富山大学水素同位体科学研究センター研究報告 22: 55-64, 2002.

論文
厚いアクリル樹脂製のトリチウム線源で観測された
Ｘ線スペクトルの解析及びシミュレーション
松山

政夫、鳥養

祐二、渡辺

国昭

富山大学水素同位体科学研究センター〒930-8555 富山市五福３１９０

Analysis and Simulation of β-Ray-Induced X-Ray Spectrum Observed
for a Thick Tritium Source Made of Methylmethacrylate Resin
Masao Matsuyama, Yuji Torikai and Kuniaki Watanabe
Hydrogen Isotope Research Center, Toyama University
Gofuku 3190, Toyama 930-8555, Japan(Received July 7, 2003; Accepted January 23, 2004)

Abstract
The β-ray-induced X-ray spectra observed for a polymer disk (1 mm thickness), which was made ofpoly-methylmethacrylate labeled with tritium, were analyzed and they were reproduced bycomputer simulation based on the uniform distribution of tritium in the polymer disk. The X-ray
spectra were measured in both helium and argon atmospheres. An X-ray spectrum observed in thehelium atmosphere consisted of only a broad bremsstrahlung X-ray peak, while in the argon
atmosphere a characteristic X-ray peak appeared in addition to bremsstrahlung X-rays. Fromdifferences in the shape and intensity of X-ray spectra observed in both atmospheres, the conversion
fraction of the bremsstrahlung X-rays to the characteristic X-rays in an argon atmosphere wasdetermined to be 7.1x10-2 by taking the absorption coefficient of X-rays into account. The spectra
observed in both atmospheres could be reproduced quite well by using the equations to estimate
generation and attenuation of X-rays in various materials. It was suggested, therefore, that a tritium
depth profile in carbonaceous materials can be evaluated by the numerical simulation. Furthermore,
the simulation indicated that nitrogen could be also used as a promising alternative gas of helium
for evaluation of a tritium depth profile in bulk.
55

松山政夫・鳥養祐二・渡辺国昭

1. Introduction

In the International Thermonuclear Experimental Reactor (ITER) and a future advanced
reactor, a huge amount of tritium will be required as fuel in comparison with that in theconventional tracer studies. Therefore, quantitative evaluation of tritium activity not only in agaseous state but also a dissolved state in materials is indispensable from a viewpoint of safe
handling in the fusion reactors. Especially, evaluation of the amount and depth profile in the latterstate is of a great importance for safe management of tritium wastes. However, the penetration
depth of β-rays from tritium is very short because of their low energy. This is a reason why it isdifficult to measure the amount of tritium retained in bulk of a material by means of β-ray detection.
Electromagnetic radiation, however, is emitted with β-rays as a result of interactions between
β-rays and constituent atoms, when tritium dissolves in a material: characteristic and bremsstrahlung X-rays are emitted. Penetration power of the X-rays is much higher than that of the β-rays,
and therefore X-rays give information on the amount of tritium in a deeper region of a material.
Intensity and shape of these X-ray spectra depend on the amount and the depth profile of tritium inbulk of the material. In particular, the shape of a bremsstrahlung X-ray spectrum basically reflects
the depth profile of tritium. Analyzing the shape of a bremsstrahlung X-ray spectrum by numericalsimulation, therefore, the depth profile of tritium can be estimated. The present method has been
applied so far to some inorganic materials to examine the amount and changes in the depth profileof tritium [1-4], but in most of cases the depth profile of tritium was only a near surface region
shallower than 1 µm.
In the present study, a polymer disk (1 mm in thickness) labeled with tritium was employed forthe examination, and the X-ray spectra observed in argon and helium atmospheres were analyzed indetail. In addition, to examine the applicability of the present simulation method to a thicker
material, reproduction of the X-rays spectra was carried out by numerical simulation based on a
uniform distribution of tritium in the polymer disk.

2. Experimental

2.1. Materials
A polymer disk used in this study was made of poly-methylmethacrylate that was uniformly
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厚いアクリル樹脂製のトリチウム線源で観測されたＸ線スペクトルの解析及びシミュレーション

labeled with tritium (hereafter described as T-PMMA), and the size was 25mm in diameter and
1mm in thickness. This was delivered from Amersham Japan Co., and the specific activity was
178.7 MBq/g (15 March, 1999). Weight of the disk was 0.584 g. Purity of argon gas used formeasurements of β-ray-induced X-rays was 99.995%, and that of helium was 99.9995%.
2.2. Measurements of β-ray-induced X-ray spectra
A semiconductor detector equipped with a high purity Ge element was used for measurementsof β-ray-induced X-rays. Energy resolution of the present X-ray detector was determined to be 129
eV at 5.9 keV by using a 55Fe source. The radiation entrance window of the X-ray detector was
made of a specially designed thin beryllium plate (8 µm in thickness) to gain an effective
transmittance of low energy X-rays. The polymer disk was fixed at location of 5mm from the frontof the radiation entrance window of the X-ray detector. The X-ray spectra were measured in both
argon

and

heliumatmospheres.

Duringameasurement, these gases were kept at theconstant flow rate of 40 cm3/min. In the former
atmosphere X-rays induced by tritium of surface
and bulk can be detected, while in the latter

BERRA

Cryostat

T-PMMAbe mainly measured. To reduce the effects ofnatural radiations on the X-ray measurements, the
X-ray detector was surrounded with two leadbricks during a run. The schematic drawing of the

Sample holder
Lead brickatmosphere X-rays induced by tritium in bulk can

Lead brickDetector(HP-Ge)

Enclosure

Ar(He) atmosphere

Fig. 1: Cross sectional view of the β-ray-induced
X-ray measuring device.

present measuring device is shown in Fig. 1.

2.3. Simulation of the observed X-ray spectra
The simulation of the observed X-ray spectra was carried out by the aid of computer. Basicequations for numerical calculations of the simulated spectra were shown elsewhere [5]. In thecalculation process, absorption coefficients of various materials are important parameter to calculate
the attenuation of X-rays, which affect the shape and intensity of X-ray spectra. Table 1 shows thesummary of energy dependence of mass absorption coefficient for each material in the present
measuring condition.

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松山政夫・鳥養祐二・渡辺国昭

3. Results and discussion
0.05

background level for the present measuringsystem. The X-ray spectrum was obtained byaccumulating

for

72

accumulation

is

to

hrs.

The

long

obtainaprecise-1

Ar atmosphere
0.04

Accumulation time: 72 hours-1

Figure 2 shows a typical spectrum of theCounting rate, N / counts min (∆E)

3.1. Analyses of the observed X-ray spectra

0.03

0.02

0.01

0.00

background spectrum. The background level

0

2

4

6

8

10

12

14

16

18

Energy of X-rays, E / keV

was as low as (2–5 )x10-3 counts/min∆E in theinteresting region, while a steep increase

Fig. 2: A typical background spectrum observed in theargon atmosphere.

appeared below 1 keV. It is considered that
this is mainly due to noise of electric circuits of the detector. The value of ∆E was set at 34.5 eV
under the present measuring conditions. Total intensity of the background was 1.03 counts per
minute (hereafter described as cpm) in a range from 1.0 to 18.6 keV.
Figures 3 and 4 show the X-ray spectra observed in helium and argon atmospheres,
respectively. A broad X-ray peak was observed as shown in Fig. 3, and this is bremsstrahlung
X-rays based on interactions between β-rays and constituent atoms in the polymer disk. Intensity of

Ar atmosphere

He atmosphere
1.2Counting rate, N / counts (min) (∆E)

1.0

-1

1.0

-1

Counting rate, N / counts (min) (∆E)

-1

-1

1.2

0.8

0.6

0.4

0.2

0.8

0.6

0.4

0.2

0.0

0.0
0

2

4

6

8

10

12

14

16

0

18

2

4

6

8

10

12

14

16

18

Energy of X-rays, E / keV

Energy of X-rays, E / keV

Fig. 4: The X-ray spectrum observed in theargon atmosphere.

Fig. 3: The X-ray spectrum observed in thehelium atmosphere.

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厚いアクリル樹脂製のトリチウム線源で観測されたＸ線スペクトルの解析及びシミュレーション

Table 1: Summary of energy dependence of a mass absorption coefficient for each material employed in thepresent measuring device.

Absorber / thickness

K-Absorption Edge
(keV)

T-PMMA (1 mm) #1

0.2838 #2

Ar gas (5 mm)

3.2029Be window (8 µm)

0.111

Al-evaporated film
(200nm)Poly-carbonate film
(2 µm)
Dead layers of Ge crystal(100nm)1.55990.2838 #2
11.1036

Mass Absorption Coefficient#3(cm2 / g)
µ(1)

µ(2)
2835E-2.8984

3350E-2.7104

40519E-2.8169

620E-2.9250
1200E-2.5750

23100E-2.9250

1753E-2.8777
16015E-2.6268

110571E-2.6268#1 T-PMMA: poly-methylmethacrylate labeled with tritium (T-C4H6O2)n.
#2 The energy is available for carbon atoms.
#3 Values of µ(1) and µ(2) correspond to a energy range below and above the K-absorption
edge, respectively.

the bremsstrahlung X-rays was 198.8 cpm. As is shown in Fig. 4, on the other hand, a characteristic
X-ray peak of argon appeared in addition to the bremsstrahlung X-ray peak, although a total X-ray
intensity observed in argon atmosphere was a little lower. Intensities of the bremsstrahlung and thecharacteristic X-rays were evaluated to be 145.4 and 4.82 cpm, respectively.
Two kinds of generation processes for characteristic X-rays are considered: the excitation ofargon atoms is caused by not only collisions with β-rays but also the photoelectric effect ofbremsstrahlung X-rays. The former excitation is led by colliding with β-rays from tritium existing
within a few µm beneath the surface, whereas the latter excitation is responsible for all photons
having energy above 3.203 keV (absorption edge of the K-shell in argon atoms), which are emitted
from the bulk of the polymer disk. In this paper, the surface means a shallower depth than apenetration depth of β-rays, and the bulk means a deeper region than the penetration depth.
The absorption fraction of bremsstrahlung X-rays in argon atmosphere can be determined froma difference in the intensity of bremsstrahlung X-rays in both atmospheres, while one can also
estimate it by using a mass absorption coefficient of X-rays for argon. The calculated X-ray

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松山政夫・鳥養祐二・渡辺国昭

spectrum (solid line) is shown in Fig. 5 together: Obs. spectrum in He

1.4

with the spectrum in helium atmosphere, where: Calc. spectrum

the mass absorption coefficient for argon shown inCounting rate, N / counts (min) (∆E)

-1

1.2

-1

Table 1 was used. The open circles again represent
the X-ray spectrum shown in Fig. 3. Both X-ray
spectra agreed quite well except for the part ofcharacteristic X-rays. Namely, this indicates thatthe absorption of the bremsstrahlung X-rays inhelium atmosphere is negligibly small, and that thebremsstrahlung X-ray spectrum emitted from the

1.0

0.8

0.6

0.4

0.2

surface of the polymer disk in argon atmosphere0.00

can be reproduced by the calculation. Agreement

2

4

6

8

10

12

14

16

18

Energy of X-rays, E / keVof the two spectra plays an important role forcomputer simulation of the observed X-ray spectra.
In addition, it was revealed that the difference inthe bremsstrahlung X-ray intensity above 3.203

Fig. 5: Comparison of the bremsstrahlung spectrum
calculated from the X-ray spectrum observed inargon atmosphere (solid line) with that observed inhelium atmosphere (open circles).

keV in both atmospheres should be mainly responsible for the absorption of X-rays by photoelectriceffect, and it was evaluated as 44.28 cpm.
To examine a conversion efficiency (fluorescence yield) of bremsstrahlung X-rays tocharacteristic X-rays due to the photoelectric effect in argon, an X-ray spectrum was measured in asimilar manner by packing the polymer disk with a thin poly-propylene film of 6 µm to shieldperfectly the β-rays. As a result, a similar spectrum to that shown in Fig. 4 appeared, but aconsiderable decrease in the characteristic X-ray intensity was observed, suggesting that thephotoelectric effect of bremsstrahlung X-rays is not negligible for the generation of characteristic
X-rays of Ar(Kα). The fluorescence yield for argon was finally determined to be 7.1x10-2 from thepresent examination, assuming that absorption of bremsstrahlung X-rays in the poly-propylene film
is negligibly small.
The photoelectric effect gives rise to a competitive emission between Auger electrons andcharacteristic X-rays, and the ratio of both emission processes depends on the atomic number. It is
known that a fluorescence yield ω(K) for the emission of characteristic X-rays can beapproximately estimated by the following equation [6]:ω(K) = 1/(1+1.12x106 Z-4),
６０

厚いアクリル樹脂製のトリチウム線源で観測されたＸ線スペクトルの解析及びシミュレーション

where Z represents the atomic number of a target.

8.5x10-2, which agrees well with the value
obtained from the experiment mentioned above. It
can be seen, therefore, that the characteristic X-ray
intensity described in Fig. 4 consist of the sum of
characteristic X-rays induced by β-rays (1.68
cpm) and those induced by bremsstrahlung X-rays

Attenuation of β-rays in PMMA, F / -system, the value of ω(K) is calculated to be

1

1

0.5

0.5

0.1

0.1

Integrated intensity, I / arb. units

For example, applying this equation to the argon(3.14 cpm). A conversion efficiency of β-rays tocharacteristic X-rays of argon has been already

0.05
0.01

1

Thickness, d / µm

reported to be 3.1x10-4 photons/β-particle by
Matsuyama et al., which was determined from the

0.05
0.1

Fig. 6: Attenuation and integral intensity of β-rays
as a function of thickness of T-PMMA.

irradiation experiments of graphite with tritium
ions [3].

3.2. Simulation of the observed X-ray spectra
In order to simulate a β-ray-induced X-ray spectrum by numerical calculation, it is necessary
to determine basic two parameters prior to the calculation. The first parameter is the penetration
depth of β-rays in T-PMMA. The penetration depth can be estimated by determining the absorption
coefficient of β-rays. The absorption coefficient can be calculated from results of total and surface
activity measurements for T-PMMA. It was determined to be 4.89x104 cm-1. The details aredescribed elsewhere [7]. Assuming that the attenuation of β-rays obeys a simple exponentialfunction, as shown in Fig. 6, the average penetration depth is expected to be 2 µm from the above
value. Namely, it was assumed in the numerical calculation that the initial kinetic energy of theβ-rays is consumed during plowing through T-PMMA of 2 µm in thickness. This penetration depth
is remarkably small in comparison with the thickness of T-PMMA.
The second parameter is energy dependence of absorption coefficients of X-rays for
T-PMMA, argon and construction materials (Be, Al, Ge, and a thin poly-carbonate film) of the Ge
detector. Those values used in the numerical calculation are represented in Table 1.
Figure 7 shows the comparison of the simulation spectra (solid line) with the spectra observedin the argon atmosphere. The detailed numerical calculation process of an X-ray spectrum by６１

松山政夫・鳥養祐二・渡辺国昭

computer simulation is described in the literature
1.280Counting rate, N / counts (min) (∆E)-1

bremsstrahlung X-rays in the polymer disk and

1.0

-1

the Ge detector was calculated using parameterssummarized in Table 1. The simulation was
carried out by basing on the uniform distributionof tritium in the polymer disk. It was seen thatthe simulation spectra agreed fairly well with theobserved spectrum although there appeared to be

60
0.8

0.6

40

0.4
20
0.2

a little deviation from the observed intensity at a00.0

low energy side.

Intensity of X-rays (Simulation), I / arb. units: Ar atmosphere[5]. Reduction of the characteristic and/or

0

2

4

6

8

10

12

14

16

18

Energy of X-rays, E / keVA

comparisonofsimulation

spectracalculated in three kinds of atmospheres (He, N2

Fig. 7: Comparison between the simulated and theobserved spectrum in argon atmosphere.

and Ar) is shown in Fig. 8. The same calculation
parameters were used to calculate for each100

atmosphere, except that a different parameter is: Ar

an energy dependence of the mass absorption
80

Intensity of X-rays, I / arb. units

coefficient. It is clear that the shape of asimulation spectrum for helium atmosphere wasquite similar to that of the observed spectrum
shown in Fig. 3. This indicates, therefore, thatthe present simulation of a β-ray-induced X-ray
spectrum is applicable to tritium-containing

thesimulation

60

40

20

carbonaceous materials as thick as about 1mm.
Furthermore,

: He
: N2

spectrum0

expected for helium atmosphere was perfectly

0

2

4

6

8

10

12

14

16

18

Energy of X-rays, E / keV

overlapped with that expected for nitrogen
atmosphere, although absorption coefficients ofFig. 8: Simulation spectra for He, Ar, and N2
atmospheres.

X-rays for both atmospheres considerably
differed: the mass absorption coefficient (cm2/g) for helium is 56.89E-2.8838, and that for nitrogen is3354E-2.8940, where E describes the X-ray energy (keV). The observation that little difference of
X-ray spectra in both atmospheres appeared is due to the following multiplier effects: the first is
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厚いアクリル樹脂製のトリチウム線源で観測されたＸ線スペクトルの解析及びシミュレーション

difference in the conversion efficiency to bremsstrahlung X-rays, and the second is the closed
distance between the polymer disk and the beryllium window. From viewpoint of practicalmeasurements of a tritium-containing material, the simulation spectra indicate that nitrogen is more
useful than helium, because a long time measurement in helium atmosphere is difficult owing to thepermeation through a beryllium window of the Ge detector

4. Conclusions
The β-ray-induced X-ray spectra observed for a thick polymer tritium disk, which was made ofpoly-methylmethacrylate, were analyzed and the reproduction of them was attempted by computer
simulation based on the uniform distribution of tritium. The X-ray spectra were measured in bothhelium and argon atmospheres. An X-ray spectrum observed in the helium atmosphere consisted ofonly a broad bremsstrahlung X-ray peak, while in the argon atmosphere a characteristic X-ray peak
appeared in addition to bremsstrahlung X-rays. Total X-ray intensity observed in the argon
atmosphere was about 75% as low as that in the helium. The bremsstrahlung X-ray spectrum
calculated using the absorption coefficient of X-rays for argon agreed quite well with that thebremsstrahlung X-ray spectrum observed in helium. The characteristic X-rays of argon were
attributed to excitation by both β-rays from tritium in surface layers of the polymer disk and thephotoelectric effect of bremsstrahlung X-rays. It was seen that the conversion fraction of thebremsstrahlung X-rays to the characteristic X-rays in an argon atmosphere was 7.1x10-2. The
observed spectra in both atmospheres could be reproduced quite well by computer simulation,suggesting that a tritium depth profile in tritium-containing carbonaceous materials can be estimatedby simulation analyses. Furthermore, it was seen from the simulation that nitrogen could be used asa promising alternative gas of helium.

References[1] M. Matsuyama, T. Murai, K. Watanabe, K. Tsuzuki and N. Noda, Ann. Rept. Hydrogen Isotope
Research Center, Toyama University, 20 (2000) 53.
[2] M. Matsuyama, T. Tanabe, N. Noda, V. Philipps, K.H. Finken and K. Watanabe, J. Nucl. Mater.,
290-293 (2001) 437.
[3] M. Matsuyama, T. Murai and K. Watanabe, Fusion Sci. Technol., 41 (2002) 505.
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松山政夫・鳥養祐二・渡辺国昭[4] M. Matsuyama, T. Murai, K. Yoshida, K. Watanabe, H. Iwakiri and N. Yoshida, J. Nucl. Mater.,
307-311 (2002) 729.
[5] M. Matsuyama, K. Watanabe and K. Hasegawa, Fusion and Eng. Design, 39-40 (1998) 929.
[6] “Hyoumenbunseki”, Eds. M. Someno and I. Yasumori, Kodansha Scientific, (1976), p.128.
( in Japanese)[7] M. Matsuyama and K. Watanabe, Ann. Rept. Hydrogen Isotope Research Center, Toyama
University, 16 (1996) 81.

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