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University of Michigan Department of Physics 4
Figure 4. Six converter plates available for this experiment, From left to right,carbon, aluminum, copper, tin, tungsten & lead.
The main focus of this experiment is the measurement of the pair production yield as a
function of the atomic number of the target material. Six converter plates are provided with the physical characteristics listed in Table I below.
Z A X (cm)
Y (cm)
Z (cm)
M (g)
C 6 12.0107 7.620 8.635 2.547 294.0
Al 13 26.981538 7.605 8.637 1.750 311.3
Cu 29 63.546 7.623 8.638 0.537 315.7
Sn 50 118.71 7.785 8.730 0.730 362.4
W 74 183.84 7.634 8.652 0.275 307.7
Pb 82 207.2 7.635 8.640 0.394 291.6
Table I. Physical dimensions of pair production converter plates.
To compare the relative effects of different atomic number, you will need to divide the number of detected pair events by the number of target nuclei per unit area. From the numbers provided above, that can be determined from the formula:
# nuclei/area AN M
A X Y
where NA is Avogadro’s Number.
The key component of this experiment is the high purity Ge solid state detector which is efficient for detecting gamma-rays while providing excellent energy resolution. The basic geometry of the active volume is a cylinder 52.7 mm in diameter by 54.1 mm long. This device should be operated with a positive potential of 3000 v and must be maintained at cryogenic temperatures with liquid nitrogen. Make sure the detector is adequately cooled before switching on the detector bias voltage. A diagram and photograph of the detector and its housing are shown in Figure 5 below.
University of Michigan Department of Physics 5
Figure 5a. Cross-section of the highpurity Ge detector. The germaniumis shown in cyan with electrodesdrawn in magenta. The green linesindicate the internal liquid nitrogen shield and the outer vacuumhousing is drawn in red.
Figure 5b.Photograph of the high purity Ge detector encased in its vacuum housing and surrounded by lead bricks andbracket to support radioactive sources.
The Ge detector is connected by a coaxial cable to the rear panel of the NIM HV bias
supply. The detector analog signal output is connected via coax to the input of a linear amplifier module as shown in Figure 6. The output of this unit is, in turn, fed to an MCA (multi-channel analyzer) which is read out by the desktop PC nearby. The only electronic controls that you should possibly change are the linear amplifier gains. For this experiment, the COARSE and FINE gains should be adjusted to put the 1460.830 KeV γ-ray that follows the 40K → 40Ar electron capture into an MCA channel close to 2297, assuming a total of 4096 (see Figure 8). The 40K source is a small bottle of “NoSalt” salt which was purchased at Kroger’s.
The Amptek MCA8000A ‘POCKET MCA’ is accessed via the desktop computer standing nearby. Log on to the PC using the username, umroot\phys-advlab2. The password is prominently posted in the classroom. The data acquisition program for the MCA can be initiated by double clicking on the desktop icon shown below:
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University of Michigan Department of Physics 9
Figure 9. EXCEL spreadsheet format for pair production data. Store MCA data starting on line10. Text identification should be on line 6 and integration time on line 8.
Naively one would expect that each individual gamma-ray line would be a symmetric Gaussian shape. In fact, probably due to inefficiencies in charge collection in the Ge detector, the waveform is decidedly skewed with a much longer tail on the low energy side of the peak. A mathematical model for this behavior is shown graphically in Figure 10. The curve is the concatenation of a simple exponential on the left (in red) and a Gaussian on the right (in blue). The two curves are joined slightly to the left of the maximum value with continuous values and first derivatives at the breakpoint, xb = - σ2/λ. This model is used in the pair_prod_peaks program.
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University of Michigan Department of Physics 11
The setup for measuring e+e– pair production is shown in Figures 12a & b. The critical trick of this procedure is to make sure that direct radiation from the Ra source never directly illuminates the Ge detector. The tungsten brick (with the white plastic handle) is extremely dense (Don’t Drop!!!) and is quite effective as a shield. For this reason, keep the source at the back edge of the W block, as shown. The various converter plates should be placed on the inclined support directly above the Ge detector. Gamma-rays with energies above the 2mec
2 threshold can convert to positrons and electrons and the positron will quickly slow down, capture an electron and annihilate into two 511 KeV γ-rays. This effective fluorescence is the signature that you will detect in the spectra taken with the six elemental converter plates. The conversion efficiency of this process is low so make sure you integrate for a long enough time to obtain sufficient statistics. Also make sure to take a background run with no absorber!
Fig. 11b Attenuated measurement of the 226Ra spectrum with a Cu absorber.
University of Michigan Department of Physics 12
Fig 12a. Side view of the source,converter plate and detectorhousing.
Fig 12b. Close-up view of the 226Ra source and Cu converter plate.
Data Analysis
The first task for data analysis is to estimate the photon absorption cross sections for carbon and lead and compare these measurements with values obtained from the NIST Web site, http://www.nist.gov/pml/data/xcom/index.cfm. Accessing this URL will get you to the NIST XCOM: Photon Cross Sections Database. If you need instructions for use, go to option 4: How to Run the XCOM Program. For the less timid, proceed directly by clicking Database Search Form on the right-hand side of the screen, then click Submit Information. Make sure to select the “All quantities in barns/atom” option under Options for output units:. You will be interested in the spectral range from 290 KeV to 2500 KeV. Select the element of choice and click the second Submit Information button. From your data, you should be able to measure the count attenuation for at least 20 different spectral lines. To obtain the atomic cross sections, divide log(n1/n2) by the number of nuclei per unit area. Compare with the predictions obtained from the NIST facility. Comment on the cross section behavior in the energy range of this experiment and any qualitative differences between carbon and lead. The central focus of this experiment is the measurement of the relative yield of positrons as a function of the converter element and its thickness. Determine the relative yield per number of nuclei per unit area and make a log-log plot of the results as a function of target atomic number, Z. Fit this data to the functional form shown below to find the best fit values for C and n. (Use Solver in Excel or an equivalent non-linear fitting algorithm.)
1/3+e e
183 2log
7ZC Z n
ø
University of Michigan Department of Physics 13
How does the value of n compare to the expectation based on quantum electrodynamics?
Table III. Gamma‐ray energies of various isotopes.(This data is also available in a file,pair_prod_lines.xlsx.)
Appendix A
The IDL gamma_peaks analysis code is stored in the rtorres1 user account in the
directory, C:\Users\rtorres1\Documents\e+e- progs. This keeps the code protected from random modifications. Two source code files are required, gamma_peaks.pro and gamma_shape.pro. The code can be compiled and saved to the executable file, gamma_peaks.sav, using the procedures outlined in IDL_instr.pdf and IDL_instrux.txt. Access to the SAV file must be permitted for student use, ie. phys-advlab1 and phys-advlab2.
University of Michigan Department of Physics 15
References
1. P. A. M. Dirac, The Quantum Theory of the Electron, Proceedings of the Royal Society of London. Series A 117, 610-624 (1928)
2. P. A. M. Dirac, The Quantum Theory of the Electron. Part II, Proceedings of the Royal
Society of London. Series A 118, 351-361 (1928).
3. P. A. M. Dirac, A Theory of Electrons and Protons, Proceedings of the Royal Society of London. Series A 126, 360-365 (1930).
4. P. A. M. Dirac, Quantised Singularities in the Electromagnetic Field, Proceedings of the Royal Society of London. Series A 133, 60-72 (1931).
5. Carl D. Anderson, Energies of Cosmic-Ray Particles, The Physical Review, Series II 41, 405-421 (1932).
6. Carl D. Anderson, The Positive Electron, The Physical Review, Series II 43, 491-494 (1933).
7. J.H. Hubbell, Electron–positron pair production by photons: A historical overview, Radiation Physics and Chemistry 75, 614–623 (2006).
8. G. 't Hooft, Magnetic Monopoles in Unified Gauge Theories, Nuclear Physics B79, 276-284 (1974).
9. John. P. Preskill, Cosmological Production of Superheavy Magnetic Monopoles, Physical Review Letters 43, 1365-1368 (1979).
10. Peter W. Higgs, Broken Symmetries and the Masses of Gauge Bosons, Physical Review Letters 13, 508–509 (1964).
