ABSORPTION OF GAMMA RAYS

Transcription

1 6 Sep 11 Gamma.1 ABSORPTIO OF GAMMA RAYS Gamma rays is the name given t high energy electrmagnetic radiatin riginating frm nuclear energy level transitins. (Typical wavelength, frequency, and energy ranges are: t 0.15 nm, t Hz, and 10 kev t 2.5 MeV, respectively.) The terms gamma rays, nuclear x-rays, and high-energy phtns are ften used interchangeably. Gamma rays traversing matter are absrbed due t a number f prcesses. The ability f a substance t absrb gamma rays is expressed by the absrptin cefficient fr that substance. In this experiment an attempt will be made t verify the theretical expressin describing the absrptin f gamma rays as a functin f absrber thickness, and the absrptin cefficients fr lead and aluminum fr gamma rays frm 137 Cs will be measured and cmpared t accepted values. Thery: Gamma ray absrptin is a randm type f prcess; it is nt pssible t say whether a particular gamma ray will interact with the absrber r pass thrugh unaffected. The prcesses by which gamma ray absrptin ccur are: 1) the phtelectric effect; 2) Cmptn scattering, and; 3) pair prductin. The phtelectric effect and Cmptn scattering are discussed in experiments 5 and 6 respectively. Pair prductin is the prcess whereby, in the vicinity f a nucleus, a phtn (gamma ray) spntaneusly materialises int an electrn and a psitrn. Pair prductin can nly ccur fr gamma ray energies 1.02 MeV. In all three f these prcesses the gamma ray is either scattered away frm the incident directin r cmpletely absrbed. That is, if a detectr is placed n the ppsite side f the absrber, alng the incident directin f a beam f gamma rays, nly thse gamma rays which did nt interact with the absrber will be detected. An expressin can be derived which gives the number,, f gamma rays that will pass thrugh an absrber withut interacting, as a functin f the absrber thickness and the incident number f gamma rays. Cnsider a number,, f gamma rays incident n an absrber f thickness x. Suppse the absrber is divided int n sectins f equal thickness x (see Figure 1). Figure 1 Since gamma ray absrptin is a randm prcess, it is reasnable t expect that the change in the number f gamma rays,, due t absrptin in a sectin f the absrber, is prprtinal t the number f gamma rays incident n the absrber sectin and the absrber sectin thickness:

2 6 Sep 11 Gamma.2 i.e. x (1) That is, the likelihd f a gamma ray interacting increases as the thickness f the absrber thickness increases, and increasing the number f incident gamma rays increases the number that will be absrbed. T make equatin (1) an equality, define, the absrptin cefficient, as the cnstant f prprtinality. is a measure f the effectiveness f a given type f absrber. Als, nte that is intrinsically negative since the number f gamma rays is decreasing due t absrptin. x (2) The relative change in the number f gamma rays, due t absrptin, is x (3) Cnsider the absrber t be separated int its n sectins: Figure 2 The number f gamma rays remaining after each sectin f the absrber is traversed is given by; 1 1 ( 1 x) 2 1 x 1 x ( ) and n = (1 x) n is the number remaining after passing thrugh the cmplete absrber. w recall that x = x/n. n n 2 x 1 (4) n

3 6 Sep 11 Gamma.3 te that the abve analysis assumes that the number f gamma rays changes linearly ver the width f each absrber sectin. i.e. fr 1, 1 = x = c 1 + c 2 x c 1, c 2 cnstants Hwever, the prper expressin is 1 = x, where decreases cntinuusly as the gamma rays pass thrugh the absrber sectin. This prblem can be vercme by taking smaller and smaller sectin thicknesses. Therefre, frm equatin (4): x lim e x n lim 1 n n n n (5) where is the incident number f gamma rays, and is the number transmitted thrugh the absrber f thickness x. The abve result can be btained directly frm equatin (3) by integratin: x d lim implies x0 dx d x dx 0 ln ln x = e x That is, the number f gamma rays remaining decreases expnentially as the absrber thickness is increased. Althugh the desired result fllws rather easily by integrating equatin (3), such is nt always the case. In this instance, equatin (3) can be written as d dx which is an easily slved differential equatin. Hwever, fr sme types f prblems, the differential equatin may be quite cmplicated. In that case, it is useful t use an iterative type f slutin as was dne initially. Als, nte that the iterative calculatin lends itself rather nicely t cmputer prgramming.

4 6 Sep 11 Gamma.4 Apparatus: The surce used in this experiment is 137 Cs, which emits gamma rays with an energy f MeV. There are fur lead absrber disks f thickness 1.0 mm, 1.6 mm, 3.2 mm, and 6.5 mm (each ±0.1 mm), and numerus aluminum absrber plates whse thicknesses are stamped n the plate ends. The surce is cllimated t prvide an incident beam f gamma rays, and the detectr is well-shielded and cllimated t reduce backgrund cunts and t detect nly thse gamma rays which cme directly frm the surce. The detectin and analysis system cnsists f a ai(tl) scintillatin crystal and phtmultiplier tube cnnected t a high vltage supply and a multichannel analyser (MCA) cnnected t a PC. Gamma rays passing int the ai(tl) crystal cause flashes f light (scintillatins) inside the crystal. These flashes f light release electrns frm the phtcathde f the phtmultiplier tube (by the phtelectric effect). The high vltage applied t the phtmultiplier tube causes the electrns t be channelled thrugh the varius stages f the tube, with amplificatin f the number f electrns ccurring at each stage. The result is a pulse at the utput f the phtmultiplier tube, the vltage f the pulse being prprtinal t the energy depsited in the crystal by the gamma ray. After linear amplificatin the vltage pulse is digitized by the analgue-t-digital-cnverter (ADC) in the multichannel analyser, and the cmputer mnitr displays the number f pulses versus channel number. The channel number is directly prprtinal t the phtmultiplier tube pulse vltage and hence t depsited gamma ray energy. The mnitr thus shws the energy distributin f the gamma rays being detected. A diagram and phtgraph f the apparatus are shwn in Figure 3. Figure 3

5 6 Sep 11 Gamma.5 Detectr Absrber Hlder Surce (shielded) Multichannel Analyser HV Supply/ Amplifier Figure 4 shws a typical energy spectrum fr a mnenergetic gamma surce: Figure 4 A number f features f the spectrum are wrthy f mentin. The large peak results frm cmplete gamma ray absrptin whether by a single phtelectric event, r by Cmptn

6 6 Sep 11 Gamma.6 scattering fllwed by a phtelectric event. (Because the pulse amplitude per MeV is nearly independent f the kinetic energy imparted t the electrns fr ai(tl), the respnse f the detectr is linear. Thus the pulse amplitude is directly prprtinal t the amunt f gamma ray energy depsited, n matter what the prcess.) Althugh the incident gamma ray is mnenergetic, the peak has a width due mainly t fluctuatins in the number f electrns released at the phtcathde per flurescent phtn. The cntinuum f energies frm zer t the start f the peak is due t the varius amunts f gamma ray energy absrbed by the crystal fr Cmptn scattering. (A gamma ray that interacts with the crystal via a single Cmptn event and then exits the crystal will nt depsit all f its energy.) The small lw-energy peak is due t gamma rays that are backscattered frm the surce shielding r the phtmultiplier windw int the crystal. Prcedure and Experiment: OTE: In the thery sectin, the discussin invlved the number f gamma rays. Hwever, since the surce emits gamma rays cntinuusly in all directins, the terms and shuld have been defined as numbers f gamma rays per unit area per unit time. This will nt affect the results, thugh, as lng as cunts are nrmalised t a cnstant time interval. (i.e. cnvert t cunts per secnd r cunts per minute, r cunts in 5 minutes, etc.) The area ver which measurements are made is cnstant because the active frntal area f the scintillatin crystal des nt change. Als, recall that fr a randm prcess such as absrptin f radiatin, the experimental uncertainty in a cunt measurement is given by. Thus the relative uncertainty 1 decreases as the number f cunts recrded increases. Therefre, the lnger the time interval ver which cunts are recrded, the better the experimental accuracy. Fr example, suppse a ne minute measurement yields 100 cunts and a fur minute measurement yields 400 cunts. Althugh the result in bth instances is a cunt rate f 100 cunts/min, in the first case the result is (100 ± 100 )/1 min = 100 ± 10 cunts/min, while in the secnd case it is (400 ± 400 )/4 min = 100 ± 5 cunts/min. When perfrming a cunting experiment a cmprmise must be reached between the amunt f time available fr the experiment and the desired accuracy. When chsing time intervals fr the cunts t be made in this experiment, be sure that all f the measurements can be made in the lab perid, and remember that as the absrber thickness is increased the cunt rate will decrease, s lnger time intervals will be required t maintain a desired degree f accuracy. 1. Turn n the pwer and high vltage switches n the scintillatin amplifier/high vltage pwer supply. Check that the settings are:

7 6 Sep 11 Gamma.7 COARSE GAI: 160 FIE GAI: HIGH VOLTAGE: kv If any f these settings are different, cnsult yur lab instructr. 2. Allw five minutes fr the high vltage pwer supply t warm up. 3. Turn n the UCS30 device. 4. Duble-click n the UCS30 icn n the desktp. 5. Click n the Mde menu and select PHA (Direct In), the 3 rd item n the list. 6. Data acquisitin is cntrlled using the buttns n the tlbar. Fr the mst part, the functins f these buttns are bvius, and a TlTip will appear if yu hver ver a buttn. Data acquisitin is begun by clicking the GO buttn. Data acquisitin is stpped by clicking the STOP buttn. Data is deleted using the eraser buttn (3 rd frm left). Data can be acquired fr a pre-set time by clicking the clck buttn. Ensure that Live Time is selected. T determine the ttal number f cunts in sme regin, r t determine the channel number/energy f a peak in the spectrum, a regin f interest (ROI) must be defined. This is dne using the ROI buttn. A ROI is defined by clicking the ROI buttn, placing the cursr at the left edge f the desired regin, and then clicking with the left muse buttn and dragging the cursr t the right edge f the regin. The ROI will change clur t shw the regin that has been selected. The ttal number f cunts in the regin is given by the GROSS number (nt the ET number). The CETROID is the channel number r energy f the peak within the ROI. T clear the ROI, g t Settings ROIs. The vertical axis can be tggled between a linear r lgarithmic scale with the Y/lin and Y/lg buttns. The vertical axis scale is changed by mving the slider at the far right side f the prgram windw. 7. Ensure that the three large lead bricks are in frnt f the surce. It will be assumed that these bricks absrb all radiatin frm the surce that wuld therwise strike the detectr. Measure the backgrund radiatin (due t ther surces in the building, csmic rays, the earth, etc.) by cunting fr 600 secnds. Recrd the ttal number f cunts btained in all channels f the display. The backgrund rate is the number f cunts detected divided by 600 secnds. This backgrund rate must be subtracted frm yur measurements t btain the rate due t the surce nly. Once the backgrund measurement has been cmpleted, remve the three lead bricks. (DO OT REMOVE AY OF THE OTHER LEAD SHIELDIG THAT SURROUDS THE SOURCE). 8. Visually check that the absrber hlder is in line with, and abut midway between, the surce and detectr.

8 6 Sep 11 Gamma.8 9. With n absrber, measure the incident gamma ray cunt rate. Use a time f 100 s. The spectrum (energy distributin) f gamma rays that yu bserve is due t characteristics f the detectr system. The incident gamma rays are mnenergetic at MeV. As well as measuring the gamma cunt rate as described abve, recrd the channel number f the gamma energy peak. 10. Measure the thicknesses f the 4 available lead absrber disks. 11. Measure the gamma ray cunt rate and peak channel number fr all pssible cmbinatins (15) f the fur lead absrber disks. Remember t set and recrd the cunt time, and t increase the cunt time as the absrber thickness is increased. 12. Measure the gamma ray cunt rate and peak channel number fr varius thicknesses f cpper absrber plates. (BE SURE TO RECORD THE THICKESS OF EACH PLATE AS IT IS USED.) 13. Measure the gamma ray cunt rate and peak channel number fr the aluminum plate absrbers. Use the available C clamp t ensure that the plates are munted vertically (perpendicular t the incident gamma rays). Since aluminum is nt as effective an absrber as lead, and since mst f the plates are apprximately the same thickness, take measurements fr n plate, ne plate, tw plates, etc. until all the aluminum plates are between the surce and detectr. (BE SURE TO RECORD THE THICKESS OF EACH PLATE AS IT IS USED.) Analysis Fr each set f results (lead, cpper, and aluminum) plt the natural lgarithm f the gamma ray cunt rate (crrected fr backgrund) versus absrber thickness. i.e. Plt ln versus x. Accrding t thery, since e x ln = ln x Since and are cnstants, the theretical predictin is that ln versus x is linear with a slpe f. D yur results verify the theretical relatinship between cunt rate f transmitted gamma rays and absrber thickness? Determine the experimental values f the absrptin cefficients fr lead, cpper, and aluminum fr gamma rays frm 137 Cs. Hw d yur values cmpare with the accepted values f 1.21 cm 1, cm 1, and cm 1 respectively? In yur reprt discuss any surces f errr which may be inherent in the design f the experiment. (HIT: Cnsider the gemetry f the apparatus and the prcesses by which gamma rays interact with matter.) What assumptins were made in the thery? D these assumptins hld fr the actual experiment? Wuld yu expect yur values t be higher r lwer than the accepted values? Explain.) Which absrber type is mre effective: lead, cpper, r aluminum? Try t think f a few reasns t explain why. Hw des the energy (peak channel number) f the transmitted gamma rays vary with absrber thickness? Discuss.