E hf. hf c. 2 2 h 2 2 m v f ' f 2f ' f cos c

Transcription

1 EXPERIMENT 9: COMPTON EFFECT Rlatd Topics Intractions of photons with lctrons, consrvation of momntum and nrgy, inlastic and lastic scattring, intraction cross sction, Compton wavlngth. Principl Whn photons ar scattrd on lctrons, thir momntum and nrgy gts changd. Th chang of nrgy in dpndnc on scattring angl is masurd by g-spctroscopy. Th Compton wavlngth is dtrmind from th masurmnt data. Tasks - Calibrat th st-up with th aid of th 34 kbq 137Cs and th Na (74kBq) sourc. - Masur spctra of th radiation scattrd by a stl rod at various angls. - Calculat th Compton wavlngth from th spctra. Thory and Evaluation Compton scattring is lastic scattring of photons on lctrons. Both momntum and nrgy consrva-tion ar fulfilld and momntum and nrgy ar xchangd btwn photon and lctron th sam way as on would xpct of mass points. Th nrgy rang is that of th lctron's rsting mass so th cal-culation has to b rlativistic. Th nrgy E of a photon dpnds on it's frquncy f and th Planck constant h and is E hf and th momntum p of a photon with wavnumbr k is hf p k c If th lctron is at rst at th bginning, all th momntum coms from th photon and stays constant throughout th raction. Aftr th raction th initial momntum is split up into th momntum of th pho-ton. Th photon movs now undr th angl φ to it's initial dirction and has th altrd frquncy f. Th momntum of th lctron aftr th scattring is p c = mv with th mass as a function of vlocity (m m ). Th vctor sum of both quals th initial momntum and thus holds for th squars of th vctors: h m v f ' f f ' f cos c Th nrgy has to b constant throughout th raction, too and for simplicity counting th lctron rst-ing mass quivalnt in th quation (th point of zro nrgy is arbitrary) hf m c hf '

2 with th rlativistic rlation for lctron spd v m m 1 ( v ) c m v c m c m c m c m c h f ' f f ' f cos m c m c h (f f ') m m c h f f '(1 cos ) m (m m )c m c E 4 kin h f f '(1 cos ) m c h(f f ') f c, f '= c ' and c(f f ') ' is f f ' h (1 cos ) which is Compton s formula fort h wavlngth shift. Fig.1: Dcay schm of Cs-137. Most of th csium-137 (Cs-137) nucli (94%) dcay to an xcitd stat of barium-137 (137-Ba*), which thn gamma dcays to a stabl stat. is calld Compton wavlngth, with h 0

3 hc E hf is th corrsponding nrgy E c = m c th nrgy quivalnt of th lctron's rsting mass of 511 kv. So th nrgy scal for th Compton ffct is st by th lctron mass which can b intrprtd in th way that an lastic scattring occurs whn th photon is about as "havy" as th lctron. Fig. 1 shows th dcay schm of th usd nuclid 137-Cs. Th proportions of th nrgy scal ar not displayd corrctly. Th main mission is th sharp 66 kv lin. But thr is a probability of th 11/- xitd stat of th daugthr nuclid 137-mBa to dcay by innr convrsion bcaus of th high diffrnc of spin quantum numbr btwn ground and xitd stat in th cas of 137-mBa lading to a 3 kv X-ray lin and a long half lif of th xitd stat of two and a half minut. Only th photons rach th dtctor, lctrons cannot lav th sourc pllt. Incoming photons of a dfind nrgy ar dtctd in th scintillation countr by th lctrons thy xit in th scintillator crystal ithr by photo ffct, whr thy transfr all thir momntum and nrgy to th lctron (photon absorption or compltly inlastic scattring), or by Compton scattring, whr momntum and nrgy ar xchangd btwn photon and lctron in an lastic scattring. So th masurmnt rsult of a sharp photon nrgy is a whol spctrum consisting of th photo pak and th compton background. Th Compton scattring th photons undrgo in th dtctor is hr not of intrst only th incidnts dtctd by photo ffct thus showing th original photon nrgy should b countd for as intrsting incidnts laving othr ffcts in th spctrum ignord you ar sarching for th photo pak of photons Compton scattrd by th stl rod. Th st-up is mad in a way that only thos of th 66 kv photons that hav undrgon scattring on th stl rod in a dfind angl rach th dtctor and can b countd and thir nrgy is valuatd in th rcordd g-spctrum. Th dpndnc of th nrgy E of th scattrd photons that had rachd th stl rod with nrgy E 0 (hr 66 kv) on th scattring angl is thn: E ' (1 cos ) E This function has a maximum for ϕ = 180, whr no nrgy is tranfrrd to th lctron and th photon kps its initial nrgy and a minimum for, whr th fraction of th initial nrgy is rflctd. E ' 1 E E

4 For th spctrum of th lctrons xitd in th stl rod by Compton ffct, though not masurd, th following can b said: In th cas of compton scattring thr is a highst nrgy fraction of th initial nrgy of th photon that can b transfrrd to th lctron. This nrgy is transfrrd, if th photon gts rflctd back into th dirction whr it cam from (back scattring). Equipmnt Cs kbq, Cs MBq, Na- 74 kbq sourcs, lad blocks, gamma dtctor Fig.: Exprimntal st-up for compton ffct. St-up and Procdur St up th quipmnt as sn in Fig.. Bfor turning on th oprating unit for th scintillation countr, connct th high voltag cabl corrctly to oprating unit and photomultiplir and rad th instructions in th manual of th gamma-dtctor. St th multiturn potntiomtr of th oprating unit to.00. Connct th multi channl analyzr (MCA) to th computr's USB port or a RS3 srial intrfac and start th "masur" program. Slct th Gaug "Multi Channl Analyzr". 1. Slct "Spctra rcording" (s Fig. 3), st th "Gain" to "Lvl 1", st th "Offst" to 0 %, choos "Channl numbr" as x-data (s Fig. 4) and start data rcording. Put th 137-Cs pllt into th slot of th scrning cylindr for th g-dtctor nar to th dtctor. Incras th high voltag with th multiturn potntiomtr until th 66 kv pak gts to about channl If you ar not sur about th high voltag stting, start with low sttings and incras th high voltag, until th 66 kv pak wandrs to th right nd of th spctrum. Cancl th masurmnt and lav th high voltag st-ting unchangd from now on.

5 Fig. 3: Start window of th MCA Now start th MCA gaug again and slct "Sttings and calibration". Th window sn in Fig. 5 appars. Us th "Calibrat" button. Prform th 3-point calibration with th -Na and th 137-Cs sourc and us th "Apply" button. Sav th calibration as sn on Fig. 6. Rmov th 34 kbq sourc from th slit of th cylindrical dtctor scrning. B carful with dtctor handling th scintillation crystal braks asily and cracks in it will rduc snsitivity and nrgy rsolution. Fig. 4: Window for spctrum rcording hr th spctrum of 137-Cs with gain lvl 1.

6 Fig. 5: Calibration window Fig. 6: Saving th calibration. Now rturn to "Spctra rcording" and st th "x-data" to "Enrgy". Put th 18.5 MBq sourc into th lad brick with hol. Adjust th stup in a way that mainly scattrd photons from th stl rod gt rcordd. Th 66 kv lin should b wll supprssd by th shilding. Th prsnc of th stl rod should incras th impuls rat distinctly if you tak it away, it should drop clarly. Th spctrum should show a distinct maximum from th prfrrd Compton scattring angl. Rcord such a spctrum for ach angl (.g. for 30, 60, 90, 10 ) and sav th data with th "Accpt data" button. Start with high or mdium angls. 3. Sav th rcordd spctra to your disc driv. Diffrnt ways may b suitabl for finding th maximum of th Compton scattring pak: You may us "Analysis" > "Smooth " to rduc th statistical nois in th spctrum and valuat th pak position with th "Survy" tool. Els you may mark th intrsting rgion of th spctrum with th "Mark" tool that looks lik a cross and thn us "Analysis" > "Function fitting " to fit a scald normal distribution with offst to th data and thn us "Analysis" > "Show xtrma " to find th position of th pak of th fit. Plot th Compton scattring pak nrgy vrsus th scattring angl. Plot th wavlngth λ = hc/e that corrsponds to th nrgy E ovr th scattring angl and th wavlngth shift, too.