A. Instrument

The multi-sphere neutron spectrometer used in this work is shown schematically in Fig. 1. A Φ5.08 cm ³He spherical proportional counter (LND-27036) was used as the thermal neutron detector. The moderator was made of high-density polyethylene (0.94 g/cm^-3), being 8 cm, 11 cm, 15 cm and 23 cm in diameter or nothing (bare detector). The moderator balls and the configuration are shown in Fig. 2.

Fig. 1.Full-screen View

(Color online) Schematics of the multi-sphere neutron spectrometer system.

Fig. 2.Full-screen View

(Color online) The moderator balls and detector configuration.

The response functions of the multi-sphere neutron spectrometer were calculated with the MCNPX code, using the method in Ref. [12], and the results are shown in Fig. 3. Before the survey, the neutron spectrometer was tested, so as to check its performances. Energy resolutions of the detector coated with different moderator balls were measured at about 7% at 765 keV of reaction ³He(n,p)T, while the detection efficiencies were about 10% as calibrated with ²⁵²Cf and ²⁴¹Am-Be neutron sources. These agreed well with the simulation results.

Fig. 3.Full-screen View

(Color online) The response functions of the multi-sphere neutron spectrometer.

B. Measurement

Spots of different altitudes in Tibet were chosen and natural neutron spectra were measured at each of the spots using the neutron detector coated with different moderator balls. Conditions of the spectrometer system kept unchanged to measure all the neutron spectra. And each spectrum was recorded in over two hours, with the counts of each moderator ball being greater than 300. The Global Positioning System was used for getting the coordinates and altitudes of the measurement spot.

A. Neutron energy spectra

The natural neutron spectra obtained using an unfolding program of the least square method are shown in Fig. 4(a), with the altitudes, longitudes and latitudes listed in Table 1. It can be seen that the neutron fluence rates of each energy range increase with the altitude, because the cosmic-ray intensity increase with the altitude. Figure 4(b) shows the neutron spectra normalized to the total fluence rate. The spectrum fractions of neutrons of greater than 0.1 MeV do not differ obviously, while those of the thermal neutrons at different altitudes differ greatly from each other, due possibly to differences in ground media and vegetation at the measurement sites of different altitudes, hence the different moderation and absorption to the natural neutron.

Fig. 4.Full-screen View

(Color online) Spectra of natural neutrons at spots of different altitudes in Tibet. (a) as-measured, (b) normalized.

B. Neutron fluence rate and the estimated neutron dose rate

Total fluence rate, effective dose rate and ambient dose equivalent rate were calculated from the measured spectra at each altitude, as given in Table 2. In the calculation, the effective dose per unit fluence for monoenergetic neutrons incident in isotropic geometries to adult male and female reference phantoms calculated by PHITS [13] were used, and the conversion coefficients of ambient dose equivalent rate for monoenergetic neutrons were adopted from the GBZ/T 202-2007 [14].

By fitting the data in Table 2, the altitude variations of neutron fluence rate and neutron dose rate can be obtained, as shown in Fig. 5. It can be seen that the total neutron fluence rate, effective dose and the ambient dose equivalent rate increase exponentially with altitude of the measurement sites, as pointed out in Refs. [1, 15].

Fig. 5.Full-screen View

(Color online) Altitude dependence of the total neutron fluence rate (a), effective dose rate (b) and ambient dose equivalent rate (c).

The variations of the total neutron fluence rate φ, effective dose rate E and ambient dose equivalent rate H*(10) can be fitted by exponential function of R·e^α·h, where, h is altitude of the measurement sites, R and α are the fitting parameters. The fitted functions were obtained as Eqs. (1), (2) and (3).

where φ is in cm^-2 s^-1, h is in m, and E and H*(10) are in nSv/h.

Standard deviations of the α -values are given in Table 3. It can be seen that the α-values of φ, E and H*(10) are almost the same. This means that the natural neutron spectra changed just a little, so all the α-values calculated from the spectra varied with the altitude nearly in the same way.

Table 4 compared the α-values obtained at various geomagnetic latitudes by different groups. Both the α -value and the latitudes (18°–21°) of the present work are the smallest. This confirms that the α-values increase with the geomagnetic latitude, and that magnitude of the attenuation of natural neutrons is influenced by the geomagnetic intensity [1]. As a result, in order to assess the natural neutron dose in Tibet more accurately, the local α-value should be applied.