Atomic and Nuclear Physics

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1 Atomi and Nulear Physis X-ray physis Compton effet and X-ray physis LD Physis Leaflets P Compton effet: Measuring the energy of the sattered photons as a funtion of the sattering angle Objets of the experiment g Reording the energy spetra of X-rays sattered on a sattering body under various angles. g Determining the energy of the sattered photons as a funtion of the sattering angle. g Comparing the measured energies with the energies alulated from energy and momentum onservation Iv/Sel Priniples When X-rays pass through matter, part of them is sattered. Aording to lassial physis, the frequeny of the radiation should not be hanged by the sattering proess. However, in 193 the Amerian physiist A. H. Compton observed that the frequeny was redued in some of the X-rays. In order to explain this phenomenon, the entire sattering proess has to be treated in terms of quantum physis, and the X-rays have to be onsidered, for example, aording to the partile aspet. Moreover, it is assumed that the sattering eletrons are free, whih is a good approximation for the outer atomi eletron shells at energies in the range of X- rays. Thus, in a sattering proess, a photon with the frequeny ν 1, i.e. with the energy E 1 = h ν 1, hits a free eletron at rest with the rest mass m 0. The photon is sattered by the angle ϑ, and the eletron moves at the veloity v with the angle ϕ relative to the diretion of the inoming photon (see Fig. 1). For this ollision proess, onservation of energy and momentum is postulated as in an elasti ollision of two lassial partiles. As the photon has no rest mass, energy onservation in the relativisti formulation gives m0 h ν 1+ m0 = h ν + (I) v 1 : veloity of light in vauum and onservation of the omponents of the momentum gives h ν1 h ν m0 = osϑ+ v osϕ v 1 and h ν m0 0 = sinϑ+ v sinϕ v 1 (II). From Eqs. (I) and (II), the following equation is derived for the energy of the sattered radiation: E E1 = E 1+ 1 osϑ m 1 0 ( ) (III). In the experiment, Compton s investigations are repeated on a sattering body made of plexiglass. The results are ompared with Eq. (III). The spetrum is reorded with the aid of the X-ray energy detetor. Fig. 1 Shemati illustration of Compton sattering 1

2 P LD Physis Leaflets Apparatus 1 X-ray apparatus with X-ray tube Mo and goniometer Compton aessory Xray II X-ray energy detetor Sensor-CASSY MCA box CASSY Lab BNC able, 1 m PC with Windows 98/NT or higher version Setup The experimental setup is illustrated in Fig.. Put the Zr filter (from the sope of delivery of the X-ray apparatus) onto the beam entrane side of the irular ollimator (from the sope of delivery of the Compton aessory Xray II). Mount the irular ollimator in the ollimator mount of the X-ray apparatus. Guide the onnetion able of the table power supply through the empty dut of the X-ray apparatus, and onnet it to the Mini-DIN soket of the X-ray energy detetor. Fasten the assembly of the X-ray energy detetor and the sensor holder in the sensor arm of the goniometer. Use the BNC able supplied with the X-ray energy detetor to onnet the signal output of the detetor to the BNC soket SIGNAL IN of the X-ray apparatus. Push a suffiient length of the onnetion able into the dut so that the sensor arm an perform a omplete rotation. Fig. Experimental setup for measuring the primary beam (above) and for measuring the energy of the sattered photons as a funtion of the sattering angle (below) Zr filter (a), irular ollimator (b), absorption sreen (), X- ray energy detetor (d), sattering body (e) The X-ray apparatus fulfils all regulations on the design of an X-ray apparatus and fully proteted devie for instrutional use and is type approved for shool use in Germany (NW 807 / 97 Rö). The built-in protetive and shielding fixtures redue the dose rate outside the X-ray apparatus to less than 1 µsv/h, whih is of the order of magnitude of the natural bakground radiation. g Before putting the X-ray apparatus into operation, inspet it for damage and hek whether the high voltage is swithed off when the sliding doors are opened (see instrution sheet of the X-ray apparatus). g Protet the X-ray apparatus against aess by unauthorized persons. Avoid overheating of the X-ray tube. g When swithing the X-ray apparatus on, hek whether the ventilator in the tube hamber starts rotating. The goniometer is positioned solely by means of eletri stepper motors. g Do not blok the target arm and sensor arm and do not use fore to move them. Press the SENSOR key and, using the ADJUST knob, adjust a sensor angle of 150 manually. If neessary, push the goniometer to the right. Adjust the distane between the X-ray energy detetor and the axis of rotation so that the detetor housing just does not over the X-ray beam at this sensor angle. Then push the goniometer to the left so that the detetor housing just does not touh the irular ollimator (approx. 8 m distane between the irular ollimator and the axis of rotation). Connet the Sensor-CASSY to the omputer, and plug in the MCA box. Use a BNC able to onnet the output SIGNAL OUT on the terminal panel of the X-ray apparatus to the MCA box. Carrying out the experiment Connet the table power supply to the mains (after approx. minutes the LED shines green and the X-ray energy detetor is ready for operation). Call CASSY Lab, and selet the measuring parameters Multihannel Measurement, 56 Channels, Negative Pulses, Gain -3, Measuring Time 300 s.

3 LD Physis Leaflets P Estimating the ounting rate in the sattering arrangement: Put the plexiglass sattering body on the target stage, and lamp it. Press the TARGET pushbutton, and, using the ADJUST knob, adjust the target angle manually to 0. Selet the tube high voltage U = 35 kv and the emission urrent I = 1.00 ma, and swith the high voltage on. Start reording the spetrum with or with the F9 key. Vary the sensor angle slowly between 150 and 30, and eah time read the total ounting rate above on the right in the CASSY Lab window. Redue the emission urrent if the total ounting rate learly exeeds 00 1/s. Adjusting the ounting rate of the primary beam: Remove the target holder with the target stage, and take the sensor into the 0 position. Put the absorption sreen onto the irular ollimator, and align it arefully (the srews should point upwards and downwards, respetively). Redue the emission urrent to 0.1 ma, and swith the high voltage on. Start reording the spetrum with or with the F9 key. In steps of 0.1 around 0 look for the sensor angle at whih the total ounting rate is only slightly greater than the ounting rates measured in the sattering arrangement (if neessary, hange the emission urrent slightly). Selet the emission urrent I = 1.00 ma (or the urrent determined previously for estimating the ounting rate), and swith the high voltage on. Adjust a target angle of 0 and a sensor angle of 30. Reord a new spetrum with or with the F9 key. Then reord further spetra at onstant target angles for the sensor angles 60, 90, 10 and 150. Store the entire measurement with an appropriate name. Measuring example Fig. 3 shows the primary spetrum, i.e. the emission spetrum of the X-ray tube with Mo anode after monohromatization with a Zr filter. In Fig. 4 a superposition of the spetra reorded under various sattering angles ϑ in an energy interval around the Mo Kα line is shown. It an be seen that the energy of the sattered radiation dereases with inreasing sattering angle. The intensity of the sattered radiation has its minimum at ϑ = 90. Fig. 3 Emission spetrum of the X-ray tube with Mo anode after monohromatization with a Zr filter (ϑ = -0.1 ) If no or only a small ounting rate is measured: Chek the alignment of the absorption sreen and possibly rotate the absorption sreen by 180. Reording the primary spetrum: The X-rays to be measured produe additional fluoresene X-rays in the housing of the Si-PIN photodiode of the X-ray energy detetor, whih are also registered. Therefore the Au Lα and the Au Lβ lines are to be expeted in the primary spetrum apart from the Mo Kα and the Mo Kβ lines (see Fig. 3). With the aid of these lines, the energy alibration an be arried out. Delete registered events, and reord the primary spetrum with or with the F9 key. Next open the Energy Calibration dialog window with the shortut Alt+E, selet Global Energy Calibration, and enter the energies of the Au Kα line (9.71 kev) and the Mo Kα line (17.44 kev [1]). Selet the menu item Other Evaluations Calulate Peak Center in the pop-up menu of the diagram window, mark the region of the Au Kα line, and enter the result in the Energy Calibration dialog window. Then determine and enter the peak enter of the Mo Kα line. Fig. 4 Energy interval of the primary spetrum (0 ) and the energy spetra measured under the sattering angles 30, 60, 90, 10 and 150. Reording the spetra in the sattering arrangement: Remove the absorption sreen. Mount the target holder with the target stage on the goniometer. Put the plexiglass sattering body on the target stage, and lamp it. 3

P6.3.7. LD Physis Leaflets Evaluation Fig. 5a Setion of the spetrum N 1 (0, primary spetrum) with the unshifted Mo Kα line Fig. 5b Shifted Mo Kα line from the spetrum N (30 ) and unshifted Fig.

4 P LD Physis Leaflets Evaluation Fig. 5a Setion of the spetrum N 1 (0, primary spetrum) with the unshifted Mo Kα line Fig. 5b Shifted Mo Kα line from the spetrum N (30 ) and unshifted Fig. 5 Shifted Mo Kα line from the spetrum N 3 (60 ) and unshifted Fig. 5d Shifted Mo Kα line from the spetrum N 4 (90 ) and unshifted Fig. 5e Shifted Mo Kα line from the spetrum N 5 (10 ) and unshifted Fig. 5f Shifted Mo Kα line from the spetrum N 6 (150 ) and unshifted 4

LD Physis Leaflets P6.3.7. Preparation for further evaluation in CASSY Lab: Create the new quantity Sattering Angle (as parameter, symbol: &J, unit:, from: 0, to: 180, deimal plaes: 0).

5 LD Physis Leaflets P Preparation for further evaluation in CASSY Lab: Create the new quantity Sattering Angle (as parameter, symbol: &J, unit:, from: 0, to: 180, deimal plaes: 0). Create the new quantity Energy (as parameter, symbol: E_, unit: kev, from: 0, to: 0, deimal plaes: ). Create the new display Evaluation with the sattering angle as x-axis and the energy as y-axis. Results When X-rays pass through matter, part of them is sattered and experienes an energy shift (Compton effet). The energy shift an be alulated by desribing the sattering proess as a ollision between an X-ray photon and a free eletron at rest and by postulating the onservation of energy and momentum in this proess. Determining the energy as a funtion of the sattering angle: Selet an energy spetrum and a suitable interval. Call the menu item Other Evaluations Calulate Peak Center in the pop-up menu of the diagram window, and mark the region of the energy-shifted peak (starting from ϑ = 90 the energy resolution of the detetor is suffiient to separate the unshifted and the shifted peaks, see Fig. 5d to 5f). Enter the peak enter obtained and the assoiated sattering angle in the table of the display Evaluation (see Fig. 6). Comparison of the measured energies with the energies alulated from energy and momentum onservation: Selet the display Evaluation, and open the Free Fit dialog window with the shortut Alt+F. Enter f(x,a,b,c,d) = 17.44/( *(1-os(x))/A) and the initial value for A: 511 (onstant). Clik on Continue with marking a range, and mark the data points in the diagram. The result is a theoretial urve alulated aording to Eq. (III) with the parameters E 1 = kev and m = 511 kev, whih is in good agreement with the measured values (see Fig. 6). Supplementary information Alternatively, the omparison between measurement and theory an be arried out as a free fit with the free fit parameter A (the rest mass of the ollision partner of the X-ray photon). As a result a value for the parameter A is obtained, whih agrees with the rest mass of an eletron (m = 511 kev) to a good approximation. Literature [1] weighted mean value from C. M. Lederer and V. S. Shirley, Table of Isotopes, 7th Edition, 1978, John Wiley & Sons, In., New York, USA. Fig. 6 Energy E determined from the measured energy spetra as a funtion of the sattering angle ϑ and urve alulated aording to Eq. (III). LD Didati GmbH Leyboldstrasse 1 D Huerth / Germany Phone: (033) Fax: (033) info@ld-didati.de by LD Didati GmbH Printed in the Federal Republi of Germany Tehnial alterations reserved

Atomic and Nuclear Physics

Atomic and Nuclear Physics Atomi and Nulear Physis X-ray physis Compton effet and X-ray physis LD Physis Leaflets P6.3.7. Compton effet: Measuring the energy of the sattered photons as a funtion of the sattering angle Objets of