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									Title
Calculation of Energy Response of Cylindrical G-M Tubes with EGS4 Monte Carlo Code
Boxue LIU, Yanchun WANG, Bo XIE, Hao ZHANG Research Institute of Chemical Defense, China PO Box 1044-200, Beijing 102205
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Abstract
The energy response of cylindrical G-M tubes were calculated using the electron-photon cascade Monte Carlo code EGS4. One G-M counter was GJ4401 ,sensitive length 9cm, diameter 1cm. The other was J5 ,sensitive length 2cm, diameter 0.3cm. The restricted sampling technique of source photon was used. Good tendency agreements between the simulations and the experiments were achieved for gamma radiation with energies ranging from 40 keV to 1.25 MeV. For GJ4401, the difference of response between simulations and experiments at 662 keV was 34%, the difference for J5 was 27%.
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Introduction
G-M counter tubes are simple, easy to use radiation detectors. One disadvantage of the G-M counter tube was that its energy response varied considerably over the range from 50 keV to 3 MeV. If we study the energy response of G-M counter tubes by experiments only, there will be lots of experiments to do. The energy response of G-M counter tubes had previously been analyzed approximately, the difference between the calculations and the experiments could not be ignored. The method was developed to simulate the coupled transport of electrons and photons by Monte Carlo method and to verify by a few of typical experiments.
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The EGS4 system of computer codes
The EGS4 code is a general purpose package for the Monte Carlo simulation of the coupled transport of electrons and photons in an arbitrary geometry for particles with energy above a few keV up to several Tev. In our study, transports of photons and second electrons with the energy ranging from 1 keV to 10 MeV was simulated using the EGS4 codes. The Rayleigh scattering for photons were taken into account besides the photoelectric effect, Compton scattering and electron pair effect had been considered.

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4

The geometry of G-M counter tubes
The G-M counter tubes were approximately thought as axial ratio right cylinders. The cross-sectional view along Z axis was shown in the left figure.

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The model of cylindrical G-M counter
Two cylindrical GM tubes were studied. GJ4401: the sensitive length is 9cm, diameter is 1cm. J5: the sensitive length is 2cm, diameter is 0.3cm. Both cathode and anode are made of alloy mixed with Cr (Chromium) and Fe (Iron). Neon is used as ionization gas. Small amount of bromine gas is enclosed as a quenching agent to extinguish the continuouing discharge in tubes.
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Expose condition
Photon radiation is uniform parallel beam, the energy range is from 40keV to 1.25MeV. Monoenergetic incident photons arrived at the outer layer uniformity (parallel to Y-axis, vertical to X-axis and Z-axis).

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7

Forcing the incident photon to interact
The technique of forcing the incident photon to interact in the geometry was taken. The distributing density function of mean free paths could be taken from the following equation, where ρ is mean free paths and Dm is weight.

f (ρ) = e
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−ρ

⋅1 /(1 − e

− Dm

)
8

History stopping conditions
For electrons: enter into the sensitive region left the geometry region energy less than the cutting energy 1 keV For photons: left the geometry region energy less than the cutting energy 10 keV

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9

Computer simulations
The detection efficiency could be obtained by summing the number of electrons that got into sensitive zone. The total traced photons (N) is decided on condition that the calculation error less than 5 percent at 95% confidence level. N was about one million. The calculated value was N/Φ as the following equation, where Φis the influence, wt is photon weight, S is side area of GM tube.

n S = φ N
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∑

N

wt
10

i=1

The data transfer
The energy response for Ka and H*(10) could be deduced from the follow equation, where Ka is air kerma, H*(10) is ambient dos equivalent, coefficient of Ka/Φ and H*(10)/Φ could be referenced to the ICRP74. Hp (10) could be also deduced as H*(10) . n n φ = ⋅ Ka φ Ka n n n φ Ka φ = ⋅ * ⋅= ⋅ ⋅ * * H (10) φ H (10) φ Ka H (10)

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11

The result of bare GJ4401
10 9 8 7 6 5 4 3 2 1 0 1 10 *--experiment curve o--calculated curve

The Ka response of GJ4401 at 662 keV obtained from experiments was 2.86*104s-1 /mGy/h •and the calculated result was 1.89*104s-1 /mGy/h. The latter was smaller by 34%. The calculation and experiment were agreed very well.
10
4

10

2

10

3

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12

The result of compensated GJ4401
4 3.5 o--calculated curv e * --experment curv e 3

2.5

2

1.5

GJ4401 tube with 0.5 mm Sn (length was 72 mm) as filter were calculated and experimented, the results were shown in the left figure.

1

0.5 1 10

10

2

10

3

10

4

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13

The result of bare J5 tubes
14 12 10

8

6 *--experiment curve 4 o--calculated curve

2

The experimental Ka response of J5 at 662 keV was 1.78* 103s-1 /mGy/h, and the calculated value was 1.29*103s-1 /mGy/h. The latter was smaller by 27%. The calculation and experiment were agreed also well.
10
4

0 1 10

10

2

10

3

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14

Conclusion
For bare tube and thinner compensation filters, the energy responses curves of EGS4 calculations were agreed with experimental curves over the gamma energy range from 40 keV to 1.25 MeV. With thickness of the compensation material increasing, the difference between the simulations and experiments appeared, which maybe due to the deep penetrating question. This will be further studied.

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Thanks•
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