. * i i; THE TRANSMISSION OF

PARTICLES THROUGH VARIOUS MATERIALS

BY

DUANE RICHARD QUAYLE B.Sc., UNIVERSITY OF MASSACHUSETTS LOWELL (1995)

SPONSORED BY THE OAK RIDGE INSTITUTE FOR SCIENCE AND EDUCATION

SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

DEPARTMENT OF PHYSICS UNIVERSITY OF MASSACHUSETTS LOWELL

Signature of Author: ate: 44/5-- 9d

19980416 020

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use- fulness of any information, apparatus, product, or process disclosed, or represents that 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, recorn- mendktion, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

List of Tables

Table I : 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: SrN-90 Source Transmission through Aluminum Absorbers ............................................. 10

Table 6: SrN-90 Source Transmission through Iron Absorbers .................................................... 11

Table 7: SrN-90 Source Transmission through Zirconium Absorbers ............................................ 14

Table 8: TI-204 Source Transmission through Aluminum Absorbers .............................................. 16

Table IO: TI-204 Source Transmission through Zirconium Absorbers ............................................ 20

Table I I : Mass absorption coefl of beta particles in AI. Fe. and Zr. in cm2 gm-' ............................ 24

Table 9: TI-204 Source Transmission through Iron Absorbers ..................................................... 18

List of Fiqures

Figure I : 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: SrN-90 Source Transmission through Aluminum Absorbers. .................................................. lof i Figure 6: SrN-90 Source Transmission through Iron Absorbers ............................................................ 13

Figure 7: SrN-90 Source Transmission through Zirconium Absorbers .................................................. 15

Figure 9: TI-204 Source Transmission through Iron Absorbers ............................................................. 19

Figure IO: TI-204 Source Transmission through Zirconium Absorbers .................................................. 21

Figure 8: TI-204 Source Transmission through Aluminum Absorbers .................................................... 17

1

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 fhction. 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 fknction seemed to fit well over a particular region of

the transmission curve. Upon hrther investigation, I decided to verify McCarthy’s results

by the use of different absorber materials and attempt to reproduce the experiments. A

theoretical method’ 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 code’ (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 fknction of

electron energy (E) and atomic number (Z), p(z,E,Z), to calculate the transmission of mono.

McCarthy, William B., Monte Carlo code (1995)

Nelson, EGS4 Monte Carlo code (1985)

2

energetic electrons through a foil thickness z: This is done by integrating the electron range

distribution from z to 00.

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 fbnction of the atomic number, Z, and foil thickness,

z, for a given beta emitting radionuclide. This resultant fbnction is for a pencil beam of beta

particles impinging on a foil that is infinite in the x-y plane.

Methodo1op;v

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 T1-204, 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

3

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.

4

Table 1 Figure 1

45000

40000

35000 n

30000 2 d 6 25000 c,

2 c, 20000 C

0 15000

10000

5000

0

Voltage Plateau for Gas Flow Proportional Counter using various radionuclides

Choosen Operatinu Voltaue of 1900 volts for all three sources

A

0

a 0 Pm-I 47 Voltage Plateau

SyiY-90 Voltage Plateau I, A TI-204 Voltage Plateau

1500 1600 1700 1800 1900 2000 2100 2200 2300

Voltage, [volts]

5

Table 2

Pm-147 source with Aluminum absorbers 3/27/96 deadtime 6.1E-06 Rb= 8.37

’ Absorber thickness

0.00 6.86 13.70 20.60 27.50 34.30 41.16

GmSS Counts 1 5620 5223 7742 7496 17533 10530 1 5057

rA2= 0.9995 source cap = 0.0 g/cmA2

Absorber thickness

0.00 6.86 13.70 20.60 27.50 34.30 41.16

time Transmission sigma T secs 120 1 .00E+00 1.21 E-02 120 2.89E-01 9.91 E-03 360 1.08E-01 8.82E-03 600 3.39E-02 8.67E-03 1800 1.13E-02 8.61 E-03 1200 3.37E-03 1800

Pm-147

1 2.9E-01 9.9E-02 3.3E-02 1 .OE-02 3.OE-03 8.1 E-04

expected %

difference 0.0% 1.4% -9.1 % -3.1 % -9.1% -1 1.2%

Pm-147 EGSQ code

8908 2337 860 263 87 22 5

Monte Carlo Resuits

EGSQ total

1 .OE+00 2.6E-01 9.7E-02 3.OE-02 9.8E-03 2.5E-03

?IO

difference 0.0%

-10.0% -1 1.7% -14.7% -15.6% -36.3%

6

L *

6 It! r

m 0

4 r

m (v

0 (v

m

0

dead time = 6.1E-06

1 .E-04 --

1 .E-05

Absorber thickness

0.00 19.68 39.35 59.03

--

Absorber thickness

0.00 19.68 39.35 59.03

Gross counts 15620 4455 41 51 6683

Table 3 Rb= 5.57

time secs 120 360 600 1200

rA2 = 0.9999 source cap = 0.0 g/cmA2

Pm-147 expected l.OOE+OO 2.29E-02 5.02E-04 5.86E-06

% difference

0.0% -1 38.8% -2056.2%

74.1%

Transmission sigma T

I 1.00E+00 1.1 8E-02 5.46E-02 8.53E-03 1.08E-02 8.44E-03 1.52E-06

Monte Carlo Results

Pm-147 EGS4 9241 332 6 0

Figure 3

Pm-147 beta through Iron absorbers

T 1 .E+01

EGS4 % Total difference

l.OOE+OO 0.0% 3.59E-02 -51.9% 6.49E-04 -1 566.7%

" 11-1 - ~ _ 1 _ 1 - -

Experimental values

c - , ,, , , , , EGS4codev: , , , 1 -__- Experimental fit to 80% of range

Expected values from Theroy

A

e 1 .E-06 ! I I

0 10 20 30 40 50 60

Mass density thickness of Iron, [mg/cm2]

8

Table 4

Pm-147 source with Zirconium absorbers 3/27/96 dead time =

Absorber thickness

0.00 12.98 25.96 38.94 51.92

Absorber thickness

0.00 12.98 25.96 38.94 51.92

6.7 E-06 Rb = 6.08

Gross counts 881 5 975 1202 3665 7291

time Transmission sigma T secs 60 1.00E+00 1.57E-02 60 7.22E-02 1.17E-02 180 4.27E-03 1.12E-02 600 2.32E-04 1.12E-02 1200 1.60E-06 1.1 1 E-02

rA2 = 1.0000 source cap = 0.0 g/cmA2 Monte Carlo Results

Pm-147 % Pm-147 EGS4 expected differenc EGS4 code Total

e 1 0.0% 8630 l.OOE+OO

5.89E-02 -22.6% 435 5.04E-02 4.46E-03 4.1% 39 4.52E-03 2.75E-04 15.6% 3 3.48E-04 1.28E-05 87.5%

% difference

0.0% -43.2% 5.5% 33.2%

Figure 4

Pm-147 beta transmission through Zirconium absorbers

I 1 .E+01

l.E-01 --

C -0 l.E-02 -- UJ

E UJ 3 l.E-03 -- I-

.-

l.E-04 --

l.E-05 --

7 -. -_lll_---ll -I__.'

I 4 Experimental values

-----e--. EGS4 code values

Fit Equation: T = I .0796e -0.21 52*r

A Expected values from Theory

- - - - Experimental fit to 80% of the range I A

, 1 4 l.E-06 I , I I I I I I I I

0 10 20 30 40 50 60

Mass density thickness of Zirconium, [mg/cm2] 9

Table 5

Absorber thickness

0.00 26.25 52.50 78.75 105.00 131.25 157.50 183.75 21 0.00 236.25 262.50 288.75 31 5.00 341.25 367.50 393.75 420.00 446.25 472.50 1050.00

Y-90 expected

1 0.828 0.696 0.587 0.496 0.41 8 0.352 0.296 0.249 0.208 0.174 0.145 0.121 0.100 0.083 0.068 0.056 0.046 0.038

0.00020

dead time = Absorber thickness

0.00 26.25 52.50 78.75 105.00 131.25 157.50 183.75 21 0.00 236.25 262.50 288.75 31 5.00 341.25 367.50 393.75 420.00 446.25 472.50 1050.00

Sr-90 expected

1 .ooo 0.243 0.062 0.014

3.OE-03 5.5E-04 8.9E-05 1.3E-05 1.6E-06 1.8E-07

6.1 E-06 Gross counts 247253 251 41 18798 14537 11516 18583 15123 12786 14870 12058 14510 1 1728 12683 10321 8304 9037 7503 9302 8083

21 891

Total

l.OOE+OO 5.35E-01 3.79E-01 3.01 E-01 2.49E-01 2.09E-01 1.76E-01 1.48E-01 1.24E-01 1.04E-01 8.70E-02 7.25E-02 6.03E-02 5.00E-02 4.14E-02 3.41 E-02 2.81 E-02 2.30E-02 1.88E-02 1.00E-04

Rb = 36.49 time Transmission sees % 60.0 l.OOE+OO 10.0 6.01 E-01 10.0 4.45E-01 10.0 3.41 E-01 10.0 2.68E-0 1 20.0 2.14E-01 20.0 1.73E-01 20.0 1.44E-01 30.0 1.10E-01 30.0 8.74E-02 45.0 6.84E-02 45.0 5.36E-02 60.0 4.18E-02 60.0 3.24E-02 60.0 2.43E-02 80.0 1.83E-02 80.0 1.37E-02 120.0 9.80E-03 120.0 7.37E-03 600.0 1.94E-06

sigma in T

7.22E-03 9.05E-03 8.46E-03 8.04E-03 7.73E-03 6.97E-03 6.87E-03 6.80E-03 6.61 E-03 6.57E-03 6.49E-03 6.47E-03 6.45E-03 6.44E-03 6.43E-03 6.42E-03 6.42E-03 6.41 E-03 6.41 E-03

Monte Carlo Results % Y-90 Sr-90

difference EGS4 code EGS4 code 0.0% 9974 971 0

-12.2% 8429 2731 -1 7.4% 7358 925 -1 3.5% 61 73 276 -7.5% 5265 76 -2.4% 4599 15 2.0% 3996 3 2.5% 3439 0 11.6% 2962 16.0% 2516 21.4% 21 07 26.1% 1696 30.7% 1488 35.3% 1256 41.2% 1024 46.5% 849 51.3% 709 57.5% 600 60.9% 481 98.1% 10

eg54 % total difference 1.000 0.0% 0.567 -5.9% 0.421 -5.8% 0.328 -4.2% 0.271 1.2% 0.234 8.6% 0.203 15.1% 0.175 17.3% 0.150 26.9% 0.128 31.6% 0.107 36.1% 0.086 37.8% 0.076 44.7% 0.064 49.2% 0.052 53.2% 0.043 57.6% 0.036 62.0% 0.030 67.8%

?

0 0 v)

c OJ 3

5

Q

4

7

4 UI 7

(v 4 w 7

0 0 d

8El E a

0 3 C

3

.-

0 sr

0 v)

0

Table 6

SrN-90 source with Iron absorbers 3/27/96 dead time = 6.1E-06

Absorber thickness

0.00 19.68 39.35 59.03 78.70 98.38 118.10 137.70 157.40 177.10 196.80 236.1 0 275.50 314.80 354.20 393.50 432.90 472.20 51 1.60 550.90 590.30 629.60 669.00 708.30 747.70 787.00 826.40 865.70 905.10 944.40 983.80 1023.00 1062.00

Gross counts 248556 31 905 25889 22300 19274 1701 3 14737 24400 21629 19548 17041 20623 16427 17599 14032 14336 22702 17990 19540 15593 16329 13226 10309 13404 1 1736 14038 16204 14934 29074 13841 13217 13055 78033

Rb = 21.68

time secs 60 10 10 10 10 10 10 20 20 20 20 30 30 45 45 60 120 120 180 180 240 240 240 360 360 480 600 600 1200 600 600 600 3600

Transmission sigma T

l.OOE+OO 7.64E-01 6.1 7E-01 5.30E-0 1 4.56E-01 4.01 E-01 3.47E-01 2.86E-01 2.52E-01 2.27E-01 1.97E-01 1.58E-01 1.25E-01 8.76E-02 6.88E-02 5.1 5E-02 3.97E-02 3.04E-02 2.06E-02 1.54E-02 1.1 OE-02 7.91 E-03 5.03E-03 3.68E-03 2.59E-03 1.79E-03 1.26E-03 7.61 E-04 6.05E-04 3.30E-04 8.41 E-05 2.02E-05 6.78E-07

2.85E-03 4.78E-03 4.39E-03 4.15E-03 3.93E-03 3.75E-03 3.57E-03 2.77E-03 2.69E-03 2.64E-03 2.56E-03 2.33E-03 2.27E-03 2.14E-03 2.12E-03 2.07E-03 2.04E-03 2.03E-03 2.03E-03 2.02E-03 2.02E-03 2.02E-03 2.02E-03 2.02E-03 2.02E-03

11

Table 6 (continued)

SrW-90 through Iron continued. ..

Absorber thickness

0.00 19.68 39.35 59.03 78.70 98.38 118.10 137.70 157.40 177.10 196.80 236.1 0 275.50 314.80 354.20 393.50 432.90 472.20 51 1.60 550.90 590.30 629.60 669.00 708.30 747.70 787.00 826.40 865.70 905.10 944.40 983.80 1023.00 1062.00

Y-90 Sr-90 expected expected

1 0.901 0.821 0.746 0.677 0.61 3 0.555 0.501 0.452 0.407 0.367 0.295 0.237 0.189 0.149 0.1 17 0.092 0.071 0.055 0.042 0.032 0.024 0.01 8 0.014 0.01 0

7.3E-03 5.4E-03 3.9E-03 2.8E-03 2.OE-03 1.4E-03 9.9E-04 6.9E-04

1 0.446 0.221 0.106 0.048 0.021

8.8E-03 3.5E-03 1.3E-03 4.7E-04 1.6E-04

Total

l.OOE+OO 6.73E-01 5.21 E-01 4.26E-0 1 3.63E-01 3.17E-01 2.82E-0 1 2.52E-0 1 2.27E-01 2.04E-01 1.83E-01 1.48E-01 1.18E-01 9.43E-02 7.46E-02 5.87E-02 4.59E-02 3.56E-02 2.75E-02 2.10E-02 1.60E-02 1.21 E-02 9.07E-03 6.76E-03 5.00E-03 3.67E-03 2.68E-03 1.94E-03 1.39E-03 9.93E-04 7.02E-04 4.94E-04 3.46E-04

% difference

0.0% -13.5% -1 8.5% -24.4% -25.7% -26.5% -23.0% -13.1% -1 1.2% -1 1.5% -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%

Monte Carlo Results

Y-90 EGS code

9973 8991 8283 7576 6971 6337 5859 5272 4924 4390 3906 3171 261 3 21 09 1668 1275 1054 814 606 404 332 247 147 126 95 44 33 21 10 7

Sr-90 EGS code

971 7 4349 2115 96 1 41 2 175 69 24 9

EGS4 total

1 0.678 0.528 0.434 0.375 0.331 0.301 0.269 0.251 0.223 0.1 98 0.161 0.133 0.107 0.085 0.065 0.054 0.041 0.031 0.021 0.01 7 0.013

7.5E-03 6.4E-03 4.8E-03 2.2E-03 1.7E-03 1.1 E-03 5.1 E-04 3.6E-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% -1 9.0% 7.1%

12

c,

c, Q Q) P

L

Q) z? E 5

s

Q)

Y- O

0 a3 0 c

E - m c c

E I3 'C Q) n

I

I

+ F 0 F cv m d rT)

0 + 0 + 4 4 4 4 4 w F

w F

w F

w F

w F

w w v- F u! F

b 4 w F

Table 7

SrN-90 source with Zirconium absorbers 3/27/96 dead time =

Absorber thickness

0.00 25.96 51.92 77.88 103.84 129.80 195.00 260.20 325.40 390.60 51 9.00 647.40 775.80 904.20 974.00

Absorber thickness

0.00 25.96 51.92 77.88 103.84 129.80 195.00 260.20 325.40 390.60 519.00 647.40 775.80 904.20 974.00

6.1 E-06

Gross counts 41432 2701 8 20286 16321 26836 221 78 14010 271 69 17043 21 723 18841 14085 15877 27345 78597

Rb = 21.83

time secs

10 10 10 10 20 20 20 60 60 120 240 360 600 1200 3600

Y-90 Sr-90 expected expected

1 1 0.839 0.265 0.714 0.074 0.609 1.9E-02 0.520 4.3E-03 0.444 8.9E-04 0.297 1 .OE-05 0.1 96 0.128 0.082 0.032

1.2E-02 4.OE-03 1.3E-03 6.9E-04

Transmission

1 .ooo 0.644 0.481 0.385 0.315 0.259 0.161 0.102 0.062 0.038

1.3E-02 4.1 E-03 1.1E-03 2.3E-04

Total

l.OOE+OO 5.52E-01 3.94E-0 1 3.14E-01 2.62E-01 2.22E-01 1.48E-01 9.80E-02 6.38E-02 4.09E-02 1.60E-02 5.84E-03 1.99E-03 6.28E-04 3.44E-04

sigma T

6.98E-03 6.35E-03 6.03E-03 5.83E-03 5.32E-03 5.26E-03 5.14E-03 4.98E-03 4.97E-03 4.95E-03 4.94E-03

% difference

0.0% -16.7% -22.0% -22.5% -20.0% -1 6.4% -8.7% -4.3% 2.6% 7.8% 16.1% 29.9% 44.8% 63.9% 100.0%

Monte Carlo Results

Y-90 EGS4 code

9975 8578 7462 6461 5675 4951 3453 2484 1582 1004 375 109 37 9 3

5r-90 EGS4 code

971 2 3026 1076 370 108 23

eg54 Total

1 0.589 0.434 0.347 0.294 0.253 0.175 0.126 0.080 0.051

1.9E-02 5.5E-03 1.9E-03 4.6E-04 1.5E-04

% difference

0.0% -9.3% -1 0.8% -1 0.9% -7.2% -2.5% 8.1% 19.0% 22.7% 26.1% 29.6% 26.1% 41.7% 50.4% 100.0%

14

Figure 7

l.E-01

1 .E-02

Sr/Y-90 beta transmission through Zirconium absorbers

--

--

I 1 .E+01

1 .E+OO

1 .E-03 I

l.E-01

1 .E-02

l.E-03

.... * .... *---:.;<...... --.a- ....... . . . . -- ..-* .-._ -..-Q ....

%-* ........... * ... -..a* .........

---. - .. .._ .._ .._

-. ..

-- *.-..-:;I.. .......

'..__ -. -.. .- -- ......... -.. m.., .. -.. * ..... .... .. - .. -. ........

.. ,.. e. ...

...... &2.. ...... e...... EGS4 code values .... .... ..*

-- ... -..".. A ...... A Expected values from Theory '..'..

Experimental fit to 80% of the range (Y-90) 4 ...

..__ ... -. -. ..

e Experimental values

...... e ..... EGS4 code values

A Expected values from Theory

j -..- Experimental fit to 80% of the range (Y-90)

Fit Equation: T = 0.9727e -0.0085*r

...... .... .... -.. .. - - >

A

l.E-04 4 I I I I I I I I I I I I

I I

0 100 200 300 400 500 600 700 800 900 1000

Mass density thickness of Zirconium, [mg/cm2]

15

Table 8

TI-204 source with Aluminum absorbers 3/27/96 dead time =

Absorber thickness

0.00 13.72 27.43 41.15 54.86 68.58 82.29 96.01 109.72 123.44 137.15 150.87 171.50 205.70 240.00 274.30 308.60

Absorber thickness

0.00 13.72 27.43 41.15 54.86 68.58 82.29 96.01 109.72 123.44 137.15 150.87 171.50 205.70 240.00 274.30 308.60

6. I€-06

Gross counts 74242 60527 44467 32058 23986 181 98 13890 21 505 17049 13938 17331 14903 25043 20669 37768 35253 169352

Rb = 282.25

time Transmission secs

10 l.OOE+OO 10 8.01 E-01 10 5.72E-01 10 3.99E-01 10 2.87E-01 10 2.08E-01 10 1.49E-01 20 1.07E-01 20 7.67E-02 20 5.57E-02 30 3.97E-02 30 2.88E-02 60 1.82E-02 60 8.40E-03 120 4.41 E-03 120 1.61 E-03 600 6.50E-05

TI-204 % TI-204 expected difference EGS4 code 1 .OOE+OO 6.69E-01 4.81 E-01 3.47E-01 2.50E-0 1 1.78E-01 1.26E-01 8.75E-02 6.02E-02 4.08E-02 2.73E-02 1.80E-02 9.33E-03 2.88E-03 8.01 E-04 1.98E-04

0.0% -1 9.7% -19.0% -14.8% -15.0% -16.7% -18.8% -22.0% -27.4% -36.5% -45.5% -60.4% -94.8% -1 91.3% -451.4% -71 0.2%

4.37E-05 -48.8%

9796 6405 4707 3445 2567 1857 1338 980 727 492 349 260 123 37 14 5

sigma T

5.40E-03 5.14E-03 4.83E-03 4.57E-03 4.39E-03 4.26E-03 4.16E-03 3.95E-03 3.93E-03 3.91 E-03 3.87E-03 3.86E-03 3.84E-03 3.83E-03 3.82E-03

Monte Carlo Results

eg54 Total

l.OOE+OO 6.54E-01 4.81 E-01 3.52E-0 1 2.62E-01 1.90E-01 1.37E-01 1.00E-01 7.42E-02 5.02E-02 3.56E-02 2.65E-02 1.26E-02 3.78E-03 1.43E-03 5.1 OE-04

% difference

0.0% -22.5% -19.1% -1 3.4% -9.6% -9.7% -9.3% -6.7% -3.3% -1 1 .O% -1 1.4% -8.6% -44.7% -122.4% -208.9% -21 5.0%

16

I

F

F 0 + w F

0 0 + w F

v) a, 3 m > m t

- - c

E 'I a, Q x W

4

a, CT) t

a, 2

5 y.. 0 g 00 0

c m C

c c

- c

.- E t a I3 I

I

cv m 4 4 w w

F F

m 4 w F

0 m m

0 0 m

0 m (v

0 0 cv

0 m F

0 0 F

0 v1

0

Ti-204 source with iron absorbers 3/27/96

dead time = 6.1E-06 Rb = 63.92

Absorber thickness

0.00 19.68 39.35 59.03 78.70 98.38 11 8.05 137.73 157.40 177.08 196.75 216.43 236.10 255.78 275.45 295.13

Absorber thickness

0.00 19.68 39.35 59.03 78.70 98.38 1 18.05 137.73 157.40 177.08 196.75

Gross counts 76092 43649 24041 14661 6998 8727 5299 7020 5222 41 24 51 46 4405 41 58 8277 7899 7670

TI-204 expected l.OOE+OO 5.1 3E-01 2.93E-01 1.68E-01 9.45E-02 5.23E-02 2.82E-02 1.49E-02 7.67E-03 3.84E-03 1.87E-03

time secs

10 10 10 10 10 20 20 40 40 40 60 60 60 120 120 120

% difference

0.0% -8.9% -2.4% -6.7% 14.6% 9.7% 9.8% 5.4% -9.9% -29.1% -47.7%

Transmission sigma T

1 .OOE+OO 5.58E-01 3.OOE-01 1.79E-01 8.07E-02 4.72E-02 2.55E-02 1.41 E-02 8.43E-03 4.96E-03 2.77E-03 1.20E-03 6.84E-04 6.43E-04 2.44E-04

5.1 7E-03 4.59E-03 4.2OE-03 4.00E-03 3.82E-03 3.71 E-03 3.69E-03 3.67E-03 3.67E-03 3.66E-03

Monte Carlo Results

TI-204 EGS4 % EGS4 code

9741 4855 2774 1624 949 531 320 162 82 47 16

Total l.OOE+OO 4.98E-01 2.85E-01 1.67E-01 9.74E-02 5.45E-02 3.29E-02 1.66E-02 8.42E-03 4.82E-03 1.64E-03

difference 0.0%

-1 2.0% -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 4.1 1 E-04 -66.5%

18

F 0 + u!

4 4

t

4 i 4 i

i

. A 4 ?'

2 0 a, E E

4= 0

v) a, 3 m > U a, 0 a, Q

- c

I3 4

- __I-

0 0 + u!

F F

rn 4 u! F

m 4 4

u! u! F F

0 0 0

0 v) N

0 0 cv

0 v) F

0 0 F

0 v)

0

Table 10

TI-204 source with Zirconium absorbers 3/27/96 dead time =

Absorber thickness

0.00 12.98 25.96 38.94 51.92 64.90 77.88 90.86 103.84 116.82 129.80 142.78 155.76 168.74 194.70 220.66 246.62 272.58

Absorber thickness

0.00 12.98 25.96 38.94 51.92 64.90 77.88 90.86 103.84 116.82 129.80 142.78 155.76 168.74 194.70 220.66

6. I€-06

Gross counts 76384 46381 29496 19339 131 02 9042 6384 8909 6421 9505 71 16 8875 7332 6364 51 85 941 1 861 1 8251

TI-204 expected l.OOE+OO 5.91 E-01 3.87E-01 2.58E-01 1.71 E-01 1.14E-01 7.48E-02 4.88E-02 3.16E-02 2.02E-02 1.28E-02 8.03E-03 4.97E-03 3.05E-03 1.1 1 E-03 3.82E-04

Rb = 68.76

time Transmission sigma T secs

10 10 10 10 10 10 10 20 20 40 40 60 60 60 60 120 120 120

% 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% -21 9.6%

l.OOE+OO 5.92E-0 1 3.69E-01 2.38E-01 1.58E-01 1.06E-01 7.20E-02 4.76E-02 3.1 8E-02 2.1 3E-02 1.38E-02 9.98E-03 6.74E-03 4.71 E-03 2.23E-03 1.22E-03 3.82E-04

TI-204 EGS4 code

9740 5441 3627 2463 1652 1102 786 494 336 233 156 96 64 35 13 4

5.17E-03 4.63E-03 4.30E-03 4.09E-03 3.95E-03 3.86E-03 3.80E-03 3.71 E-03 3.69E-03 3.67E-03 3.66E-03 3.66E-03 3.66E-03 3.66E-03

Monte Carlo Results

EGS4 Total

l.OOE+OO 5.59E-0 1 3.72E-01 2.53E-0 1 1.70E-01 1 .13E-01 8.07E-02 5.07E-02 3.45E-02 2.39E-02 1.60E-02 9.86E-03 6.57E-03 3.59E-03 1.33E-03 4.1 1 E-04

246.62 1.26E-04 -203.2% 2 2.05E-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 .O% -67.0% -197.5% -85.9%

20

2-

4

v) a, 3 m > m c

- - c

.- E b Q X w

e

21 0 a, e E 2 Y- v) a, 3 m > U a, 0 a, a X w

4

-

c

a, cn c

a, 2 5 rc 0 g a3 0

i;=

m c a,

c c

- c

E b .- Q

I3 I

I

CI)

4 u! 2-

-r 4 w 2-

0 0 c)

0 m (u

0 0 N

0 rr, 2-

0 0 F

0 rT)

0

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 hnction 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 21 5.2 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 3 1.1 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 not 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 cm* Ern-1

Radionuclide Energy (MeV) Aluminum Iron zirconium

147Pm 0.2247 168.8 147.8 215.2 9OSr/Y 2.2839 9.2 7.9 8.5 2@n 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 using Monte Carlo techniques. Health Physics Supplement to 68(6): S35; 1995

Ozmutlu, C. and Cengiz, A., Mass attenuation Coefficients of Beta Particles. Appl. Radiat. hot. 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 Beta Particles 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 Linear Accelerator Report SLAC-256; 1985

26

bolt I -w r

Appendix A

stainless s

Detector Setup Diagram

c - lead brick

source 6, I bolt

collimator c foils

stainless s gas inlet

i i a l a d kill vofiage connection

gas outlet

L

suppart

detector volume

c

high voltage wire

stainless steel dector backing I

7 support

27

M97053615 I 1111Il11 Ill IIlIl I1111 111ll lllll11111 lllll1111111111111

Report Number (14) b0€/0&/00033--T73~

Publ. Date (11) / 9 7 @ 4 X/=

Sponsor Code (18)

UC Category (19)

E H 1

DOE