The main fission products from the Fukushima Daiichi nuclear power plant (FDNPP) accident are 129mTe-129Te, 131I, 132Te-132I, 134Cs, 136Cs and 137Cs [1–4]. These radionuclides emit gamma rays and beta rays through β− decay. However, there are few studies about dose estimation from beta-ray irradiation following the FDNPP accident [5–7]. The beta-ray dose contributes to the whole-body dose among small biota, such as insects, plant leaves, and human skin. Therefore, beta-ray dose estimations are important for the risk assessment of the impact of the FDNPP accident (including on small biota) to clarify the effects of this large-scale radiological accident.
Retrospective dosimetry with brick samples has been used to evaluate the gamma-ray dose of the Hiroshima atomic bomb [8–10], the Chernobyl nuclear power plant accident [11–14], and the Semipalatinsk nuclear weapon testing [15, 16]. Recently, Stepanenko et al.  used retrospective dose evaluation of brick samples to estimate gamma-ray doses and perform beta-ray dose reconstruction for the FDNPP accident with a similar method to that used for a Hiroshima tile sample . They used a single-grain quartz optically stimulated luminescence (OSL) method (similar to that of Ballarini et al. , although layer-by-layer consequences for very thin layers of the sample’s aliquots were used for analysis, with separate dose calibration for each quartz grain) with brick samples taken in 2014 from Odaka, Minami-Soma City, Fukushima Prefecture, Japan . Dose enhancement near the surface of the brick was identified by the OSL measurements . Stepanenko et al. suggested that the enhancement was caused by the beta-ray dose from the deposited fission products .
To establish the cause of the dose enhancement near the brick surface, we performed a Monte Carlo simulation of a small brick building with radionuclides uniformly distributed on the ground surface. The calculated results were compared with the data measured by Stepanenko et al. . The depth profiles of the dose in the brick sample for beta rays and gamma rays were estimated separately, and the dose enhancement near the brick surface was discussed.
MATERIALS AND METHODS
Particle and Heavy Ion Transport code System calculation
The energy deposition as a function of depth in the brick wall of a small building was calculated using the Particle and Heavy Ion Transport code System (PHITS) Monte Carlo code Ver. 2.52 . The calculation geometries are shown in Fig. 1. The calculation regions were 1 m × 1 m for beta rays and 21 m × 21 m for gamma rays. The calculation regions consisted of ground, air, and the small brick building (red region: 0.5 m × 0.5 m square, 1.5 m high, wall thickness of 10 cm). The brick building was located in the center of the soil surface. Beta- or gamma-ray sources were uniformly distributed in the 5-mm-thick soil surface (brown region). To save calculation time, the previously reported mirror condition was used for these calculations . Figure 1a shows the geometry used to calculate the radiation that entered the calculation region (outer source calculation) via the mirror boundary. First, the histories for the particles were accumulated near the mirror boundary (green lines) without the brick building. Second, the particles were generated from the mirror boundary (back line) in Fig. 1b according to the accumulated histories. The generated particles were transported to the brick wall cells (yellow box) of the brick building. Third, radiation was generated from the surface of the 5-mm-thick soil layer (brown region) in the calculation region (inner source calculation) in Fig. 1b. The energy deposition in brick cell layers of 10 m × 10 cm and thicknesses of 0.1, 0.2, 0.3, 0.4, 0.5, 1, 3, 5, 7.5, 10, 20, 40, 60, 80 and 100 mm were obtained by summing the outer and inner source calculations corrected with the number of particles generated per unit area.
Beta and gamma rays from 129mTe, 129Te, 131I, 132Te, 132I, 134Cs and 137Cs were calculated separately. Beta-ray energy spectra were taken from the literature , and the internal conversion electrons of 137Cs were taken from the website of the National Nuclear Data Center . The gamma-ray energies and emission rates for the radionuclides were taken from the National Nuclear Data Center .
The elemental composition of the brick sample was Si: 28.9, Si: 50.4, Al: 17.5, Fe: 1.4 and Ti: 1.8 wt %, and those of soil and air were taken from the literature .
Air dose and tissue dose calculation
where Eijk is the energy deposition (J) at the i-th depth by beta or gamma rays from the k-th radionuclide, mb is the brick sample mass (kg), and aj is the area of the source (0.75 and 1 m2 for inner and outer beta calculations, 440.75 and 441 m2 for the inner and outer gamma calculations, respectively). Ij is the emission rate for beta or gamma rays per Bq and fc is the conversion factor of the stopping power ratio  for beta rays and the kerma ratio  for gamma rays between air or tissue and brick to convert from the brick dose to the air or tissue doses.
Cumulative dose estimation
where Tk is the half-life for each radionuclide of k = 129mTe, 129Te, 131I, 132Te, 132I, 134Cs and 137Cs (Table 1), and τ is the time period from deposition to the brick sampling date.
RESULTS AND DISCUSSION
Calculated dose rate for beta and gamma rays
A 137Cs deposition density of 308 kBq/m2 and the ratio of each radionuclide to 137Cs deposition density taken from the literature  were used to obtain Ak for each radionuclide. The deposition densities for the seven radionuclides are listed in Table 2. The beta-ray dose rates on the brick surface and gamma-ray dose rate at a depth of 0.5 mm in the brick at a height of 80 cm are shown in Fig. 2a and b, respectively. 129m, 129Te contributed less to the gamma-ray dose rate, and accounted for the third and fourth largest contribution to the beta-ray dose rate. This is due to the small gamma-ray emission rate per decay of 129m, 129Te of <10%. The gamma- and beta-ray doses decreased by ~10% and ~30%, respectively, over 1 month. The calculated beta-ray dose rate decreased slower than the calculated gamma-ray dose rate.
Beck reported conversion factors for various radionuclides to estimate the air dose rate at a height of 1 m from the unit deposition density of radionuclides . The initial gamma-ray air dose rates (15 March 2011) at a height of 80 cm from the ground for each radionuclide obtained by our calculations were compared with the values estimated by Beck conversion factors  interpolated at a relaxation depth of 0.65 g/cm2 (Table 2). The present dose rates were estimated to be 57% lower than those calculated by Beck conversion factors. The present dose rates were in-brick values in one of the walls of the brick building, whereas the Beck conversion factor values were free-in-air values. Therefore, the difference of 57% can be explained by shielding effects, whereby gamma rays from behind the building are neglected.
The cumulative dose over 3 years, from 12 March 2011 (Unit 1 explosion) to 19 March 2014 (brick sampling by Stepanenko et al.) and the dose rate change over time are shown in Fig. 3. The solid line shows the calculation result, the dashed histograms are the averaged calculation values for the measured sample thickness, and the open circles are Stepanenko’s data . The calculation agreed well with the data measured by Stepanenko et al. in the region deeper than 10 mm. The results indicated that the cumulative dose deeper in the brick was due to gamma rays, and that the dose enhancement at the surface was dominated by the beta-ray contribution. The difference between the calculated and measured doses at the surface was about 2 standard deviations. A possible explanation might be connected with the contributions of low γ emission rate radionuclides, such as 89Sr, 127mTe-127Te, 140Ba-140La, etc. However, the trend in the dose increase at the brick surface was supported by the calculations. Therefore, the single-grain OSL measurement by Stepanenko et al. shows the advantage of dose estimations not only the cumulative gamma-ray dose but also the cumulative beta-ray dose. Thus, we concluded that the single-grain OSL method is a good tool for retrospective beta-ray dose estimation.
The calculated tissue dose at a brick depth of 50 μm was assumed to be a skin dose, and would be similar to a 70-μm tissue dose. The skin dose was estimated to be 164 mSv for 3 years at the sampling location.
To confirm the cause of the dose enhancement near the surface of a brick sample taken from Odaka, Minami-Soma City, Japan, a Monte Carlo calculation was performed using PHITS code and the calculated results were compared with measurements. The calculated results agreed well with previously published measured data. The dose enhancement at the brick surface in the measured data was explained by the beta-ray contribution, and the gentle slope in the dose profile deeper in the brick was due to the gamma-ray contribution. The calculated result estimated the skin dose to be 164 mGy (164mSv) over 3 years at the sampling location.