THE TRANSMISSION OF DIFFERING ElNERGY BETA PARTICLES ...
Transcript of THE TRANSMISSION OF DIFFERING ElNERGY BETA PARTICLES ...
THE TRANSMISSION OF DIFFERING ElNERGY BETA-T??B
PARTICLES THROUGH VARIOUS MATERIALS
By
DUANE RICHARD QUAYLEB.Sc, UNIVERSITY OF MASSACHUSETTS LOWELL (1995)
SPONSORED BY THEOAK RIDGE INSTITUTE FOR SCIENCE AND EDUCATION
SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FORTHE DEGREE OF MASTER OF SCIENCE
DEPARTMENT OF PHYSICSUNIVERSITY OF MASSACHUSETTS LOWELL
urn & m DOCUMENT IS
Signature of Authority u J)ate:
19980416 020
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of theUnited States Government Neither the United States Government nor any agencythereof, nor any of their employees, makes any warranty, express or implied, orassumes any legal liability or responsibility for the accuracy, completeness, or use-fulness of any information, apparatus, product, or process disclosed, or representsthat its use would not infringe privately owned rights. Reference herein to any spe-cific commercial product, process, or service by trade name, trademark, manufac-turer, or otherwise does not necessarily constitute or imply its endorsement, recom-mendation, or favoring by the United States Government or any agency thereof.The views and opinions of authors expressed herein do not necessarily state orreflect those of the United States Government or any agency thereof.
List of Tables
Table 1: Voltage Plateau for various beta emitters for Gas Flow Proportional Counter 5
Table 2: Pm-147 Source Transmission through Aluminum Absorbers 6
Table 3: Pm-147 Source Transmission through Iron Absorbers 8
Table 4: Pm-147 Source Transmission through Zirconium Absorbers 9
Table 5: Sr/Y-90 Source Transmission through Aluminum Absorbers 10
Table 6: Sr/Y-90 Source Transmission through Iron Absorbers 11
Table 7: Sr/Y-90 Source Transmission through Zirconium Absorbers 14
Table 8: Tl-204 Source Transmission through Aluminum Absorbers 16
Table 9: Tl-204 Source Transmission through Iron Absorbers 18
Table 10: Tl-204 Source Transmission through Zirconium Absorbers. 20
Table 11: Mass absorption coeff. of beta particles in A I, Fe, and Zr, in cm2 gml 24
List of Figures
Figure 1: Voltage Plateau for various beta emitters for Gas Flow Proportional Counter 5
Figure 2: Pm-147 Source Transmission through Aluminum Absorbers 7
Figure 3: Pm-147 Source Transmission through Iron Absorbers 8
Figure 4: Pm-147 Source Transmission through Zirconium Absorbers : 9
Figure 5: Sr/Y-90 Source Transmission through Aluminum Absorbers 10f\
Figure 6: Sr/Y-90 Source Transmission through Iron Absorbers 13
Figure 7: Sr/Y-90 Source Transmission through Zirconium Absorbers 15
Figure 8: Tl-204 Source Transmission through Aluminum Absorbers 17
Figure 9: Tl-204 Source Transmission through Iron Absorbers 19
Figure 10: Tl-204 Source Transmission through Zirconium Absorbers. 21
Introduction
The transmission of beta particles is frequently calculated in the same fashion as that
of gamma rays, where the mass attenuation coefficient is defined by the slope of the
exponential function. Numerous authors have used this approximation including Evans
(1955), Loevinger (1952), and Chabot et. al. (1988). Recent work by McCarthy et. al.
(1995) indicated that the exponential function seemed to fit well over a particular region of
the transmission curve. Upon further investigation, I decided to verify McCarthy's results
by the use of different absorber materials and attempt to reproduce the experiments. A
theoretical method1 will be used to estimate the transmission of the beta particles through
the three absorbers, aluminum, zirconium, and iron. An alternate Monte Carlo code, the
Electron Gamma Shower version 4 code2 (EGS4) will also be used to verify that the
experiment is approximating a pencil beam of beta particles. Although these two methods
offer a good cross check for the experimental data, they pose a conflict in regards to the
type of beam that is to be generated. The experimental lab setup uses a collimated beam of
electrons that will impinge upon the absorber, while the codes are written using a pencil
beam. A minor discrepancy is expected to be observed in the experimental results and is
currently under investigation by McCarthy. The next process is to perform the experiments
and verify if the results can accurately be interpreted by the two other methods.
The theoretical method uses the mono-energetic range distribution as a function of
electron energy (E) and atomic number (Z), p(z,E,Z), to calculate the transmission of mono-
1 McCarthy, William B., Monte Carlo code (1995)
2 Nelson, EGS4 Monte Carlo code (1985)
energetic electrons through a foil thickness z. This is done by integrating the electron range
distribution from z to oo.
(1) r\ e ( z , E , Zot
z
p ( z , E , Z ) dz
This is interpreted that all electrons that come to rest at a distance greater than the foil
thickness, z, will be transmitted. The resulting transmission equation for mono-energetic
electrons can be integrated over the range of beta particle energies that lie from 0 MeV up
to Emax by applying a weighting factor for the beta particle energy distribution. This will
yield the beta particle transmission as a function of the atomic number, Z, and foil thickness,
z, for a given beta emitting radionuclide. This resultant function is for a pencil beam of beta
particles impinging on a foil that is infinite in the x-y plane.
Methodology
The purpose of this study was to evaluate the transmission of beta particles through
aluminum, iron, and zirconium absorbers using three pure beta emitters. Pm-147, maximum
beta energy of 0.2247 MeV, Sr/Y-90, maximum beta energies of 0.564 and 2.2839 MeV
respectively, and Tl-204, maximum beta energy of 0.7634 MeV. By using different
absorber and beta emitters an evaluation can be made on the effects of the atomic number
of the absorber and energy distribution on the transmission of the beta particles.
The absorbers were placed layer by layer in direct contact above a gas flow
proportional counter which was covered by a thin Mylar window (0.83 mg cm"2) as
observed in appendix A (Detector Setup Diagram). The collimator was a 1" polyethylene
slab with a 9/64" diameter hole drilled in the center to allow the transport of the beta
particles, and was placed in direct contact with the absorbers. The collimator configuration
was used in the experiment to reduce any air gaps that may exist between the multiple layers
of absorbers, and to provide a collimated beam of beta particles. The use of polyethylene as
a collimator was to minimize the additional production of bremsstrahlung radiation. It was
thick enough to stop the most energetic beta particles.
In order to evaluate the contribution due to bremsstrahlung radiation a sufficient
thickness of absorber material was inserted between the detector window and the
collimator. The thickness of the absorber exceeded the range of the most energetic beta
particle, but was thin enough not to attenuate the x-rays emitted as bremsstrahlung. The
count obtained with this absorber was used as a pseudo background count rate during the
experiment. Although this does not evaluate the contribution due to bremsstrahlung
exactly, it provides a reasonable approximation of the bremsstrahlung count to be
subtracted from counts obtained at smaller absorber thickness.
Table 1
Voltage
volts
1500
1600
1700
1750
1800
1850
1875
1900
1937
1950
1975
2000
2025
2050
2075
2100
2125
2150
2175
2200
2225
22502275
Pm-147
cpm
2080
7305
12995
14820
16255
17545
17910
18355
17855
18280
18065
18355
18515
19175
Sr/Y-90
cpm
1020
2880
7350
10215
13860
16260
15945
17355
17745
17850
17580
17385
18000
20025
TI-204
cpm
1370
6971
19930
26027
31353
33315
33518
33311
33896
34004
34032
34551
35025
34405
34776
34704
34940
34733
34649
34519
35298
35811128000
Figure 1
Voltage Plateau for Gas Flow Proportional Counterusing various radionuclides
Q.O
3O
o
45000
40000 +
35000
30000 +
25000
20000
15000
10000
5000
Choosen Operating Voltaae of 1900 volts for all three sources
•*•••• Pm-147 Voltage Plateau
• Sy/Y-90 Voltage Plateau
A TI-204 Voltage Plateau
1500 1600 1700 1800 1900 2000
Voltage, [volts]
2100 2200 2300
Table 2
Pm-147 source with Aluminum absorbers 3/27/96dead time 6.1E-06 Rb = 8.37
Absorberthickness
0.006.8613.7020.6027.5034.3041.16
Grosscounts15620522377427496175331053015057
timesees120120360600180012001800
Transmission
1.00E+002.89E-011.08E-013.39E-021.13E-023.37E-03
sigma T
1.21E-029.91E-038.82E-038.67E-038.61 E-03
rA2 =source cap
Absorberthickness
0.006.8613.7020.6027.5034.3041.16
0.9995= 0.0g/cm'
Pm-147expected
12.9E-019.9E-023.3E-021.0E-023.0E-038.1E-04
v2
%difference
0.0%1.4%
-9.1%-3.1%-9.1%-11.2%
Monte Carlo Results
Pm-147EGS4code
8908233786026387225
EGS4total
1.0E+002.6E-019.7E-023.0E-029.8E-032.5E-03
%difference
0.0%-10.0%-11.7%-14.7%-15.6%-36.3%
Figure 2
Pm-147 beta transmission through aluminum absorbers
1.E+00 (
UO
ISS
E 1.E-01 -10
iran
1.E-02 -
1.E-03 -
" " " • " . " ! " • •»«»
• Experimental values
« EGS4 code values
• Expected values from Theroy
Experimental fit to 80% of the range
Fit Eauation:.T=1.0714e* fM8* r
" " " ' • ' • * • - .
1 1 1 1
10 15 20
Mass density thickness of Aluminum, [mg/cm2]
25 30 35
Table 3
dead time = 6.1E-06
Absorberthickness
0.0019.6839.3559.03
Grosscounts15620445541516683
Ri
timesees1203606001200
5= 5.57
Transmission
, 1.00E+005.46E-021.08E-021.52E-06
sigma T
1.18E-028.53E-038.44E-03
rA2 = 0.9999source cap = 0.0 g/cmA2
Absorber Pm-147thickness expected
0.00 1.00E+0019.68 2.29E-0239.35 5.02E-0459.03 5.86E-06
Monte Carlo Results
%difference
0.0%-138.8%
-2056.2%74.1%
Pm-147EGS4924133260
EGS4Total
1.00E+003.59E-026.49E-04
%difference
0.0%-51.9%
-1566.7%
Figure 3
Pm-147 beta through Iron absorbers
1.E+00I
1.E-01 -
1 1.E-02-mSIU
ISI
2 1.E-03 -
1 .E-04 -
1.E-05-
1.E-06-
A_ . . _
1—
:-.
Experimental values
Expected values from Theroy
- Experimental fit to 80% of range
Fit Equation:
T = e"01478 r
" * • • - . *
" • • • - .
i
""• 8
1 1—
A
•1
10 20 30 40
Mass density thickness of Iron, [mg/cm2]
50 60
Table 4
Pm-147 source with Zirconium absorbers 3/27/96dead time - 6.1E-06 Rb - 6.08
Absorberthickness
0.0012.9825.9638.9451.92
Absorberthickness
0.0012.9825.9638.9451.92
Grosscounts8815975120236657291
rA2 =
timesees60601806001200
1.0000
Transmission
1.00E+007.22E-024.27E-032.32E-041.60E-06
source cap = 0.0 g/cm*2
Pm-147expected
15.89E-024.46E-032.75E-041.28E-05
%differenc
e0.0%
-22.6%4.1%15.6%87.5%
Pm-147EGS4 code
8630435393
sigma T
1.57E-021.17E-021.12E-021.12E-021.11E-02
sMonte Carlo Results
EGS4Total
1.00E+005.04E-024.52E-033.48E-04
%difference
0.0%-43.2%5.5%
33.2%
Figure 4
Pm-147 beta transmission through Zirconium absorbers
1.E+01
1.E+00 IK*
1.E-01
| 1-E-02.2
to
| 1.E-03
1.E-04
1.E-05 -
1.E-06
--
• Experimental values
© EGS4 code values
A Expected values from Theory
Experimental fit to 80% of the
1 1
..
range
h
Fit Equation:T = 1.0796e"°-2152*r
A
•
10 20 30 40 50 60
Mass density thickness of Zirconium, [mg/cm2]
Table 5
Absorberthickness
0.0026.2552.5078.75105.00131.25157.50183.75210.00236.25262.50288.75315.00341.25367.50393.75420.00446.25472.501050.00
Y-90expected
10.8280.6960.5870.4960.4180.3520.2960.2490.2080.1740.1450.1210.1000.0830.0680.0560.0460.038
0.00020
dead time -Absorberthickness
0.0026.2552.5078.75105.00131.25157.50183.75210.00236.25262.50288.75315.00341.25367.50393.75420.00446.25472.501050.00
Sr-90expected
1.0000.2430.0620.014
3.0E-035.5E-048.9E-051.3E-051.6E-061.8E-07
6.1E-06Grosscounts2472532514118798145371151618583151231278614870120581451011728126831032183049037750393028083
21891
Total
1.00E+005.35E-013.79E-013.01 E-012.49E-012.09E-011.76E-011.48E-011.24E-011.04E-018.70E-027.25E-026.03E-025.00E-024.14E-023.41 E-022.81 E-022.30E-021.88E-021.00E-04
Rb =timesees60.010.010.010.010.020.020.020.030.030.045.045.060.060.060.080.080.0120.0120.0600.0
%difference
0.0%-12.2%-17.4%-13.5%-7.5%-2.4%2.0%2.5%11.6%16.0%21.4%26.1%30.7%35.3%41.2%46.5%51.3%57.5%60.9%98.1%10
36.49Transmission
%1.00E+006.01 E-014.45E-013.41 E-012.68E-012.14E-011.73E-011.44E-011.10E-018.74E-026.84E-025.36E-024.18E-023.24E-022.43E-021.83E-021.37E-029.80E-037.37E-031.94E-06
sigma in T
7.22E-039.05E-038.46E-038.04E-037.73E-036.97E-036.87E-036.80E-036.61 E-036.57E-036.49E-036.47E-036.45E-036.44E-036.43E-036.42E-036.42E-036.41 E-036.41 E-03
Monte Carlo ResultsY-90
EGS4 code997484297358617352654599399634392962251621071696148812561024849709600481
Sr-90EGS4 code
97102731925276761530
EGS4total1.0000.5670.4210.3280.2710.2340.2030.1750.1500.1280.1070.0860.0760.0640.0520.0430.0360.030
%difference
0.0%-5.9%-5.8%-4.2%1.2%8.6%15.1%17.3%26.9%31.6%36.1%37.8%44.7%49.2%53.2%57.6%62.0%67.8%
Figure 5
Sr/Y-90 beta transmission through Aluminum absorbers
cojo
coc
s
l.l_TUI
1.E+00 i
1.E-01 -
1.E-02-
1.E-03 -
1.E-04 -
' • • • • - . .
• • • • - • • - . . . ;
•
©
Experimental values
EGS4 code values
Expected Values from Theory
Experimental fit to 80% of the
1 1 h
••-«.
range
- • •* • • • •
(Y-90)
h-
• • #
Fit Eauation:T = 0.7527e° 0092*r
... * * - t .
4
4 >
—1 1 1 1 150 100 150 200 250 300 350
Mass density thickness of Aluminum, [mg/cm2]
400 450 500
Table 6
Sr/Y-90 source with Iron absorbers 3/27/96dead time = 6.1E-06 Rb = 21.68
Absorberthickness
0.0019.6839.3559.0378.7098.38118.10137.70157.40177.10196.80236.10275.50314.80354.20393.50432.90472.20511.60550.90590.30629.60669.00708.30747.70787.00826.40865.70905.10944.40983.801023.001062.00
Grosscounts2485563190525889223001927417013147372440021629195481704120623164271759914032143362270217990195401559316329132261030913404117361403816204149342907413841132171305578033
timesees6010101010101020202020303045456012012018018024024024036036048060060012006006006003600
Transmission
1.00E+007.64E-016.17E-015.30E-014.56E-014.01 E-013.47E-012.86E-012.52E-012.27E-011.97E-011.58E-011.25E-018.76E-026.88E-025.15E-023.97E-023.04E-022.06E-021.54E-021.10E-027.91 E-035.03E-033.68E-032.59E-031.79E-031.26E-037.61 E-046.05E-043.30E-048.41 E-052.02E-056.78E-07
sigma T
2.85E-034.78E-034.39E-034.15E-033.93E-033.75E-033.57E-032.77E-032.69E-032.64E-032.56E-032.33E-032.27E-032.14E-032.12E-032.07E-032.04E-032.03E-032.03E-032.02E-032.02E-032.02E-032.02E-032.02E-032.02E-03
11
Table 6(continued)
Sr/Y-90 through Iron continued...
Monte Carlo Results
Absorberthickness
0.0019.6839.3559.0378.7098.38118.10137.70157.40177.10196.80236.10275.50314.80354.20393.50432.90472.20511.60550.90590.30629.60669.00708.30747.70787.00826.40865.70905.10944.40983.801023.001062.00
Y-90expected
10.9010.8210.7460.6770.6130.5550.5010.4520.4070.3670.2950.2370.1890.1490.1170.0920.0710.0550.0420.0320.0240.0180.0140.010
7.3E-035.4E-033.9E-032.8E-032.0E-031.4E-039.9E-046.9E-04
Sr-90expected
10.4460.2210.1060.0480.021
8.8E-033.5E-031.3E-034.7E-041.6E-04
Total
1.00E+006.73E-015.21 E-014.26E-013.63E-013.17E-012.82E-012.52E-012.27E-012.04E-011.83E-011.48E-011.18E-019.43E-027.46E-025.87E-024.59E-023.56E-022.75E-022.10E-021.60E-021.21E-029.07E-036.76E-035.00E-033.67E-032.68E-031.94E-031.39E-039.93E-047.02E-044.94E-043.46E-04
%difference
0.0%-13.5%-18.5%-24.4%-25.7%-26.5%-23.0%-13.1%-11.2%-11.5%-7.7%-7.1%-5.5%7.1%7.8%12.3%13.5%14.7%25.1%26.9%31.4%34.6%44.5%45.5%48.3%51.2%52.8%60.7%56.6%66.8%88.0%95.9%99.8%
Y-90EGS code
9973899182837576697163375859527249244390390631712613210916681275105481460640433224714712695443321107
Sr-90EGS code
97174349211596141217569249
EGS4total
10.6780.5280.4340.3750.3310.3010.2690.2510.2230.1980.1610.1330.1070.0850.0650.0540.0410.0310.0210.0170.013
7.5E-036.4E-034.8E-032.2E-031.7E-031.1E-035.1E-043.6E-04
%difference
0.0%-12.8%-16.8%-22.1%-21.6%-21.4%-15.1%-6.2%-0.7%-2.0%0.5%1.8%6.0%18.2%18.8%20.5%25.9%26.6%33.2%25.1%34.9%36.9%32.6%42.5%46.4%19.8%24.7%28.6%-19.0%7.1%
12
Figure 6
Sr/Y-90 beta transmission through Iron absorbers
1.E+01
1.E+00
1.E-01
1.E-02 --
onMI 1.E-03to
1.E-04
1.E-05 -
1.E-06
1.E-07
I I
; * * * * * *
--
__
--
• Experimental values
• EGS4 code values
A Expected values from Theory
Experimental fit to 80% of the range (Y-90)
Fit Equation:T = i.063ie00079*r
JL ^ ""i^ -S- i A
' • • • • A
• 5? ^
•
1 1 : 1 1
200 400 600 800
Mass density thickness of Iron, [mg/cm2]
1000 1200
13
Table 7
Sr/Y-90 source with Zirconium absorbers 3/27/96dead time = 6.1E-06 Rb = 21.83
Absorberthickness
0.0025.9651.9277.88103.84129.80195.00260.20325.40390.60519.00647.40775.80904.20974.00
Grosscounts414322701820286163212683622178140102716917043217231884114085158772734578597
timesees
10101010202020606012024036060012003600
Transmission
1.0000.6440.4810.3850.3150.2590.1610.1020.0620.038
1.3E-024.1E-031.1E-032.3E-04
sigma T
6.98E-036.35E-036.03E-035.83E-035.32E-035.26E-035.14E-034.98E-034.97E-034.95E-034.94E-03
Monte Carlo Results
Absorberthickness
0.0025.9651.9277.88103.84129.80195.00260.20325.40390.60519.00647.40775.80904.20974.00
Y-90expected
10.8390.7140.6090.5200.4440.2970.1960.1280.0820.032
1.2E-024.0E-031.3E-036.9E-04
Sr-90expected
10.2650.074
1.9E-024.3E-038.9E-041 .OE-05
Total
1.00E+005.52E-013.94E-013.14E-012.62E-012.22E-011.48E-019.80E-026.38E-024.09E-021.60E-025.84E-031.99E-036.28E-043.44E-04
%difference
0.0%-16.7%-22.0%-22.5%-20.0%-16.4%-8.7%-4.3%2.6%7.8%16.1%29.9%44.8%63.9%100.0%
Y-90EGS4 code
99758578746264615675495134532484158210043751093793
Sr-90EGS4 code
97123026107637010823
EGS4Total
10.5890.4340.3470.2940.2530.1750.1260.0800.051
1.9E-025.5E-031.9E-034.6E-041.5E-04
%difference
0.0%-9.3%
-10.8%-10.9%-7.2%-2.5%8.1%19.0%22.7%26.1%29.6%26.1%41.7%50.4%100.0%
14
1.E+01 -r
1.E+00
o'vt
CO
I
1.E-01 --
1.E-02 --
Figure 7
Sr/Y-90 beta transmission through Zirconium absorbers
1.E-03 -
1.E-04
• Experimental values
• EGS4 code values
• Expected values from Theory
Experimental fit to 80% of the range (Y-90)
Fit Equation:T = 0.9727e-0.0085*r
A
A
•
100 200 300 400 500 600 700 800 900 1000
Mass density thickness of Zirconium, [mg/cm ]
15
Table 8
TI-204 source with Aluminum absorbers 3/27/96dead time = 6.1E-06 Rb = 282.25
Absorberthickness
0.0013.7227.4341.1554.8668.5882.2996.01109.72123.44137.15150.87171.50205.70240.00274.30308.60
Grosscounts74242605274446732058239861819813890215051704913938173311490325043206693776835253169352
timesees
1010101010101020202030306060120120600
Transmission
1.00E+008.01 E-015.72E-013.99E-012.87E-012.08E-011.49E-011.07E-017.67E-025.57E-023.97E-022.88E-021.82E-028.40E-034.41 E-031.61E-036.50E-05
sigma T
5.40E-035.14E-034.83E-034.57E-034.39E-034.26E-034.16E-033.95E-033.93E-033.91 E-033.87E-033.86E-033.84E-033.83E-033.82E-03
Monte Carlo Results
Absorberthickness
0.0013.7227.4341.1554.8668.5882.2996.01109.72123.44137.15150.87171.50205.70240.00274.30308.60
TI-204expected1.00E+006.69E-014.81 E-013.47E-012.50E-011.78E-011.26E-018.75E-026.02E-024.08E-022.73E-021.80E-029.33E-032.88E-038.01 E-041.98E-044.37E-05
%difference
0.0%-19.7%-19.0%-14.8%-15.0%-16.7%-18.8%-22.0%-27.4%-36.5%-45.5%-60.4%-94.8%
-191.3%-451.4%-710.2%-48.8%
TI-204EGS4 code
979664054707344525671857133898072749234926012337145
EGS4Total
1.00E+006.54E-014.81 E-013.52E-012.62E-011.90E-011.37E-011.00E-017.42E-025.02E-023.56E-022.65E-021.26E-023.78E-031.43E-035.10E-04
%difference
0.0%-22.5%-19.1%-13.4%-9.6%-9.7%-9.3%-6.7%-3.3%-11.0%-11.4%-8.6%-44.7%
-122.4%-208.9%-215.0%
16
Figure 8
TI-204 beta transmission through Aluminum absorbers
1.E+01 T
1.E+00
1.E-01 --
Fit Equation:T = 1.053e-0.0237*r
toME 1E-02V)
I1 .E-03
-a
1.E-.04
• Experimental values
© EGS4 code values
• Expected value from Theory
Experimental fit to 80% of the range
©
A
1 .E-05
•
A
50 100 150 200 250
Mass density thickness of Aluminum, [mg/cm2]
300 350
17
Table 9
TI-204 source with Iron absorbers 3/27/96
dead time = 6.1E-06 Rb = 63.92
Absorberthickness
0.0019.6839.3559.0378.7098.38118.05137.73157.40177.08196.75216.43236.10255.78275.45295.13
Grosscounts76092436492404114661699887275299702052224124514644054158827778997670
timesees
10101010102020404040606060120120120
Transmission
1.00E+005.58E-013.00E-011.79E-018.07E-024.72E-022.55E-021.41E-028.43E-034.96E-032.77E-031.20E-036.84E-046.43E-042.44E-04
sigma T
5.17E-034.59E-034.20E-034.00E-033.82E-033.71 E-033.69E-033.67E-033.67E-033.66E-03
Monte Carlo Results
Absorberthickness
0.0019.6839.3559.0378.7098.38118.05137.73157.40177.08196.75
TI-204expected1.00E+005.13E-012.93E-011.68E-019.45E-025.23E-022.82E-021.49E-027.67E-033.84E-031.87E-03
%difference
0.0%-8.9%-2.4%-6.7%14.6%9.7%9.8%5.4%-9.9%
-29.1%-47.7%
TI-204EGS4 code
9741485527741624949531320162824716
EGS4Total
1.00E+004.98E-012.85E-011.67E-019.74E-025.45E-023.29E-021.66E-028.42E-034.82E-031.64E-03
%difference
0.0%-12.0%-5.4%-7.3%17.2%13.4%22.5%15.1%-0.2%-2.8%-68.4%
216.43 8.85E-04 -36.0% 4.11E-04 -66.5%
18
Figure 9
TI-204 beta transmission through Iron absorbers
1.E+01 T
1.E+00
1.E-01
o'55v>E 1.E-02-wc2
1.E-03 -
1.E-04 -
1 .E-05
• Experimental values
• EGS4 code values
A Expected values from Theory
Experimental fit to 80% of the range
Fit Equation:T = 0.9905e° 0305*r
© A
50 100 150 200
Mass density thickness of Iron, [mg/cm2]
250 300
19
Table 10
TI-204 source with Zirconium absorbers 3/27/96dead time = 6.1E-06 Rb - 68.76
Absorberthickness
0.0012.9825.9638.9451.9264.9077.8890.86103.84116.82129.80142.78155.76168.74194.70220.66246.62272.58
Grosscounts76384463812949619339131029042638489096421950571168875733263645185941186118251
timesees
101010101010102020404060606060120120120
Transmission
1.00E+005.92E-013.69E-012.38E-011.58E-011.06E-017.20E-024.76E-023.18E-022.13E-021.38E-029.98E-036.74E-034.71 E-032.23E-031.22E-033.82E-04
i sigma T
5.17E-034.63E-034.30E-034.09E-033.95E-033.86E-033.80E-033.71 E-033.69E-033.67E-033.66E-033.66E-033.66E-033.66E-03
Monte Carlo Results
Absorberthickness
0.0012.9825.9638.9451.9264.9077.8890.86103.84116.82129.80142.78155.76168.74194.70220.66246.62
TI-204expected1.00E+005.91 E-013.87E-012.58E-011.71 E-011.14E-017.48E-024.88E-023.16E-022.02E-021.28E-028.03E-034.97E-033.05E-031.11 E-033.82E-041.26E-04
%difference
0.0%-0.2%4.6%7.7%8.1%6.9%3.7%2.5%-0.9%-5.4%-7.5%-24.4%-35.5%-54.4%
-101.6%-219.6%-203.2%
TI-204EGS4 code
9740544136272463165211027864943362331569664351342
EGS4Total
1.00E+005.59E-013.72E-012.53E-011.70E-011.13E-018.07E-025.07E-023.45E-022.39E-021.60E-029.86E-036.57E-033.59E-031.33E-034.11E-042.05E-04
%difference
0.0%-6.0%0.8%6.0%7.1%6.5%10.7%6.2%7.7%10.9%14.1%-1.3%-2.6%-31.0%-67.0%
-197.5%-85.9%
20
Figure 10
TI-204 beta transmission through Zirconium absorbers
o"55
tocE
1 . t^U 1 -
1.E+00 i
1.E-01 -
1.E-02 -
1.E-03 -
1.E-04 -
"4. Fit Eauation:^ * , T = 0.8378e°03ir r
« Experimental values
© EGS4 code values
• Expected values from Theory
Experimental fit to 80% of the range
(t
t
1 * • « » _
* • •
" • • - . * . .
1 x \ ' *
1 1 1 1 1 1
50 100 150 200 250
Mass density thickness of Zirconium, [mg/cm2]21
300
Discussion
The discussion below evaluates the results for each radionuclide, considering how
the atomic number of the absorber and the energy spectrum of the beta particles affect the
transmission.
Promethium 147 has a maximum beta energy of 0.2247 MeV, and was the lowest
energy beta emitter used in this experiment. The transmission through aluminum, atomic
number of thirteen, appeared to follow an exponential function fairly well out to
approximately eighty percent of the range, having an experimental attenuation coefficient
of 168.8 cm2/gm as observed in Figure 2. The experimental theory and the EGS4 code
were in close agreement with the experimental data. Using iron, atomic number of twenty
six, yielded poor results due, at least in part, to having only four data points in the
experiment. Thinner absorbers could have avoided this problem but were not available.
The experimental data indicates more beta particles pass through the material than
predicted by the theory or the EGS4 code. This discrepancy could be in part due to the
relatively higher atomic number which generates a larger fraction of bremsstrahlung, thus
increasing the count at a greater absorber thickness. The experimental mass attenuation
coefficient at eighty percent of the range was evaluated to be 147.8 cm2/gm as observed
in Figure 3. The results of the transmission experiment with the zirconium absorbers,
atomic number of forty, were nearly exactly as the expected theory and the EGS4 code
predicted. The calculated mass attenuation coefficient was 215.2 cm2/gm, which is
slightly higher than that of the aluminum and iron.
22
The zirconium appears to have the highest mass attenuation coefficient
corresponding with the largest atomic number as well, although no correlation can be
made with confidence seeing as the iron's mass attenuation coefficient did not follow this
pattern.
Thallium 204, emitting a maximum energy beta particle of 0.7634 MeV, showed
very good results for all of the three absorbers. Using aluminum as the absorber, as
shown in Figure 8, the experimental data agree quite well with the codes out to
approximately seventy percent of the range, and then the two codes show relatively
greater attenuation of the beta's emitted by the thallium. Again, this is due in part to the
fact that the two codes do not take into account the production of x-rays generated from
bremsstrahlung that interact within the detector, and the codes do not take into account
the buildup of electrons as they pass through the absorber. The mass attenuation
coefficient calculated for the aluminum absorber is 23.7 cm2/gm, which is fairly reasonable
for this higher beta energy spectrum impinging upon the absorber. More beta particles
are transmitted through the absorbers generating a more gradual slope than was observed
for the lower energy beta emitters. Iron again had very good agreement with the codes
and yielded a mass attenuation coefficient of 30.5 cm2/gm (Figure 9). The thallium source
using zirconium absorbers had perhaps the best results, following the codes quite well. A
mass attenuation coefficient of 31.1 cm2/gm was calculated for this absorber (Figure 10).
A correlation may appear to exist with atomic number when using a higher energy beta
emitter, as seen in the increase in the slope while using thallium and the three absorbers.
Strontium/Yttrium 90, emitting a maximum energy beta particle of 2.28 MeV, was
also used in the transmission experiment and the results are shown in Figures 5, 6 and 7.
23
Using aluminum as an absorber, the experimental data did nbt agree with the predicted
values out beyond thirty to forty percent of the range. The data demonstrated greater
attenuation of the beta particles than expected by the theory and the EGS4 code. This is
mainly due to the setup of the experiment. As stated in the introduction, the experiment
was setup for a collimated beam of beta particles to impinge upon the absorbers, while the
theory and the EGS4 code assumed a pencil beam of beta particles. The difference in
geometry's may account for the discrepancy between these results seeing that a collimated
beam from a point isotropic source would appear to have relatively fewer beta particles
impinging normally upon the surface because the beam tends to spread out as it
approaches the absorbers therefore those beta particles at the outer edge of the cone will
travel a greater distance through the absorber, and thus the appearance of greater
attenuation through the absorber. The pencil beam appears as a mono-directional beam
of beta particles with an infinitesimal diameter, and would have a greater transmission
value through the absorbers. The calculated mass attenuation coefficient using the
aluminum, iron, and zirconium absorber are 9.2, 7.9, and 8.5 cm2/gm, respectively.
Table 11. Mass absorption coeff. of beta particles in Al, Fe, and Zr, in cm2 guv1
Radionudide Energy (MeV) Aluminum Iron Zirconium
i ' ^ P m 6 " 2 2 4 7 X6&8 147.8 215.290Sr/Y 2.2839 9.2 7.9 8.5204Tl 0.7634 23.7 30.5 31.1
24
Conclusion
The results of this project supported the theory that the beta mass
attenuation coefficient was accurately represented by the slope of an exponential
function, but only for that particular region of the transmission curve that has a
minimal absorber thickness. By fitting the data beyond 50% of the beta particle
range this theory does not hold true. The theory generated by McCarthy (1995)
and the EGS4 Monte Carlo code indicated that the transmission curve for a pencil
beam was not accurately represented by an exponential function. The results of
this experiment appeared to provided additional support to this assumption.
The average depth of penetration in the infinite medium appears to be a
function of the electron energy and the associated atomic number of the absorber.
The fraction of the electrons that backscattered from the absorber is a function of
absorber thickness, and by assuming that the fraction backscattered from the foil is
a constant, the integral form of the transmission was represented by equation (1).
Table 11 summarizes the behavior of the mass attenuation coefficient by
varying atomic number and electron energy, but further research will need to be
performed using additional sources and generating better statistical results than
those presented for the iron experiment, seeing as a significant evaluation cannot
be made based on poor statistics for the iron absorption experiment.
25
Literature Cited
McCarthy, W. and Chabot, G., Estimation of the beta particle attenuation coefficient usingMonte Carlo techniques. Health Physics Supplement to 68(6): S3 5; 1995
Ozmutlu, C. and Cengiz, A., Mass attenuation Coefficients of Beta Particles. Appl. Radiat.Isot. 41(6):545-549; 1990
Loevinger, R., The Dosimetry of Beta Sources in Tissue, The Point Source Function.Radiology. 66:55-62; 1952
Nathuram, R.; Sundara, I.S.; Mehta, M.K., Mass Absorption Coefficients and Range of BetaParticles in Be, Al, Cu Ag and Pb. Pramana. 18:121-127; 1982.
Nelson, W.R.; Hirayama, H.; Rogers, D.W.O., The EGS4 Code System. Stanford LinearAccelerator Report SLAC-256; 1985
26
Appendix A
Detector Setup Diagram
bolt
gas inlet
s;gnal andnign voltage nconnection
gas outlet
source
collimatorbolt
foils ~S
detector volume
high voltage wire
stainless steel dector bac
stainless st
:ing
eel
plywood base
support lead brick support
27