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

--


© 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


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

; * * * * * *

--

__

--


• EGS4 code values


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


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



• 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


© EGS4 code values

• Expected value from Theory


©

A

1 .E-05

•

A

50 100 150 200 250


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





Fit Equation:T = 0.9905e° 0305*r

© A

50 100 150 200


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


(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

M9705361

Report Number (14) hOEJDKJ00633- -T13%

Publ. Date (11)

Sponsor Code (18)

UC Category (19)

, XF

DOE

the transmission of differing elnergy beta particles

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