The Compton Effect. c 2 E 1. m e 1 E 1 = 2. c (2) + m e. E e. c 2 E (3)

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1 PHY 19 Compton Effct 1 Th Compton Effct Introduction In this xprimnt w will study two aspcts of th intraction of photons with lctrons. Th first of ths is th Compton ffct namd aftr Arthur Holly Compton who rcivd th Nobl Priz for physics in 197 for its discovry. Th othr dals with th radiation mittd whn a tightly bound lctron from a havy lmnt is kickd out by a photon. This givs ris to charactristic X-rays that can b usd to idntify th lmnt. Kinmatics of th Compton Effct If a photon with nrgy E0 striks a stationary lctron, as in Figur 1, thn th nrgy of th scattrd photon, E, dpnds on th scattring angl, Θ, that it maks with th dirction of th incidnt photon according to th following quation: whr m is th mass of th lctron. 1 cosθ =1 m c E 1 (1) E Θ Ε Fig. 1: Schmatic diagram of Compton Effct kinmatics. For instanc, th lowst nrgy for th scattrd photon rsults whn it mrgs at 180 dgrs with rspct to its original dirction, in which cas Eq. 1 shows that th incidnt and scattrd photon nrgis ar rlatd as: 1 E 1 = m c () Th total nrgy of th lctron E is th sum of its kintic nrgy T and its rst nrgy m c, i.. E = T + m c. Th total nrgy of th rcoiling lctron can b computd from nrgy consrvation in th raction and is givn by: or quivalntly: E = + m c E (3)

2 PHY 19 Compton Effct T = - E Clarly th lctron nrgy achivs its maximum valu in this scattring whr th photon is back scattrd. Th Klin-Nishina Formula Whil Equations and 3 tll us how to comput th nrgis of th scattrd photon and lctron in trms of th photon's angl, thy do not tll us anything about th liklihood of finding a scattrd photon at on angl rlativ to anothr. For this w must analyz th scattring procss in trms of th intractions of lctrons and photons. Th lctron-photon intraction in th Compton ffct can b fully xplaind within th contxt of our thory of Quantum Elctrodynamics or QED for short. This subjct is byond th scop of this cours and w shall simply quot som rsults. W ar intrstd particularly in th angular dpndnc of th scattring or th diffrntial cross-sction and th total cross-sction both as a function of th nrgy of th incidnt photon. First th diffrntial cross-sction, also known as th Klin-Nishina formula: [ ] 1 + [ ] dσ dω = 1/ r cos Θ 1 + ε sin Θ / 4 ε sin 4 Θ / [ 1 + cos Θ]1 + ε sin Θ / [ ] (4) whr ε = /m c and r 0 is th "classical radius of th lctron" dfind as /m c and qual to about.8 x cm. Th formula givs th probability of scattring a photon into th solid angl lmnt dω = π sin Θ dθ whn th incidnt nrgy is. W illustrat this angular dpndnc in Figur for thr nrgis of photons, whr th vrtical scal is givn in units of cm Angular Distribution of Scattrd Photon =0.5 m c d d (cm ) =1.0 m c E =.0 m c Angl (dg) Fig. : Diffrntial Cross-sction of Compton scattring vs. angl

3 PHY 19 Compton Effct 3 Not that th most likly scattring is in th forward dirction and that th probability of scattring backward is rlativly constant with angl. It will b of intrst to us in this xprimnt to know th probability of masuring lctrons with a givn kintic nrgy T = E - m c. W can radily gt this xprssion by substituting for th angl Θ in Eq. 4 via Equations () and (3) and noting that: dσ dt = dσ dω dω dt = dσ dω π (ε T ) (5) In Figur 3 w plot this nrgy dpndnc for an incidnt photon with nrgy qual to th rst mass of an lctron Scattrd lctron nrgy distribution Incidnt photon nrgy = 1.0 m c d dt (cm /MV) t=(e -m c )/m c Fig. 3: Th probability of finding an lctron with rducd kintic nrgy t for a photon with incidnt nrgy = m c. Not th ris in th cross-sction with incrasing kintic nrgy up to th kinmatic limit whr it abruptly falls to zro. In our xprimnt w will b looking for this dg. Enrgy dpndnc Th Klin-Nishina formula can b intgratd to yild th total cross-sction which displays th nrgy dpndnc for th procss: 1+ ε + ε ln(1 + ε) ln(1+ ε ) σ = π r 0 ε 1+ ε ε + ε 1+ 3ε (1 + ε)

4 PHY 19 Compton Effct 4 σ ε= E/m c Fig. 4: Enrgy dpndnc of Compton scattring Charactristic X-Ray spctra Whn lctrons or photons scattr from atoms, thy somtims impart sufficint nrgy to atomic lctrons to fr thm from thir bound stats. If this happns in a multi-lctron atom, thn a hol is cratd which is rapidly filld by an lctrons cascading down from highr lvls mitting th lost potntial nrgy in th form of photons. Whn th lvl filld is th innrmost atomic lvl, thn th X-rays producd, which uniquly idntify th lmnt, ar calld charactristic K X-rays. Thir nrgis vary with th atomic numbr (Z) of th substanc as (Z - 1) whr th subtractiv constant ariss du to th shilding ffct of th othr innr shll lctron. Th nrgis of ths X-rays can b substantial.g. for Pb thy ar about 80 KV. W can mak a rough calculation of this quantity if w rcall that th ionization potntial of hydrogn (Z = 1) is about 13.6 V which multiplid by (8-1) givs a numbr of th right ordr of magnitud. Th Exprimnt Th Apparatus Dscription Th apparatus in this xprimnt consists of a NaI (Tl) crystal attachd to a photo multiplir tub. Th opration of this dvic was dscribd in th handout daling with radiation. Th output of th countr, a voltag puls proportional to th nrgy dpositd in th countr, is fd into a Multi Channl Analyzr (MCA) housd in a prsonal computr (PC). An instruction manual coms with ach dvic and computr (PC). You should tak a part of th first laboratory sssion to bcom familiar with th opration of th dtctor and th PC with th MCA card. You should larn how to rcord and ras spctra, how to stor spctra on your disk and how to subtract background spctra from spctra containing intrsting charactristics. You should also larn how to mak hard copis of your plots for inclusion into your formal writ-up. Your instructor will hlp you gt startd on this.

5 PHY 19 Compton Effct 5 Calibration W will us th 137 Cs sourc to calibrat th scal on our MCA. W will rly on four lins as standards: (1) th photo-pak of th KV gamma ray, which is th highst nrgy pak in th 137 Cs spctrum, () a smallr X-ray pak at KV which is th charactristic Barium K Xray mittd by th 137 Cs sourc, (3) th photo-pak of th 1.33 MV gamma ray of th 60 Co sourc, and (4) th photo-pak of th 1.17 MV gamma ray of th 60 Co sourc. Eithr varying th high voltag or adjusting th gain slction switchs on th amplifir can chang th amplitud of th puls. W will st th gain switchs in thir midrang sttings and thn adjust th high voltag so as to plac th KV 137 Cs gamma in th middl of th rang of th puls hight analyzr (PHA) or about channl 400. From now on w will carfully rfrain from changing th high voltag and will prform any ndd gain changs by changing th amplifir sttings. Hr too w must b carful to mov only th high gain switchs, which can b rturnd to thir prvious sttings in a rproducibl mannr. W will tak som data with both sourcs in a singl spctrum. Put th sourcs at th bottom of th sourc holdr, as far from th NaI(Tl) as possibl. Aftr accumulating data from both sourc in th sam spctrum, us th calibrat fatur of th MCA program to input th locations of all four paks and thir nrgis. Aftrwards, th MCA program will giv you th nrgis corrsponding to th cursor position instad of th channl numbrs. Chck to s that th nrgis ar corrct by putting th cursor on your paks. You will nd to rpat this procss th scond wk of th lab bfor you go on to do th rmaindr of your masurmnts. Masurmnts Gnral Ovrviw W will not masur th full Compton scattring distribution as givn by th Klin-Nishina formula. In ordr to do that xprimnt in two laboratory priods w would nd vry powrful sourcs of gamma rays. Th saf handling of ths sourcs would not b practical in this laboratory stting. W will, howvr, masur th nd point for Compton scattring by masuring th nrgy of th photon that is back-scattrd from th stationary lctron. W will also masur th nrgy of th lctron that is back-scattrd. W will do ths masurmnts using first th 137 Cs sourc and thn th 60 Co sourc rcalling that th formr mits on photon and th lattr two. In sparat masurmnts w will masur th charactristic K X-rays of Pb and an unknown mtal and us th nrgy of th charactristic spctra to idntify thm. Th Compton Platau Mak svral masurmnts of both spctra with th sourc in a shlf blow th Nal dtctor. Choos tims sufficintly long so that statistics ar not a problm. Do you nd to prform background subtraction? Transfr th fil to Kalidagraph and plot a spctrum for ach of th two sourcs On this spctra, labl th 137 Cs and 60 Co photo-paks, th Barium X-ray, th Compton plataus, th Compton dgs and writ th nrgis corrsponding to ths faturs nxt to thm on th plot. Assign som rough uncrtaintis to ths nrgis.

6 PHY 19 Compton Effct 6 Calculat th nrgis of th Compton dgs from Compton ffct kinmatics. Us th calculations to idntify th Compton dgs on th plots and labl thm according to th photo-pak from which thy originat. Ar thy consistnt? Th Back scattrd Photon Elvat your NaI(Tl) dtctor assmbly abov th tabl on th x4 blocks so as to rduc th scattring matrial undr th sourc. Put th 60 Co sourc in th lowst position in th oldr and tak a 15 minut (Liv tim) masurmnt in this configuration and stor it into background. Put svral pics 3-4 of thick aluminum on top of th blocks undr th sourc and rpat th 15 minut masurmnt. Using th strip function of th MCA program, subtract th stord spctrum from th nw on to s th spctrum of photons scattrd from th aluminum. Plot th diffrnc spctrum. Idntify and xplain th nw sourc of gamma lins in th middl of th Compton platau. How dos this lin (or lins) rlat to th masurmnts you mad on th Compton Platau? Can you dmonstrat that nrgy is consrvd in th Compton scattring procss? Th K X-ravs of Pb Count and stor a background run. Rpat th prvious masurmnt with th lad plat undr th dtctor. Aftr background subtraction, idntify a photon lin nar 80 KV. Not its nrgy and provid an xplanation for its xistnc. Idntification of Unknown Mtal Count and stor a background run. Plac th unknown mtal sampl undr your countr and count for th sam priod of tim. Not th apparanc of an X-ray lin in th subtractd spctrum. From th masurmnt of its nrgy, try to idntify th unknown lmnt. It may b usful to rfr to th CRC handbook. Th Rport Your rport should contain a brif dscription of th xprimnt, and a drivation of th Compton kinmatics formula (1). It should also contain an ordrly xposition of your masurmnts including computr printouts and graphs whr appropriat. Show xampls of ndd calculations (if any) and stat clarly your conclusions.

PHY 192 Compton Effect 1

PHY 192 Compton Effect 1 PHY 19 Compton Effct 1 Th Compton Effct Introduction In this xprimnt w will study two aspcts of th intraction of photons with lctrons. Th first of ths is th Compton ffct namd aftr Arthur Holly Compton