The Compton Effect-- Compton Scattering and Gamma Ray Spectroscopy

Transcription

1 Th Compton Effct-- Compton Scattring and Gamma Ray Spctroscopy by Dr. Jams E. Parks Dpartmnt of Physics and Astronomy 41 Nilsn Physics Building Th Univrsity of Tnnss Knoxvill, Tnnss Rvision 3. January 6, 15 Copyright July 4 & May 14 by Jams Edgar Parks* *All rights ar rsrvd. No part of this publication may b rproducd or transmittd in any form or by any mans, lctronic or mchanical, including photocopy, rcording, or any information storag or rtrival systm, without prmission in writing from th author. Objctivs Th objctivs of this xprimnt ar: (1) to study th intraction of high nrgy photons with mattr, () to study photon-lctron intractions (3) to study th photolctric ffct with high nrgy photons intracting with mattr, (4) to study th ffct of pair production and annihilation involving high nrgy photons, (5) to study th ffcts of backscattr and to larn about soft X-ray and Brmsstrahlung production, (6) to larn xprimntal tchniqus and procdurs for masuring gamma-ray nrgy distributions, (7) to larn about photomultiplirs and scintillation countrs for masuring high nrgy photons, (8) to undrstand th opration, calibration, and us of a multichannl analyzr, (9) to larn data rduction and analysis tchniqus with masurmnts involving low signal to nois ratios, and (1) to larn to idntify sourcs of background radiation and ways to minimiz thir ffct. Introduction Th Compton Effct is th quantum thory of th scattring of lctromagntic wavs by a chargd particl in which a portion of th nrgy of th lctromagntic wav is givn to th chargd particl in an lastic, rlativistic collision. Compton scattring was discovrd in 19 by Arthur H. Compton ( ) whil conducting rsarch on th scattring of X-rays by light lmnts. In 19 h subsquntly rportd his xprimntal and thortical rsults and rcivd th Nobl priz in 197 for this discovry. His thortical xplanation of what is now known as Compton scattring dviatd from classical thory and rquird th us of spcial rlativity and quantum mchanics, both of which wr hardly undrstood at th tim. Whn first rportd, his

2 Compton Effct Pag rsults wr controvrsial, but his work quickly triumphd and had a powrful ffct on th futur dvlopmnt of quantum thory. Compton scattring is th main focus of this xprimnt, but it is ncssary to undrstand th intractions of high nrgy, lctromagntic photon radiation with matrials in gnral. Gamma rays ar high nrgy photons mittd from radioactiv sourcs. Whn thy intract with mattr, thr ar thr primary ways thir nrgis can b absorbd by matrials. Ths ar th photolctric ffct, Compton scattring, and pair production. In addition to ths primary procsss, thr ar svral lssr ways such as X-ray production and Brmsstrahlung. Th Compton Effct is studid with th masurmnt of a gamma ray nrgy spctrum using a scintillator, photomultiplir tub, and multichannl analyzr. Th gamma rays intract with th scintillator producing all thr primary intraction procsss so that th vry phnomnon that is bing studid in a sampl is also taking plac in th dtctor itslf along with svral othr ffcts that mask th procss of intrst. Rfrncs: 1. Arthur H. Compton, "A Quantum Thory of th Scattring of X-rays by Light Elmnts," Th Physical Rviw, Vol. 1, No. 5, (May, 193). Thory Compton scattring involvs th scattring of photons by chargd particls whr both nrgy and momntum ar transfrrd to th chargd particl whil th photon movs off with a rducd nrgy and a chang of momntum. Gnrally, th chargd particl is an lctron considrd to b at rst and th photon is usually considrd to b an nrgtic photon such as an X-ray photon or gamma ray photon. In this xprimnt gamma rays from a csium-137 sourc ar usd for th sourc of photons that ar scattrd and ach photon has an nrgy of.66 MV whn incidnt on th targt scattrr. Th chargd particl is assumd to b an lctron at rst in th targt. Whil th thory hr is applid to gamma rays and lctrons, th thory works just as wll for lss nrgtic photons such as found in visibl light and othr particls. Th thory of Compton scattring uss rlativistic mchanics for two rasons. First, it involvs th scattring of photons that ar masslss, and scondly, th nrgy transfrrd to th lctron is comparabl to its rst nrgy. As a rsult th nrgy and momntum of th photons and lctrons must b xprssd using thir rlativistic valus. Th laws of consrvation of nrgy and consrvation of momntum ar thn usd with ths rlativistic valus to dvlop th thory of Compton scattring. From th spcial thory of rlativity, an objct whos rst mass is m and is moving at a vlocity v will hav a rlativistic mass m givn by

3 Compton Effct Pag 3 m 1 m v c (1) Th rlativistic momntum p is dfind as mv so that squaring both sids of Equation 4 (1) and multiplying by c lads to v m m m c, mc mvc mc, 4 4 mc pc mc, and E pc E, pc E E. () Equation () thn rlats th magnitud of th rlativistic momntum p of an objct to its rlativistic nrgy E and its rst nrgy E. From this quation it is radily sn that th magnituds of momntum and nrgy of a masslss particl such as a photon ar rlatd by or pc E. (3) E h h p. (4) c c Figur 1 illustrats th scattring of an incidnt photon of nrgy E h moving to th h h right in th positiv x dirction with a momntum p and intracting with an c lctron at rst with momntum p and nrgy qual to its rst nrgy, E mc. Th symbols, h,, and, ar th standard symbols usd for Planck's constant, th photon's frquncy, and its wavlngth. m is th rst mass of th lctron. In th intraction, th gamma ray is scattrd in th positiv x and y dirctions at an angl h ' h with momntum of magnitud p ' and nrgy E ' h '. Th lctron is c ' scattrd in th positiv x-dirction and ngativ y-dirction at an angl with rspct to

4 Compton Effct Pag 4 1 th positiv x-dirction with momntum p E E and nrgy c m is th rlativistic mass of th lctron aftr th intraction. E mc whr Figur 1. Compton scattring diagram showing th rlationship of th incidnt photon and lctron initially at rst to th scattrd photon and lctron givn kintic nrgy. From th law of consrvation of nrgy, th nrgy of th incidnt gamma ray, h, and th rst mass of th lctron, E, bfor scattring is qual to th nrgy of th scattrd gamma ray, h ', and th total nrgy of th lctron, E, aftr scattring, or h E h E. (5) ' From Equation (), th rlationship btwn th total nrgy, E, of th lctron aftr scattring, its rst mass, E, and its rlativistic momntum, p, is givn by and E p c E (6) E p c E. (7) Substituting Equation (7) into Equation (5) yilds h E h ' pc E. (8) Using th rlationship btwn th nrgy of a photon (masslss particl) and its momntum from Equation (4) givs

5 Compton Effct Pag 5 Rarranging givs pce pc p c E. (9) and p p c E pc E (1) p p c E p p ce p c E (11) that rsults in th following xprssion basd on consrvation of nrgy p p E p p pp p. (1) c Equation (1) is thn an xprssion rlating th momntum p of th lctron givn to it by a scattrd gamma ray whos initial momntum was p and whos final momntum is p '. Th lctron was assumd to b initially at rst and it was also assumd to b givn nough nrgy for rlativistic mchanics to apply. Equation (1) is solly basd on th law of consrvation of nrgy, but anothr indpndnt xprssion for th momntum p can b found basd on th law of consrvation of momntum. In th scattring procss momntum must b consrvd so that Sinc momntum is a vctor quantity, and Total Momntum Bfor = Total Momntum Aftr. (13) Total Momntum in X-Dirction Bfor = Total Momntum in X-Dirction Aftr (14) Total Momntum in Y-Dirction Bfor = Total Momntum in Y-Dirction Aftr. (15) For an lctron at rst, its initial momntum is zro and has no x and y componnts. For an incidnt gamma ray photon moving in th positiv x dirction and intracting with an lctron at rst, th initial x-componnt of momntum is p and th y-componnt is zro so that and p p'cos p cos (16) p'sin ( ) p sin (17)

6 Compton Effct Pag 6 whr p ' and p ar th momnta of th scattrd gamma ray and lctron aftr intracting. Rarranging Equations (16) and (17) and squaring both sids of ach producs p cos p p'cos, (18) p sin p'sin, (19) and p cos p p' cos pp'cos, () p sin p' sin. (1) Adding Equations () and (1) yilds p sin cos p p' sin cos pp'cos () That can b simplifid using th indntity cos x sin x 1 to furthr yild p p p' pp'cos. (3) Equation (3) is thn an xprssion basd on th law of consrvation of momntum that rlats th momntum givn to th lctron from its rst position by th incidnt gamma ray of momntum p intracting with th lctron so that it is scattrd off at angl with momntum p '. Equating Equations (1) and (3), on basd on consrvation of nrgy and th othr on consrvation of momntum, givs that rducs to and p p E ' 'cos (4) c p p pp p p pp p pe c pp pp 'cos, (5) 1 1 c 1 cos. (6) p' p E Using th rlationships for momntum, nrgy, wavlngth, and frquncy for photons, h h E p, Equation (6) can b transformd into c c

7 Compton Effct Pag cos (7) E' E E that rlats th nrgy of a scattrd photon and th scattring angl. E ' to th nrgy of th incidnt photon E Equation (7) is a simpl quation that can b usd to vrify th thory for th Compton Effct. Th nrgy of incidnt gamma rays E can b asily masurd with a scintillatorphotomutiplir dtctor and multichannl analyzr systm. Th nrgy of th scattrd gamma rays E ' as a function of can also b asily masurd with th sam systm. A plot of masurmnts of 1 1 vrsus masurmnts of 1 cos should rsult in a E ' E 1 linar graph whos slop is th invrs of th lctron s rst nrgy E. Gamma Ray Spctroscopy and th Scintillation Dtctor Data to vrify th Compton Scattring thory is collctd in this xprimnt using a gamma ray spctromtr that consists of a scintillation dtctor, high voltag supply, amplifir systm, and a multichannl analyzr to masur th nrgy distribution of th dtctd gamma rays. Thr ar many ways to dtct gamma rays, and ths includ: ionization chambrs, photographic film, proportional countrs, Gigr-Mullr dtctors, solid stat diods, grmanium dtctors, liquid and solid scintillation matrials with photomultiplir tubs, and a numbr of mthods using similar matrials and approachs. To study th Compton Effct a gamma ray spctroscopy mthod is ndd to masur th gamma ray s nrgy bfor and aftr an intraction. A scintillation dtctor is capabl of doing this, and th on usd in this xprimnt is composd of a sodium iodid (NaI) scintillation crystal and a photomultiplir tub. Th dtctor systm producs a voltag puls that is proportional to th nrgy dpositd in th crystal by th absorbd gamma ray. Th dtctd gamma ray may b from th radioactiv sourc ithr dirctly or by scattring. Th siz of th voltag puls, and hnc th nrgy dpositd in th dtctor, is masurd with a multichannl analyzr (MCA). Th nrgy dpositd in th scintillation crystal dpnds on th typ of intraction btwn th gamma ray and th crystal vn for a singl gamma ray of a singl nrgy. An MCA masurs th distribution of voltag puls hights, or spctrum of voltag pulss, for multipl gamma rays intracting in th crystal dpnding on th typ of intraction that occurs. Whn a gamma ray intracts with mattr, thr ar intractions that occur in th matrial othr than thos du to th Compton scattring. All of ths intractions occur in th dtctor just lik thy occur in th matrial that th ffct is bing studid. Thr ar 3 primary ways that gamma rays intract with mattr, and ths ar: (1) photolctric absorption, () Compton scattring, and (3) pair production. In addition to ths 3 primary ons, thr ar othr ffcts such as X-ray production. All of ths ffcts occur in th dtctor, just as thy do in th matrial that is bing studid and thy mak up

8 Compton Effct Pag 8 diffrnt portions of th masurd nrgy spctra. Photolctric absorption prdominats for low-nrgy gamma rays (up to svral hundrd kv), pair production prdominats for high-nrgy gamma rays (abov 5-1 MV), and Compton scattring is th most probabl procss ovr th rang of nrgis btwn ths xtrms. Of th thr typs of intractions, photolctric absorption is th most significant mchanism for making practical nrgy masurmnts of low nrgy gamma rays in an nrgy rang up to svral hundrd kv, th rang of gamma ray nrgis to b masurd in this xprimnt. In th photolctric ffct, th nrgy of a photon is transfrrd to th lctron by first supplying nough nrgy to rlas it from its bound stat to a nuclus and thn transfrring th rst of its nrgy into kintic nrgy of th frd lctron. Typically, th lctron that is jctd is a K shll lctron whos binding nrgy is a fw kv. This is rlativly a small amount compard to th nrgy of th gamma ray so that most of th incidnt nrgy is thn transfrrd to kintic nrgy of th lctron. Thrfor, if th nrgy of th gamma ray is E, its nrgy will b first transfrrd to th binding nrgy E b of th lctron to fr it from its nuclus and thn th rmaindr of its nrgy will b transfrrd to th lctron s kintic nrgy E or E E E. (8) b Th kintic nrgy of th lctron is thn givn by E E E. (9) b In this xprimnt.66 MV ( E 66 kv ) gamma rays ar mittd from th radioactiv sourc. If th binding nrgy of th lctron in th scintillator is a fw kv, tak Eb kv for an xampl, thn an lctron jctd by th photolctric ffct would typically hav an nrgy E 66 kv, narly qual to th nrgy of th gamma ray (within.3%). Th photolctric absorption procss thn convrts lctromagntic nrgy of a gamma ray photon into kintic nrgy of a chargd particl, an lctron. As illustratd in Figur, th kintic nrgy of an lctron is dissipatd in a vry short distanc by lastic and inlastic collisions with th matrial in which th photolctron was cratd. Th rang of a.66 MV lctron in NaI is about 1 millimtr (spcifically.111 cm), and givs up its nrgy by crating ionization and xcitation along its path. (S graph in Figur 3 that shows th rang of lctrons in NaI as a function of thir nrgy.) Photons of visibl light ar producd along th lctron s path as th xcitd stats giv up thir nrgy by d-xcitation back to thir normal, ground stat condition. Th amount of light that is producd is proportional to th nrgy of th photolctron which in turn is narly qual to th nrgy of th gamma ray that producd it. In othr words, Gamma Ray Enrgy Photolctron Enrgy Visibl Light (3)

9 Compton Effct Pag 9 and Gamma Ray Enrgy Photolctron Enrgy Visibl Light. (31) Figur. Illustration of th rang of an lctron jctd by a.66 Cs-137 gamma ray giving up its kintic nrgy in th production of ionization and xcitation followd by th mission of light proportional to th kintic nrgy of th lctron and hnc th nrgy of th incoming gamma ray. Figur 3. Th rang of lctrons in NaI as a function of thir nrgy. Following visibl light that is formd in th scintillator matrial, th light is dtctd by a photomultiplir tub. Figur 4 shows a photograph of various scintillators and a typical photomultiplir tub. Also shown in th figur is th lctron multiplir sction of a tub

10 Compton Effct Pag 1 with th glass nvlop rmovd. This shows th curvd dynods that th lctrons strik causing scondary lctrons to b mittd and rsulting in th multiplication procss. Th lctrods of th lctron multiplir sction ar calld dynods bcaus thr ar usually 1 of thm. Figur 5 shows a schmatic drawing of a scintillator and photomultiplir tub. Photons of visibl light mittd from th scintillator ntr th photosnsitiv window and photocathod of a photomultiplir tub whr thy jct photolctrons that ar thn acclratd to th first dynod of th lctron multiplir sction of th photomultiplir tub. As ths photolctrons ar acclratd to a highr vlocity, and hnc a highr nrgy, thy collid with th surfac of th first dynod. With ach collision with th lctrod surfac, on or mor scondary lctrons ar jctd that in turn ar acclratd toward th nxt dynod producing vn mor scondary lctrons. Th lctron multiplir sction consists of a numbr of lctrods, ach biasd mor positivly so that th lctrons mittd from ach lctrod ar acclratd to th nxt on that is at a highr positiv potntial. As th lctrons mov down th chain of lctrods, thir numbrs incras xponntially until thy rach th final lctrod, th anod. Th final numbr of lctrons raching th anod ar thn proportional to th numbr of photons that ntrd th photomultiplir tub that in turn is proportional to th light mittd by th scintillator. Th light mittd by th scintillator is proportional to th nrgy of th lctron that was givn to it by th photolctric ffct that is proportional to th nrgy of th gamma ray. In summary, whn a gamma ray intracts with a scintillator via th photolctric ffct, th nrgy of th gamma ray is convrtd to kintic nrgy of an lctron that producs visibl light proportional to th lctron s nrgy and thus th gamma ray s nrgy that producd it. This light from th scintillator thn producs photolctrons in th photomultiplir tub that ar multiplid xponntially to produc a currnt and voltag puls that is dirctly proportional to th nrgy of th gamma ray. Figur 4. A pictur of a photomultiplir tub, svral xampls of NaI and plastic scintillators and, th insids of a photomultiplir tub showing th curvd dynods.

11 Compton Effct Pag 11 Figur 5. Schmatic diagram of scintillator and photomultiplir tub. (a) (b) Figur 6. Schmatic diagrams of th lctronic configurations of photomultiplir tubs biasd (a) ngativly and (b) positivly so that lctrons ar acclratd in th dirction of incrasing potntial. If ach collision of an nrgtic lctron with th lctrod surfac producs mor that on scondary lctron on th avrag, thn th numbr of lctrons ar multiplid with ach succssiv collision with th nxt lctrod until thy rach th anod. Figur 6 shows schmatic diagrams of th lctronic configurations of photomultiplir tubs biasd ngativly (a) and positivly (b) so that lctrons ar acclratd in th dirction of incrasing potntial. In th diagrams, th primary photolctrons mittd by th photocathod and th subsqunt scondary lctrons ar acclratd to th right in th dirction of positivly, incrasing potntial. In Figur 6a, th photomultiplir tub is

12 Compton Effct Pag 1 biasd ngativly with ngativ high voltag to th photocathod itslf and with th anod at ground potntial. A sris rsistor string biass ach succssiv lctrod lss ngativly (mor positivly) until ground (zro) potntial is rachd at th anod. Th multiplid lctrons ar collctd at th anod and ar rturnd to ground through a rsistor, thus producing a voltag puls for ach gamma ray dtctd in th scintillator. Th advantag to this arrangmnt is th signal is takn nar ground, rmoving snsitiv amplifir inputs from th high voltag, fring it from inducd nois du to high voltag fluctuations, and bing safr for th oprator. It also has th advantag of allowing th dirct collction of th lctron currnt that is particularly usful for dtction of constant light sourcs. Th arrangmnt in Figur 6b sts th ground potntial at th photocathod and biass th anod with a positiv high voltag. Having th photocathod at ground potntial avoids potntial problms of spurious missions from th photocathod du to high voltag that ar gratly magnifid as th signal is multiplid as it procds down th string of lctrods. Sinc th anod is at a high potntial, it must b isolatd from amplifir inputs to avoid dstroying amplifir componnts. A blocking capacitor is usd to isolat th high voltag from th output of th circuit and th amplifir input. For th dtction of gamma rays that occur mostly as singl vnts spacd apart in tim, this is no problm. Each dtctd gamma ray producs a puls of lctrons to th anod that in turn producs a voltag puls across th load rsistor. Th voltag puls is asily transmittd through th blocking capacitor to th circuit s output. Gamma Ray Distribution by Photolctric Effct Gamma Ray Distribution by Photolctric Effct 1 Numbr Gamma Rays Gamma Ray Enrgy (kv) Numbr Gamma Rays Gamma Ray Enrgy (kv) (a) (b) Figur 7. Actual distribution of masurd gamma ray nrgis du to th photolctric ffct (a) vrsus th idal distribution (b) for th dtction of gamma rays all of th sam nrgy. Idally, individual gamma rays, all of th sam nrgy, would ach produc a voltag puls th sam as all th othrs indicating that all th gamma rays hav th sam nrgy. Such would b th cas as illustratd in Figur 7b. Howvr, bcaus ach gamma ray of th sam nrgy dos not produc th xact sam numbr of visibl photons in th scintillator, th scintillation photons do not produc th xact sam numbr of photolctrons from th photocathod of th photomultiplir tub for ach intraction. Thn th numbr of scondary lctrons producd at ach dynod ar also not th sam for ach incidnt lctron, and this givs a distribution of voltag pulss producd and a

13 Compton Effct Pag 13 distribution of nrgis masurd. Th distribution for singl nrgy gamma rays is thn a Gaussian distribution much lik that shown in Figur 7a. Photolctrons mittd nar th dgs in th scintillator can los a portion or all of thir nrgy to th walls of th scintillator s nclosur thus producing a lssr voltag puls in th dtctor. Th scond most important way a gamma ray intracts with a scintillation dtctor is by th Compton Effct, th subjct of this xprimnt. Th vry phnomna that is bing studid and masurd is an important procss that taks plac in th dtctor that is bing usd to study th sam procss in anothr matrial. Just as a gamma ray can transfr its nrgy to an lctron in a scintillator matrial by th photolctric ffct, it can also transfr a portion of its nrgy to an lctron by th Compton Effct. Whras th transfr of gamma ray nrgy to an lctron via th photolctric ffct is always narly 1%, th transfr of nrgy via th Compton Effct can rang from % to narly 1%, dpnding on th nrgy of th gamma ray and th angl that it is scattrd. Rcalling Equation (7) with E mc, cos (3) E' E m c and applying th law of consrvation of nrgy, th nrgy givn to an lctron by Compton Scattring is Emc 1 E EE' E E 1. (33) mc E1cos E 1 1cos mc Sinc th maximum kintic nrgy transfrrd to th lctron is for 18, th maximum nrgy transfrrd is givn by 1 EMax EE' E 1 E 1 mc. (34) For valus of E mc, th maximum nrgy that can b transfrrd to th lctron is narly qual to th nrgy of th gamma ray, and EMax E. For valus of E mc, th maximum nrgy that can b transfrrd to th lctron is approximatly zro or, EMax. Th prcntag of th maximum of th gamma ray s initial nrgy that is transfrrd to th lctron in Compton scattring is about 7% for a.66 MV gamma ray. Thrfor, Compton scattring with.66 MV gamma rays will giv scattrd lctrons nrgis ranging from to.477 MV.

14 Compton Effct Pag 14 Th probability of gamma rays scattring at a particular angl and imparting an nrgy E to th lctron can b calculatd from th Klin-Nashina quation for unpolarizd rays givn by 1 E' E' E sin d r d, (35) E E E' whr d is th diffrntial cross sction for scattring as a function of th scattring E ' angl, E is th ratio th gamma ray s nrgy bfor and aftr scattring, r is th classical radius of th lctron, and d is th diffrntial solid angl. From symmtry, sinc d sindd, Equation (35) may b intgratd ovr to yild or whr 1 E' E' E sin d r sind E E E' g d d (36) r sin g (37) 1 E' E' E sin E E E'. (38) Using Equation (33) for th nrgy impartd to th lctron by Compton scattring and th Klin-Nashina quation for th angular probability function, th nrgy probability as d a function of th lctron nrgy, may b found by using th chain rul, de 1 d d d d de de d de d d. (39) Diffrntiating de d 1 E givn by Equation (33) with rspct to givs th invrs of, so that givn E d, de 1 E 1, (4) E 1 1cos mc

15 Compton Effct Pag 15 de de E E E11 1cos sin, (41) d d mc mc and de E Esin, (4) d E mc 1 1cos mc E 1 1cos de d E sin 1 mc mc. (43) Insrting th xprssions for d d rspctivly, and de d 1 givn by Equations (37) and (43) E 1 1cos mc d mc r sin g de E sin. (44) Figur 8. Th diffrntial cross sction for scattring of lctrons by th Compton Effct as givn by th Klin-Nashina quation is shown as a function of th lctron s nrgy. Th diffrntial cross sction for scattring of lctrons by th Compton Effct, as givn by th Klin-Nashina quation in Equation (44), is shown in Figur 8 as a function of th

16 Compton Effct Pag 16 scattrd lctron s nrgy. Th data is for an initial gamma ray nrgy of.66 MV, th nrgy of Csium-137 gamma rays. It is shown with th idal nrgy distribution of an lctron jctd by th photolctric ffct whr narly all th gamma ray nrgy is transfrrd to kintic nrgy of th lctron. Th pak hight for th photolctric ffct is adjustd so that its rlativ hight with rspct to th Compton Effct is approximatly that for a typical masurmnt. Figur 9 shows th sam data with a typical instrumntal masurmnt rspons to singl nrgy gamma rays. Th photopak has a FWHW (fullwidth at half maximum) width of approximatly 5 kv which is typical for a masurmnt with a NaI crystal. Th photopak is Gaussian in shap, and th Compton kn, th sharp dcras at th maximum nrgy givn th lctron in th Compton procss, is roundd with much th sam shap. Figur 1 is thn th sam as Figur 9, but with a typical masurmnt of a gamma ray spctrum addd. This indicats that th lctrons scattrd by th Compton Effct hav a masurd nrgy distribution much lik that prdictd by th Klin-Nashina quation. Thr ar a fw ancillary procsss though that affct th masurmnt procss and that furthr complicat th spctrum masurmnt. Ths additional ffcts do not hindr th masurmnts for this study, howvr it is important to undrstand ths additional procsss, and thy will b addrssd latr. Compton Scattring Distribution with Instrumntal Rspons Figur 9. Typical instrumntal masurmnt rspons to lctron nrgis gnratd by th photolctric ffct and Compton scattring. Pair Production Th third important way that gamma rays intract with mattr is by pair production. Although, this procss is not ncountrd with th scattring of.66 MV gamma rays as usd in this xprimnt, this procss is nvrthlss important to b undrstood. In pair production, a gamma ray of sufficint nrgy convrts its nrgy into mass by crating an lctron-positron pair of ngativ and positiv particls ach with a mass qual to th lctron. In ordr to consrv nrgy and momntum, this raction only taks plac in th vicinity of th strong coulomb fild nar th nuclus of an atom. Th nrgy givn to th atom is ngligibl compard to th rst nrgis of th lctron and

17 Compton Effct Pag 17 positron and th kintic nrgis thy ar givn. If that intracts by pair production, thn E i is th nrgy of th gamma ray E m c m c KE KE KE (45) i N whr mc and mc ar th rst mass nrgis of th positron and lctron, KE and KE ar th kintic nrgis givn to ach, and KE N is th ngligibl amount of kintic nrgy transfrrd to th nuclus of th atom. Th rst mass nrgis of th lctron and positron ar.51 MV so that thr is a thrshold of 1. MV for this procss to tak plac. For typical gamma ray nrgis from radioactiv sourcs, this dos not lav much nrgy to giv to th kintic nrgis of th lctron and positron. Thir nrgis ar givn to th matrial in which thy cratd, just as th cas with lctrons in photolctric or Compton absorption. Typically, thir nrgis ar absorbd in lss than a millimtr and may not contribut much to th masurd spctrum. Masurmnt Rspons to Idal Photopak Figur 1. Typical instrumntal masurmnt rspons to lctron nrgis gnratd by th photolctric ffct and Compton scattring compard to an actual masurmnt. Th strngth of ach of th thr typs of gamma ray intractions dpnds on th initial gamma ray nrgy and th atomic numbr, Z, of th matrial th intraction taks plac. Th ara whr ach typ is most significant is shown in Figur 11. For low Z matrials and gamma nrgis lss than a fw hundrd kv, th photolctric ffct is th dominant procss. Pair production bcoms significant at gamma nrgis abov 5 MV. This lavs th Compton Effct to b most prominnt at mid rang nrgis around 1- MV.

18 Compton Effct Pag 18 Figur 11. Th strngth of ach of th thr typs of gamma ray intractions dpnds on th initial gamma ray nrgy and th atomic numbr, Z, of th matrial th intraction taks plac. Th ara whr ach typ is most significant is shown. Th masurmnt of a gamma ray spctrum oftn shows a coupl of othr prominnt faturs, and it is important to undrstand th sourc of ths. Ths faturs ar a backscattr pak and on or mor paks du to X-ray fluorscnc. Ths faturs ar illustratd in Figur 1. Th backscattr pak is du to gamma rays from th sourc bing Compton scattrd by matrials in th vicinity of th dtctor. Whn a gamma ray is scattrd in th backward dirction, it givs up most of its nrgy to th lctron that it intracts with, but it still rtains som of its nrgy. If this gamma ray of rducd nrgy thn is dtctd by th scintillation dtctor, it will intract with th scintillation crystal in th sam way as a primary gamma ray mittd by th dtctor. Thr will b a photopak from it as wll as a Compton scattring distribution. Both of ths will occur in th Compton distribution du to th dtction of primary gamma rays, and only th photopak will b obvious in th masurmnt. Rcall that th signal gnratd in th scintillation crystal is du to th nrgy impartd to an lctron and that thr is a maximum nrgy that can b givn to a Compton scattrd lctron. This mans that gamma rays Compton scattrd from surrounding matrials hav a minimum nrgy whn thy thn ar scattrd back to th dtctor. This mans that th position of th backscattr pak is thn qual to th nrgy diffrnc btwn th photopak and th Compton kn. Not howvr, that th pak is skwd towards highr nrgy and is consistnt with thr bing a minimum nrgy for th backscattrd gamma ray. Th scond fatur of not is th xistnc of X-ray fluorscnc paks associatd with charactristic X-rays mittd from surrounding matrials that ar activatd by th gamma rays mittd from th sourc. Sinc a lot a lad is usd around th sourc for shilding and for collimating th gamma ray bam, th X-rays that ar gnratd ar most likly from lad. Lad has two charactristic X-rays, K 1 and K with nrgis 75. kv and 7.8 kv rspctivly. Figur 1 shows a csium 137 gamma ray spctrum takn with

19 Compton Effct Pag 19 lad adjacnt to th sourc. Lad X-ray paks appar in th spctrum at approximatly 7.8 and 75. kv as xpctd. If an unshildd sourc is usd and placd clos to th dtctor, and th dtctor is isolatd as far away from any surrounding matrials as possibl, thn this pak can b narly liminatd. Barium X-ray Pak at 31.8 and 3. kv Lad X-ray Pak at 7.8 and 75. kv Backscattr Pak Figur 1. Typical masurmnt of csium-137 gamma rays showing a backscattr pak and lad X-ray pak. Th barium X-ray pak is not a fluorscnc pak, and is not a rsult of xtrnal matrials bing xcitd by th gamma rays. Ths X-rays occur in th csium sourc itslf and ar a rsult of an intrnal transition (IT) procss. Csium 137 dcays by th mission of a bta particl that occurs by th transformation of a nutron into an lctron and proton. With th mission of th bta particl (th lctron) th csium nuclus is lft with an additional proton making it a barium nuclus in a mtastabl xcitd stat, barium 137m. Th xcitd barium 137m ( 137m Ba) nuclus thn dcays down to its ground stat by th mission of a.66 MV gamma ray. This is th gamma ray that is rsponsibl for th photopak. Not all of th barium nucli d-xcit by this mchanism though. As a compting procss som nucli transfr thir xcitation nrgy to a K-shll lctron, kicking th lctron out of th atom with a kintic nrgy of.66 MV lss th binding nrgy ndd to fr th lctron from bing bound to th nuclus. This lavs a vacancy in th K shll that is filld with ithr an L-shll or M-shll lctron rsulting in th mission of ithr a K 1 or K X-ray with an nrgy of 3. kv or 31.8 kv, rspctivly. Sinc th nrgis of th X-rays ar charactristic of th matrial in which thy ar gnratd, thy can b usd to analyz matrials for unknown lmnts. This tchniqu is rfrrd to as "X-ray Fluorscnc," or XRF. Analysis using X-ray fluorscnc is calld "X-ray Fluorscnc Spctroscopy. Figur 13 has a scond X-ray pak btwn th labld barium and lad X-rays that was producd by rplacing th lad matrial with a pic of tungstn nxt th gamma sourc. Tungstn has charactristic X-rays, K 1 and K with nrgis 59.3 kv and 58. kv rspctivly. This illustrats that ths two

20 Compton Effct Pag mtals can b distinguishd by th diffrncs in th fluorscnc X-rays that ar producd whn ths two mtals ar irradiatd and xcitd with gamma rays. Th first comprhnsiv study of th nrgis of charactristic X-rays was mad by H. G. J. Mosly. H usd th Bohr thory of th atom and assumd that th atom, with a missing K-shll lctron, was a cntral, ffctiv nuclus consisting of th numbr of protons in th nuclus plus on of th rmaining innr K-shll lctrons. H thn assumd that this ffctiv nuclus had an ffctiv charg of Z-1 and that thr was a singl L-shll lctron orbiting around it. This ffctiv, Bohr atom thn producd X-rays whn th L- shll lctron droppd down into th vacant K-shll position of lowr nrgy. Th Bohr thory, using this ffctiv nuclus, prdictd charactristic X-ray nrgis of lmnts that varid as th squar of thir atomic numbr minus on, or (Z-1). Figur 14 shows a graph of charactristic X-ray nrgis as a function of (Z-1). If X-ray spctromtrs hav high nough rsolutions, and matrials can b xcitd, thn masurd X-ray nrgis can b usd for idntification of unknowns. Barium X-ray Pak at 31.8 and 3. kv Tungstn X-ray Paks at 58. and 59.3 kv Backscattr Pak Figur 13. Typical masurmnt of csium-137 gamma rays showing a backscattr pak and tungstn X-ray paks at 58. kv and 59.3 kv Figur 14. X-ray nrgis producd by thir lmnt vrsus th atomic numbr minus on squard.

21 Compton Effct Pag 1 Apparatus Th apparatus is shown in Figurs 15 and 17 and consists of: (1) a 3 millicuri csium sourc locatd in a shildd lad housing that also collimats th bam of gamma rays manating from it, () a dtctor systm consisting of a sodium iodid scintillation crystal, photomultiplir tub, and pr-amplifir, (3) a lad shild for th dtctor to allow only gamma rays to ntr th crystal from th scattrr at a small angl, (4) a scattring sampl consisting of ithr an aluminum or plastic cylindr, (5) a goniomtr to orint th dtctor systm at various scattring angls with rspct to th collimatd bam of incidnt gamma rays and scattrr, (6) a multichannl analyzr systm consisting of a Spctrum Tchniqus Modl UCS-3 Univrsal Computr Spctromtr with softwar program, and (7) a computr systm with Microsoft Offic. Figur 15. Apparatus and stup for th Compton Effct xprimnt. Th Multichannl Analyzr Stup and Calibration In gamma ray spctroscopy, a singl gamma ray may intract in on or mor diffrnt ways to produc a distribution of voltag pulss proportional to th nrgis dpositd in th dtctor. Ths voltag pulss ar primarily dtrmind by th typ of mchanism that th gamma ray intracts with th dtctor and/or th matrials surrounding th dtctor. Th voltag puls dpnds not only on th typ of intraction, but also on th high voltag of th photomultiplir tub, its fficincy, th fficincy of th scintillator,

22 Compton Effct Pag th amplifir gain, and th intraction position in th scintillator rlativ to th dgs whr loss ffcts tak plac. All of ths procsss ar subjct to statistical fluctuations, but with stabl lctronics and rptitiv masurmnts of th intractions, a tru rprsntation of th intraction distribution can b masurd. A multichannl analyzr, MCA, is usd to masur voltag distributions and hnc th nrgy distributions of gamma intractions. An MCA is an lctronic instrumnt that taks a voltag rang, divids it into a numbr of incrmnts or channls, masurs an input voltag, and thn assigns it to a channl basd on its valu bing qual to or gratr than th bginning valu of th channl but lss than its bginning valu plus th incrmntal valu. Th numbr of pulss assignd to any on channl ar countd and rcordd and can b rcalld to display th masurd distribution of pulss as a function of th valu of th pulss. For xampl, an MCA typically masurs input pulss ranging from to 1 volts, and this rang is typically dividd into 14 channls, ach rprsnting an incrmntal rang of mv. Th 14 channls ar numbrd to 13 starting with th first channl as channl to th last channl as channl 13. Channl 49 rcords th total numbr of pulss whos input valus ar qual to or mor than volts but lss that volts. Thrfor, a voltag puls of 4 volts will b rgistrd in channl 49. Whil MCAs ar dsignd to b linar dvics, this is not always th cas. In addition, it is also assumd that scintillators and photomultiplir tubs ar linar dvics. Instad of th spctromtr systm (MCA plus amplifirs and dtctor) bing linar, it may hav a small quadratic or highr powr dpndnc. To a first approximation, a MCA systm can b assumd to b linar and can b calibratd with only on known nrgy valu. Two valus ar bttr, and thr ar vn bttr for mor prcis calibrations. Thr ar sts of radioactiv sourcs, ach with diffrnt gamma ray nrgis, that can b usd as standards to calibrat th systm. Using only on gamma ray nrgy forcs th calibration to b linar and for th intrcpt of channl numbr vrsus nrgy to b zro, i.. zro nrgy coincids with channl zro. Two gamma ray nrgis still forcs th rlationship btwn nrgy and channls to b linar, but zro nrgy may lin up with som othr channl othr than channl zro. This two-point calibration is important in cass whr thr ar zro offsts, or dc voltag offsts, in th lctronic instrumntation. A thr-point calibration uss thr known gamma ray nrgis and is bst. It allows for non-zro intrcpts and for a non-linar rlationship btwn nrgy and channl numbr. It is vry difficult to build lctronic instrumntation that is prfctly linar, but with modrn computing tchnology, masurmnts can b mad that asily compnsat for non-linar rsponss. Th multichannl analyzr usd for this xprimnt is a Spctrum Tchniqus Modl UCS-3 Univrsal Computr Spctromtr. It is intrfacd to a computr via a USB port and is compltly controlld by th computr. Th manual for oprating this spctromtr can b found on lin at URL:

23 Compton Effct Pag 3 and should b rfrrd to for a mor thorough st of instructions. Only th salint information for a rudimntary opration and th ssntial componnts for prforming th xprimnt will b covrd hr. Figur 16. Schmatic diagram of a multichannl analyzr illustrating th basic componnts. A simpl schmatic diagram of th UCS-3 multichannl analyzr is shown in Figur 16 and photos of th front and back panls of th instrumnt ar shown in Figur 17. As shown in th schmatic diagram, th dtctor rquirs a high voltag supply that is supplid by th USC-3. Th signal gnratd by th dtctor is snt to th input of th pr-amplifir ( INPUT BNC trminal on back of UCS-3 unit), and is thn amplifid by anothr amplifir within th UCS-3 instrumnt. Amplifr gain and high voltag sttings ar compltly controlld with Spctrum Tchniqus UCS-3 softwar. Th softwar for oprating th UCS-3 MCA unit may b startd by clicking on th UCX icon,. This brings up th usr intrfac as shown in Figur 18. Figur 17. Front and back panls of th multichannl analyzr usd in this xprimnt, th Spctrum Tchniqus Modl UCS-3 Univrsal Computr Spctromtr.

24 Compton Effct Pag 4 Figur 18. Th UCS-3 multichannl analyzr usr intrfac. Th UCS-3 has an Auto Calibrat fatur that will automatically adjust th high voltag and gain sttings for a csium-137,.66 MV gamma sourc. In addition it will calibrat th channl numbr scal to an nrgy scal, placing th photolctric pak into a channl corrsponding to and labld as.66 MV. This fatur is locatd undr Sttings on th main mnu at th top of th intrfac and undr Enrgy Calibrat of th submnu, (s Figur 19). Th channl numbr corrsponding to th photopak dpnds on th convrsion gain that is slctd, i.. th numbr of channls th voltag rang is to b dividd. Th auto calibrat procdur is good for gnral work, but for this xprimnt a mor prcis calibration should b usd. Th auto calibration procss uss a linar rlationship and forcs th zro intrcpt to coincid with zro nrgy. A manual calibration procdur will us a non-linar fit and will allow for a non-zro channlnrgy intrcpt. Figur 19. Th UCS-3 main mnu and toolbar th pull-down, submnus for Sttings and for Enrgy Calibration slctions. In this xprimnt a thr-point calibration procdur will b usd to manually calibrat th channl-nrgy scal rlationship. A csium calibration sourc is usd that has two prominnt paks, th photopak at.66 MV (66 kv) and th barium-137m X-ray

25 Compton Effct Pag 5 pak at 3 kv (.3 MV). Ths provid two known calibration points, on at minimum nrgy and th othr at maximum nrgy. A sodium- gamma sourc will b usd to provid a third calibration point. Sodium- mits a 511 kv (.511 MV) gamma ray and provids an intrmdiat valu btwn th othr two points from th csium sourc. To prform a thr point calibration for this xprimnt, first opn th Sttings mnu and slct High Voltag/Amp/ADC from th dropdown mnu. Altrnativly, click on th icon on th toolbar, and this too will opn th High Voltag/Amp/ADC submnu. (Oddly nough, this mnu is labld Voltag Sttings. ) St th high voltag to 85 volts, th cours gain to 8, th fin gain to 1.7, and th convrsion gain to 14. Click th On radio button for th high voltag and clos th mnu by clicking OK. Locat a csium-137 calibration sourc nar th scintillation dtctor and st a tim for collcting data. Figur. Th dtctor high voltag, amplifir gains, and convrsion gain ar slctd using th Sttings and High Voltag/Amp/ADC submnus. To st a tim, click on th Tim Sttings icon,, or choos Tim undr th Sttings mnu. This will rsult in th Prst Tim popup mnu apparing. Thr ar two kinds of tim masurd by th MCA, ral tim and liv tim. Ral tim is simply th tim that your watch would dtrmin, i.. calndar tim so-to-spak. Liv tim howvr is diffrnt. It is th tim that lapss only during th tim that th MCA is snsitiv to incoming counts. Th analyzr rquirs a littl tim to procss ach signal that is bing analyzd, and during this tim it is insnsitiv to any othr signals coming in and would miss procssing thm. To compnsat for this, th timr is pausd during th procssing tim. At low signal rats, thr is littl diffrnc btwn ral tim and liv tim, but at high rats this diffrnc can b quit significant. To accumulat data for qual tims for comparison, it is bst to us liv tim sttings. Whn you want to collct data for a tim that you can tll by your watch, thn of cours ral tim should b st. To st a tim, for xampl, to accumulat data, slct Liv Tim, in th Prst Tim mnu and ntr a tim of 6 sconds (quivalnt to 1 minuts). S Figur 1. Click OK and this tim will rmain as th prst tim until it is changd or th program is trminatd.

26 Compton Effct Pag 6 Figur 1. Masurmnt tims ar st with th Prst Tim mnu accssd via th Sttings mnu or th icon. Click th Go icon,, on th toolbar and th instrumnt should bgin to accumulat data for th prst liv tim of 1 minuts. Th Stop icon will appar on th toolbar and will rmain until th prst tim is rachd or th masurmnt is pausd or stoppd. Th systm can b pausd or stoppd by clicking on th Stop icon on th toolbar. If th masurmnt is rsumd th timr will continu timing from th point that it was pausd. Th csium gamma spctrum should look similar to th on shown in Figur. Th data is displayd as it is bing accumulatd. Th numbr of counts in ach channl is plottd on th vrtical axis, and usually by dfault is displayd as a logarithmic scal whn th program is first run. Th vrtical scal can b toggld btwn a linar scal and a logarithmic scal by clicking on ithr th Log Spctrum Viw icon,, or th Linar Spctrum Viw icon,, on th toolbar. Th rang of th linar scals can b incrasd or dcrasd with th up/down arrow kys on th kyboard or with th scrollbar on th right of th scrn. Figur. Typical csium-137 gamma ray spctrum. Prpar to calibrat th systm using th thr-point calibration procdur. St th high voltag at 85 volts, th cours gain at 8, th fin gain at 1.75 and th convrsion gain at 14. Prst a liv tim of 15 minuts (9 sconds) and masur th gamma spctrum of th csium-137 calibration sourc. Aftr th masurmnt is compltd locat th channl numbrs for th main photopak at 66 kv (.66 MV) and th barium-137m X-ray pak at 3 kv (.3 MV). This can b don in two diffrnt ways. First, th channl with th highst numbr of counts can b locatd by scanning th cursor ovr th spctrum with ithr th mous or th right and lft arrows on th kyboard. Th channl

27 Compton Effct Pag 7 numbr with th numbr of counts appars in th lowr lft portion of th scrn. Car should b takn to mak sur th channl that is chosn is symmtrically in th cntr of th pak distribution. Th UCS-3 softwar includs a fatur that can assist th usr in finding th pak channl. This mthod uss th rgion of intrst (ROI) fatur that calculats th ara (sum of counts in th channls) in th ROI and th cntroid. This procdur also rquirs som judgmnt on th xprimntr s part in choosing a symmtric rgion of th pak. Undr th sttings mnu, choos ROI and thn St ROI in th xpandd mnu as shown in Figur 3. Figur 3. Th submnu for slcting rgions of intrst (ROI) is undr th Sttings mnu. Altrnativly, th St Rgion of Intrst (ROI) icon on th toolbar can b slctd. This activats th mous cursor so that whn it is placd on or blow th spctrum, lftclickd, and hld, th ara undr th spctrum will b colord as th mous cursor is movd along th spctrum to highr numbrd channls, and thn rlasd. Th colord ara indicats th rgion of intrst and should covr as much of th ara undr th pak as possibl and yt b symmtrical with it. An xampl of th rgions of intrst for th csium-137 sourc is shown in Figur 4. If th mous cursor is placd in or on th ROI, th cntroid and th FWHW (full width at half maximum) for th pak will appar in th lowr right hand cornr of th scrn. Th channl numbr for th cntroid can thn b assumd to b th pak position. ROIs can b clard individually or all at onc by choosing th appropriat option from th ROIs mnu. To clar an individual ROI, th mous cursor must b placd in th ROI. Th viw of parts of th spctrum can b xpandd and comprssd by locating th channl numbr indicator bar on th point of intrst of th spctrum and using th up/down arrow kys along with th shift ky on th kyboard. This can hlp slct th ROI with bttr prcision. Rcord th channl numbrs for th two pak positions of th csium photopak and X- ray pak. Rplac th csium calibration sourc with a sodium- calibration sourc and find and rcord th channl for th pak position of th 511 kv (.511 MV) gamma ray. Slct Sttings from th main mnu, and from th drop down submnu, choos Enrgy Calibration and th 3 Point Calibrat option. This lads to th St Enrgy data input box shown in Figur 5. Chang th units to kv in th mnu and click on th St button. This lads to a scond popup mnu to input th channl numbr and nrgy valus of th csium X-ray pak. Entr th channl numbr and nrgy of th sodium

28 Compton Effct Pag 8 photopak for calibration point and thn rpat for th csium photo pak for point 3. This will calibrat th channl scal, and it will now b calibratd in kv units. Cursor valus on th intrfac will also now appar in kv units. Figur 4. Scrn showing rgions of intrst (ROI). Figur 5. Enrgy calibration data input boxs. Th UCS-3 MCA should now b calibratd. Th valus for this stup and calibration should b savd by choosing Fil from th main mnu and Sav Stup from th pulldown mnu. This stup can b rcalld and loadd using th sam mnus for any othr futur masurmnts. Figur 6. Fil mnu for saving data.

29 Compton Effct Pag 9 Masurd spctra can b savd with this sam mnu and also loadd back in from storag for furthr data analysis. Fils may b savd as Tab or Comma dlimitd txt fils to import th data into Excl spradshts for data analysis and prsntations. Th systm should now b undrstood, calibratd, and rady to tak data for studying th Compton Effct. Masurmnt Procdurs and Analysis 1. As with all xprimnts th rsults in this xprimnt can b much improvd by incrasing th signal-to-nois ratio and counting statistics. At larg scattring angls, th numbr of Compton scattrd gamma rays from th scattrr (th signal) is small and ar masurd in a largr background (th nois) of Compton scattrd gamma rays from all th surroundings othr than th scattrr of intrst. Aftr all, th scattrr is a small objct compard to all th lad shilding and matrial making up th surroundings such as th concrt walls, tabls, and a host of othr objcts in th laboratory. Th larg amount of lad shilding and its stratgic placmnt in th stup is important to rduc th background signals. Th shilding around th sourc is lss ffctiv at th smallr scattring angls, sinc at ths angls th collimation is lss ffctiv and small dviations in th spctra du th Compton Effct ar lss noticabl. In ordr to show th ffcts of Compton scattring amidst th small signals and larg backgrounds, good counting statistics ar rquird and this mans long counting tims ar rquird to rduc th uncrtaintis. Rcall that th uncrtaintis in radioactiv counting ar proportional to th squar root of th numbr of counts. In any channl of th multichannl analyzr, th numbr N counts in that channl ar uncrtain by N. In ordr to study Compton scattring by th cntral objct, spctra ar to b takn with th scattrr in plac and thn again with th scattrr rmovd. Th diffrnc btwn th spctra should b du to Compton scattring by th scattrr. Thrfor in this xprimnt a background spctrum will b masurd with th scattrr rmovd and th dtctor placd at th Compton angl of intrst. Th scattrr is thn placd in position, and a spctrum is masurd that is th sum of th scattrd gamma rays du to Compton scattring by th scattrr and th background nois spctrum. Subtracting th background spctrum from th masurd spctrum should rsult in a spctrum that has th nois rmovd. Background subtraction can b don ways. If th data is savd as an Excl fil, thn th background data can b rmovd by subtracting th background counts from th data masurmnt, matching channl to channl. Altrnativly, th Spctrum Tchniqus softwar will do this for you. A savd signal spctrum can b loadd into th softwar by first choosing Strip Background from th main toolbar and thn Load Spctrum from th submnu. Th submnu will thn giv th option Load Background Spctrum and th background spctrum can thn b loadd. Th scrn will show both th signal and background spctra. By choosing th Strip Background for Spctrum option in th submnu, th softwar will giv a third spctrum consisting of th masurd signal spctrum minus th background spctra.

30 Compton Effct Pag 3 Figur 6. Strip background mnus and submnus for stripping th background.. As a first stp, plac th dtctor of th goniomtr stup at th position and masur th gamma ray spctrum of th Cs-137 sourc without th scattrr in plac for a liv tim of 3 minuts. Plac th 1 diamtr lad plug with a 1/16 diamtr aprtur in th dtctor shild to attnuat th count rat of dtctd gamma rays. Th purpos of this is to rduc th count rat and dad tim of th systm to rduc th probability of having two gamma rays intracting with th dtctor at th sam tim. If or mor gamma rays intract with crystal at th sam tim, th puls hight of th signal will b largr than that of a singl gamma ray and will not b a masurmnt of th dsird singl gamma photon. Onc this masurmnt is complt, sav th spctrum to a data fil using th Sav fatur in th Fil mnu. 3. Dtrmin th nrgy of th photopak by using th cursor, th ROI, or th Pak Findr fatur in th Viw mnu. Th position of th photolctron pak should b rcordd as th unscattrd photon nrgy. It should b qual to th Cs-137 nrgy that was usd to calibrat th systm. Rcord this valu as E for latr us in th Compton Effct Equation (7). 4. As a first masurmnt to tst th xprimntal procdur and thory, st th position of th dtctor of th goniomtr stup at th 6 position. With th MCA and dtctor calibratd, masur th gamma ray spctrum with th scattrr in plac for a liv tim of 3 minuts. Sav this spctrum as a data fil. Thn rmov th scattrr, and mak a background masurmnt for th sam tim. Sav this background spctrum as a data fil. Us th Spctrum Tchniqus softwar to strip th background spctrum from th signal spctrum with th scattrr in plac. Not how th strippd spctrum looks mor lik a normal Compton Scattring spctrum. Dtrmin th nrgy of th photopak and rcord this valu for E. Us your valus for E, E, and with Equation (7) to comput th rst nrgy of th lctron. Compar your valu to th known valu. 5. Prpar an Excl spradsht similar to on shown in Figur 7. Labl th first column with th angls,, that th scattring is to b masurd. Labl th succssiv columns as 1 cos, E(kV), E (kv), 1 E, 1 E ', (1 E' 1 E), and E. Entr valus for, from to 1 in 1 incrmnts. Entr formulas to comput th valus in th appropriat columns.

31 Compton Effct Pag Masur signal and background spctra for ach of th angls and sav th data to your fils. Us th Spctrum Tchniqus softwar to strip th background from th signal spctrum. Sav th strippd spctra to a third fil. Not: It is important to copy your data fils to som mdia that you can tak with you. DO NOT rly on saving your data on th systm computr in which vryon ls can accss. 7. Dtrmin th nrgy position of th photo paks in th strippd spctra and rcord ths as th nrgy of th Compton scattrd gamma ray, E, at th scattring angl,. 8. Mak a plot of your 1 E ' valus vrsus 1 cos for ach of th angls that a masurmnt was mad. It is bst to add this data as ach masurmnt is mad. If this is don, any dviations from th linar rlationship can b notd arly, possibly alrting th xprimntr to som problm that can b solvd bfor a lot of tim is wastd and th ntir masurmnt procss has to b rpatd. Figur 7. Exampl Excl spradsht and graph for rcording, graphing, and analyzing Compton Scattring data. 9. Equation (7) can b rwrittn as, 1 E' 1 E 1 E 1 cos of a linar quation, y ax b, whr y 1 E', b 1 E, x 1 cos and is in th form, and a 1 E Th slop of th lin, a, is thn th invrs of th rst nrgy of th lctron, E. 1. Find th slop of your graph and compar it with th known valu. Th advantag of analyzing th data this way is that random rrors can b avragd out and systmatic rrors can b dtctd in th masurmnts.