Altitude Variation of cosmic-ray neutron energy spectrum and ambient dose equivalent at
Mt.Fuji in Japan
M. Kowatari1, K. Nagaoka1, S Satoh1 ,Y Ohta1, J.Abukawa1
Division of Radioactivity Analysis, Japan Chemical Analysis Center, 295-3,Sanno-cho, Inage-ku,
Chiba-shi, Chiba, Japan
E-mail: m-kowatari@jcac.or.jp
1
Abstract. The experimental studies on the cosmic-ray neutron energy spectrum and the neutron dose rate were
performed in the Mt.Fuji area (altitude: 40m – 2400m) by using a Multi-sphere neutron Spectrometer (Bonner
Sphere: BS) with the 5.07-cm diam. spherical He-3 proportional counter to assess the natural background neutron
dose rate in Japan with good accuracy. The spectra measured at each altitude were compared with each other and
with other environmental neutron spectra and the neutron energy spectra measured at each altitude are confirmed to
be almost the same in their shapes. The total neutron fluence rate, the ambient dose equivalent H*(10) were
estimated to be about 0.0073 cm-2·s-1, and the neutron dose rate (ambient dose rate H*(10)) at sea level is estimated
to be about 6.0 nSvh-1. The altitude variations of neutron fluence rate and neutron dose rate were also evaluated and
they vary according to an exponential law with the altitude, ~exp(αZ), where α = 0.00070 m-1. This α-value is
smaller than those of other researches obtained at high geomagnetic latitude.
1.Introduction
The experimental studies on the cosmic-ray neutron energy spectrum and the neutron dose rate in low
geographical latitude area are quite few [1] , although many researches in high geographical latitude
area have been performed [2-5] . According to the recommendation of ICRP Publication 60, the
contribution of neutrons to public dose should be more emphasized. The more detailed knowledge about
the cosmic-ray induced neutrons in the environment is therefore essential to estimate the natural
background dose. The neutron dose rate in the environment varies with the altitude. In this study, the
altitude variation of cosmic-ray neutron energy spectrum and the ambient dose equivalent has been
measured in the Mt.Fuji area (altitude: 40m – 2400m) by using a Multi-sphere neutron Spectrometer
(Bonner Sphere: BS) to assess the natural background neutron dose rate in Japan with good accuracy.
The cosmic-ray neutron energy spectrum and the ambient dose equivalent obtained in this study were
then compared with those of other researches obtained at high geomagnetic latitude area.
2.Experimental Setup and Measurement
The energy spectrum of the cosmic-ray induced neutrons was determined by using a Multi-sphere
neutron Spectrometer (BS). The BS consists of five 5.07-cm diam. spherical He-3 proportional counters
filled with 5 atom He-3 gas. Spherical polyethylene moderators with different thickness are attached to
each counter. The diameters of the polyethylene moderators are 0cm(bare), 8.0cm, 11cm, 15cm, and
23cm, respectively. As the response of the BS to neutron in the energy range from thermal to 400MeV,
the set of response functions determined by Uwamino et al. [6] was used except for the bare He-3
counter. The response function of bare He-3 counter was given by Nunomiya [7]. Figure 1 shows the
response functions used in this study. Calibration of the BS was performed using monoenergetic
neutrons with the energy range of 250keV to 15MeV at Dynamitron facility of Tohoku University [8].
The BS was also calibrated using thermal neutrons and a Cf-252 neutrons source at Facility of Radiation
Standard of JAERI (Japan Atomic Energy Research Institute). Throughout the series of these calibrations,
the mean errors between the measured and calculated response was within the range of 20%. The
cosmic-ray neutron energy spectra were obtained by unfolding with the SAND2 code. The SAND2 code
calculates the neutron energy spectrum from the counting rate obtained in each He-3 counter. In this
study, the cosmic-ray neutron spectrum at sea level obtained by Goldhagen et al. [5] was employed as an
initial guess spectrum. The energy range selected for the unfolding calculation was 0.01eV to 400MeV.
Response Function (Calcurated)
bonner 23cm (uwamino)
bonner 15cm (uwamino)
bonner 11cm (uwamino)
bonner 8cm (uwamino)
bonner bare (Nakamura)
100
bonner experimental
23cm (experimental)
15cm (experimental)
11cm (experimental)
8cm (experimental)
bare (experimental)
2
Response (counts/(#/cm ))
10
1
0.1
0.01
0.001
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
1.0E+08
1.0E+09
Neutron energy (eV)
Fig. 1 Measured and calculated response functions of the Multi-sphere neutron spectrometer
The BS was installed in a air-conditioned freight car. The temperature in the cargo container was kept
within 23 ±2°C. The BS was placed so that the centers of each counter locate on the horizontal plane,
which is about 2.0m height above the ground level. A series of measurement of the cosmic-ray neutron
around Mt.Fuji area (40m, 620m, 1020m, 1660m, and 2400m altitude: about 26°N geomagnetic latitude)
were performed until the counting errors of each He-3 proportional counter become lower than 3%. In
parallel with the cosmic-ray neutron measurement, temperature, atmospheric pressure and geographical
position were also measured. The conversion of geographical position into geomagnetic coordinate was
carried out according to IGRF 2000. After obtaining neutron spectra, the ambient dose equivalent rate
H*(10) and the effective dose rate of the cosmic-ray at each altitude were estimated based on ICRP
Pubication74. To estimate the ambient dose equivalent rate H*(10), we used neutron fluence to ambient
dose equivalent conversion factor calculated by Sannikov and Savitskaya [9] in the energy range of
200MeV to 400MeV. The fluence to effective dose (AP and ISO geometries) conversion factors
calculated by Ferrari et al. [10] were used for the estimation of the effective dose in the energy range of
200MeV to 400MeV.
3. Results and Discussion
3.1 Neutron energy spectra
Figure 2 shows the neutron energy spectra measured by BS (Sea level and 2400m height) around Mt.Fuji
area and those of other researchers for comparison. At sea level, neutron energy spectra obtained in this
study is in good agreement with that of obtained by Nakamura et al. [1], except in the high energy region
(above 10MeV). The neutron spectrum obtained at 2400m altitude is in quite good agreement with that
of obtained by Florek et al. [3], especially in the range up to 1MeV. In contrast, in the lower energy
region (below several hundred keV) the spectrum obtained by Florek et al. [3] is higher than our result.
This discrepancy might be caused by the differences of the measuring location (differences of
geomagnetic latitude and altitude) and the number of energy bin for spectrum unfolding process. Taking
these differences into consideration, both spectra are in good agreement each other.
Present Work (at Sea Level)
Present Work (at 2400 m)
Florek et al. [3]
Nakamura et al. [1]
1.0E+06
1.0E+05
1.0E+04
1.0E+02
-1
Fluence rate (s ・cm ・MeV )
1.0E+03
-2
1.0E+01
-1
1.0E+00
1.0E-01
1.0E-02
1.0E-03
1.0E-04
1.0E-05
1.0E-06
1.0E-07
1.0E-03
1.0E-02
1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09
Neutron energy (eV)
Fig. 2 Neutron energy spectra measured by BS (Sea level and 2400m height) around Mt.Fuji area
Figure 3 shows the neutron fluence rate per lethargy obtained at each altitude around Mt.Fuji area. As
mentioned in UNSCEAR 1993 [11] and other articles [4,5], three major peaks (thermal neutron region,
evaporation peak around 1MeV and peak around 100MeV caused by nuclear spallation reaction) are
clearly confirmed. Figure 4 depicts the normalized neutron spectra using the highest flunence rate around
evaporation peak. At the 2400m-altitude measurement, relative fluence rate of peak around 100MeV is
slightly lower than those of at other altitude. Except for the high-energy region of spectrum at
2400m-altitude, the neutron energy spectra measured at each altitude are almost the same in their shapes.
sea level
600m
1020m
1600m
2400m
4.5E-03
Fluence rate per lethargy E dN/dE
-2 -1
(neutrons·cm s )
4.0E-03
3.5E-03
3.0E-03
2.5E-03
2.0E-03
1.5E-03
1.0E-03
5.0E-04
0.0E+00
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
1.0E+08
Neutron energy (eV)
Fig.3 Measured neutron spectra at various altitudes around Mt.Fuji
1.0E+09
sea level
600m
1020m
1600m
2400m
1.2
Relative fluence rate per lethargy
1
0.8
0.6
0.4
0.2
0
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
1.0E+08
1.0E+09
Neutron energy (eV)
Fig.4 Measured neutron spectra at various altitudes around Mt.Fuji (Normalized using highest count)
3.2 Neutron fluence rate and the estimated neutron dose rate
Total fluence rate, ambient dose equivalent rate H*(10) and effective dose rate have been determined
from the measured spectra at each altitude. The results of these values are shown in Table I.
Table I. Measured neutron fluence rate and dose rate at various altitude around Mt.Fuji area
altitude
(m)
Atmospheric
Depth
(g·cm-2)
Neutron Fluence
Rate
(#·cm-2·s-1)
Effective Dose
Rate (AP geometry)
(nSv·h-1)
Effective Dose
Rate (ISO geometry)
(nSv·h-1)
Ambient Dose
Equivalent Rate (H*(10))
(nSv·h-1)
40
1025
0.0073
6.3
4.5
6.0
620
965
0.0099
8.9
6.4
8.5
1020
923
0.0130
11
8.1
11
1660
856
0.0190
17
13
16
2400
785
0.0400
33
23
32
All values vary with measuring altitude. The cosmic-ray neutron fluence rate obtained at sea level is
estimated to be about 0.0073 cm-2·s-1, and the neutron dose rate (ambient dose equivalent rate H*(10)) at
sea level is about 6.0 nSvh-1. These values are both lower than those of other researches. It is pointed out
by some references that cosmic-ray neutron intensity decreases against geomagnetic latitude of the
measuring location [3,11-12]. Taking it into consideration that a series of measurement in this study was
carried out in the lower geomagnetic latitude area, these results are quite reliable. As shown in Table I,
ambient dose equivalent rate H*(10) and effective dose rate (AP geometry) obtained at each altitude
indicate values of almost the same level, although ambient dose equivalent rate H*(10) are slightly lower
than effective dose rate (AP geometry). In contrast, effective dose rate (ISO geometry) at each altitude is
estimated to be lower than those of AP geometry and ambient dose equivalent rate. The similar tendency
is pointed out by reference [5]. It might be caused by the fact that the fluence to dose conversion factors
of ISO geometry is especially lower in the energy region (below 1MeV) than those of AP geometry and
ambient dose equivalent H*(10).
3.3 Altitude variation of neutron fluence rate and neutron dose rate
As shown in Figs. 5 and 6, the total neutron fluence rate and the ambient dose equivalent rate H*(10)
indicate exponential dependence on the altitude of measuring location Z (m), as pointed out by some
references [3,12]. The variations of the total neutron fluence rate and the ambient dose equivalent rate
could be fitted by exponential function in the form of ~exp(αZ). In this study, the α-values are
consequently determined to be about 0.00070 m-1 using least squares method. The α-values for the total
neutron fluence rate and the ambient dose equivalent rate are almost the same.
Total Fruence Rate
fitting curve
-2 -1
Total neutron fluence rate (neutrons·cm ·s )
0.1
0.01
y = 0.0066×e0.00070Z
R = 0.990
0.001
0
500
1000
1500
2000
2500
3000
Altitude (m)
Fig.5 Altitude dependence of the total neutron fluence rate
Neutron Dose rate
fitting curve
Ambient dose equivalent rate (nSv·h
-1
)
100
10
y = 5.6×e0.00070Z
R = 0.995
1
0
500
1000
1500
2000
2500
3000
Altitude (m)
Fig.6 Altitude dependence of the ambient dose equivalent (H*(10)) rate
Table II indicates the comparison of the α-values obtained for various geomagnetic latitudes. The value
introduced in UNSCEAR 2000 [12] is derived by converting the attenuation factor per atmospheric
depth into attenuation factor per altitude in unit of m-1 assuming the standard air. The α-value obtained in
this study is smaller than those of other researches. It is confirmed that the α-value decreases according
to geomagnetic latitude and that the magnitude of the attenuation of cosmic-ray neutron is influenced on
the geomagnetic intensity.
Table II. Comparison of α-value obtained by various geomagnetic latitudes
Geomagnetic latitude
α-value
(degrees)
(×10-3·m-1)
26.0
48.0
49.0
50.0
0.7
*1
0.78 [12]
0.85 [3]
1.04 [13]
*1 converted value of attenuation factor per atmospheric depth assuming the standard air
UNSCEAR 2000 [12]
Florek et al. [3]
Bouville et al. [13]
Figure 7 shows the comparison of the altitude variation of the relative neutron dose rate using various
α-values. In Fig.7, neutron dose rate is normalized by dividing the values by the dose rate at the altitude
of 0m.
Present work
UNSCEAR 2000 [12]
Florek et al. [3]
Bouville et al. [13]
16
14
Relative neutron dose rate
12
10
8
6
4
2
0
0
500
1000
1500
2000
2500
Altitude (m)
Fig.7 Comparison of the altitude variation of the relative neutron dose rate using various α-values
In estimation of the neutron dose rate at a certain altitude, the use of larger α-value will result in higher
dose values. Since the α-values obtained by other researchers [3,12-13] were determined for higher
geomagnetic latitudes, the use of these α-values will possibly lead to an overestimation of the natural
neutron dose rate in lower geomagnetic latitude including Japan. In order to assess the cosmic-ray
neutron component of the natural background dose in Japan more accurately, it is therefore indispensable
to adopt reliable α-values obtained in lower geomagnetic region in the evaluation of the altitude
variation.
4.Conclusions
Measurement of the cosmic-ray neutron energy spectra and estimation of the ambient dose equivalent
and effective dose around Mt.Fuji (altitude: 40m – 2400m) area were performed. From the results of the
measurement, we compared the shape of cosmic-ray neutron spectra obtained at various altitudes with
each other, and with those of other researches. In this study, the following facts were clarified:
1) The neutron energy spectra measured at each altitude are almost the same in their shapes.
2) The cosmic-ray neutron fluence rate obtained at sea level is about 0.0073 cm-2·s-1, and the neutron
dose rate (ambient dose equivalent rate H*(10)) at sea level in Japan is estimated to be about 6.0
nSv·h-1 at the geomagnetic altitude of around 26°N. These values are both smaller than those of other
articles reflecting the difference of the geomagnetic latitude of the measuring location.
3) The cosmic-ray neutron fluence rate varies according to an exponential law with the altitude,
~exp(αZ), where α = 0.00070 m-1. The value α for neutron dose rate is almost the same as that for
neutron fluence rate. This α-value is smaller than those of other researches obtained in high
geomagnetic latitudes. The α-value decreases according to geomagnetic latitude.
Acknowledgement
The authors thank to Dr. Uwamino and Dr. Nunomiya for having provided them with the response
function of BS. And we also wish to thank Prof. T. Nakamura for the suitable advise about the evaluation
of the data and about English expression and also for his continuous encouragement of this study.
This work was performed under the commission of Ministry of Education, Culture, Sports, Science and
Technology in Japan.
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