn WirH INCIDENT ENERGIES FROM :4-00 TO 500 MeV Author EDWA..9.D LAWRENCE MATHIE MAY, 1976
Thesis/Dissertation
eng
Unreviewed
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Low Energy Pion Production by Protons with Incident Energies from 400 to 500 MeV
Text