Schematic drawings of the calculation geometries are shown in Figure 1.

The ω normalized to 4 π was calculated as

ω = 1 2 π ∫ F O V cos Φ l 2 ( θ ) d S (1)

where FOV is the detector field of view. The parameters in this equation are these given in Figure 1(c). In most of cases, the NEAs have irregular shapes rather than spherical shapes. However, we considered the target as a sphere with equivalent volume here. Since cos Φ can be shown as ( L − R cos θ ) / l , Equation (1) is calculated as

ω = R 2 L 2 ( R 2 − L 2 l max + l max + 2 R ) (2)

The value of ω has been tested by using the parameter H / R in the range of 0.5 - 5.0 In this range, the observation target is inside the FOV; i.e., l max = L 2 − R 2 . Therefore, we can obtain ω = R 2 / ( L 2 ) . The relation between H / R and ω is shown in Figure 2. The values in this figure are normalized to those of H / R = 2.0 . When observation backgrounds are negligible, minimum acquisition time for detection varies depending on reciprocal of ω. The normalized minimum acquisition time depending on H / R is also shown in Figure 2. Including ω, the gamma-ray and neutron emission spectra were implemented into the gamma-ray and neutron detectors, respectively.

The gamma-ray and neutron emissions are obtained based on the nuclear interactions of GCR particles with both the observation target and the spacecraft. The sample volume was assumed to be 20 m × 20 m × 20 m, while gamma-ray and neutron spectra emitted from the central 10 m × 10 m of this volume surface are obtained. The sample compositions of elements are described in the next section. The spacecraft was assumed as being made of 30 - 100 kg aluminum charged with xenon fuel in the 1.0 - 10 kg range. The case of no fuel was also considered for the estimation of background at the end of mission. 50 kg of hydrazine fuel with its oxidizer (H₂N₄ + 1.3 N₂O₄) was considered in order to compare backgrounds with those originated from electric and chemical engines. The hydrazine mass is decided as delivering the similar specific impulse to that

of 5.0 kg xenon since an ion thruster engine has ~7 - 10 times larger specific impulse than chemical propulsion system [35]. The backgrounds emitted by a spacecraft similar to Mars Odyssey (331.8 kg spacecraft with 348.7 kg fuel [36] ) were also estimated for the comparison as a typical case of large scale missions.

NEAs are classified by their reflectance spectra and orbital parameters [37]. M-type and X-type asteroids are mainly composed by iron and siderophile elements (e.g. [38] ). Those together with undifferentiated primitive asteroids are expected to be appealing sources of space resources [39] for microsatellite based exploration. Four types of elemental compositions have been selected to simulate these target asteroids just described.

One is the type of Earth’s core with some light elements [40]. This is the profile used for M-type and X-type asteroids since both asteroid types are considered to be produced by collisions that remove crust from the celestial body with a metallic core. The others are the elemental compositions of meteorites which are considered to originate from different types of planetary bodies; C-type and S-type asteroids, and Mars [41] [42] [43]. The C-type asteroid is considered to be the most primitive celestial body with large abundances of hydrogen and carbon [41]. The S-type asteroid is a primitive celestial body next to the C-type, being higher Si and Ca, and lower C and H concentrations than C-type asteroid [42]. The Martian meteorite was selected as a typical basaltic composition of a body finishing thermal evolution [44]. All the considered asteroid type specific elemental compositions are listed with their average atomic mass in Table 1. To check the effects of hydrogen concentration, the water equivalent hydrogen concentrations in C-type and Martian compositions were varied in the 0 - 20,000 ppm range.

For the simulations of gamma-rays from radioactive elements K, Th, and U, characteristic gamma-ray lines from the relevant radioisotope decays of these elements have been added to the gamma-ray emission spectra obtained by the simulations. The potassium concentration was varied in the 0 - 1000 ppm range while the thorium and uranium concentrations were used as variables in the 0 - 1000 ppb range.

The GCR Hydrogen and helium particles were chosen as primaries hitting the asteroid surface. Their energy fluxes J were obtained after [45] [46].

J ( E , ϕ ) = ω g c r C × E ( E + 2 m p c 2 ) ( E + χ + ϕ e × Z A ) − γ ( E + ϕ e × Z A ) ( E + 2 m p c 2 + ϕ e × Z A ) [ cm − 2 ⋅ s − 1 ( MeV / n ) − 1 ] χ = a exp ( − b E ) (3)

Here, E (MeV/n), ϕ (MV), m p c 2 (MeV), Z, A, and γ are particle kinetic energy, solar modulation parameter, proton rest mass energy, atomic number, mass number and power law index, respectively. C (cm⁻²∙s⁻¹⁽MeV/n)⁻¹), a (MeV), and b (MeV⁻¹) are normalized constants. The values of constants and γ for hydrogen and helium were determined from the PAMELA measurements during 2006-2007 [47] [48]. These values are summarized in Table 2. The value

of ϕ was fixed to 440 MV, which corresponds to the above 2006-2007 measurement periods [49]. The energy spectra obtained by Equation (3) were shown in Figure 3. The data acquired by PAMELA during 2006-2007 and BESS in 1997 are also shown for cross check of Equation (3) [47] [48] [50]. The solar activity during 1997 was a solar minimum activity phase as well as the PAMELA measurement periods [49]. Hence, it is considered that the modulation parameter of 440 MV is consistent with both periods. It is found that Equation (3) reproduces GCR fluxes well, especially hydrogen flux. We used the approximation of the GCR solid angle seen from the flat celestial body surface as π i.e., ω g c r = 1 / 4 . The GCR density at the asteroid surface was fixed to 1.0 × 10⁴ particles/m², corresponding to an exposure time of ~1.0 s.

For the evaluation of gamma-ray detector performance, important parameters are its detection efficiency ε ( E ) and energy resolution R ( E ) as a function of

energy E . When the gamma-ray count rates of interest are low, the minimum detectable activity, D m i n , is given by

D m i n = N m i n ε f t (4)

= F m i n ε ( E ) f t ( [ 2 n B ¯ + F m i n 2 / 4 ] 1 / 2 + F m i n / 2 ) (5)

where N m i n , f , and t are the minimum of detectable counts N , the decay branching ratio, and acquisition time, respectively [51]. N m i n is obtained from the fractional reciprocal error minimum F m i n , the number of channels defined around the peak n determined by the energy resolution R ( E ) , and the background average B ¯ . The fractional reciprocal error F is called the detector figure of merit and is also used as the parameter for detector performance evaluation. In the case of N ≪ B ¯ , F is given as N t / 2 n B ¯ . Therefore, the relation between F, ε ( E ) , R ( E ) , is F ∝ ε ( E ) / R ( E ) . As stated above, we use F, to compare the gamma-ray detectors performances. A high-purity germanium semiconductor (HPGe), a CeBr₃, a LaBr₃(Ce), and Cs₂LiYCl₆(Ce) (CLYC) scintillators are taken as the gamma-ray detectors in order to realize the optimal detection system.

Semiconductors and scintillators have been studied and used as gamma-ray detectors. Generally, scintillators have a large atomic mass and high density, which results in a high detection efficiency, while the energy resolution is low compared to semiconductor detectors. The Ge, CdZnTe, and CdTe detectors are the most commonly applied semiconductor radiation detectors. Semiconductors show a high energy resolution due to their low ε -values (2.98 eV for Ge, 5.0 eV for CdZnTe, and 4.43 for CdTe) [52]. On the other hand, density and atomic mass of Ge are lower than the scintillator’s ones. Compound semiconductors with a high density and large atomic mass such as CdZnTe and CdTe have been studied for their high detection efficiency. However, they show problems in transport properties and limitations in achieving the needed thickness for gamma-ray detection [53]. A lot of devices are required for the large capacity of compound semiconductor detector. We evaluated and compared a semiconductor detector and several scintillators as model cases of gamma-ray detectors. The HPGe, which have been employed in previous missions such as Mars Odyssey [8] , SELENE [9] , and MESSENGER [12] , was selected as the semiconductor detector. CeBr₃, LaBr₃(Ce) and CLYC were selected as scintillators having the highest energy resolution. Actually, CeBr₃ and LaBr₃(Ce) scintillators have been studied and compared as gamma-ray detectors for space missions (e.g. [54] [55] ). A LaBr₃(Ce) scintillator have been loaded on Chang’E-2 [11] and will also be used in Bepi Colombo mission [54].

The HPGe achieved energy resolution of ~3.0 keV FWHM at 1332 keV in SELENE ground test [56] , requiring cooling below ~100 K for optimal operation. This value corresponds to ~2.1 keV FWHM at 662 keV by the square root law of energy. Previous missions with the HPGe also employed a refrigerator, increasing the weight and power consumption of the gamma-ray spectrometer as well as imposing a heat flow on the spacecraft. Moreover, the energy resolution degrades by the radiation damage during cruising phase. Although the degradation of the energy resolution can be recovered by crystal annealing, the actual energy resolution in previous missions were worse: 3.9 keV FWHM in Mars Odyssey [8] and 6 - 7 keV FWHM in SELENE [56] at 1461 keV, and 4.8 keV FWHM in MESSENGER at 1368 keV [57]. In our calculations, we assumed the highest energy resolution achieved by Mars Odyssey. The CeBr₃ scintillator has larger average atomic number than the HPGe detector, so it has a higher detection efficiency for the same depth, while its energy resolution is inferior to that of HPGe, showing ~31.1 keV FWHM at 663 keV [55]. LaBr₃(Ce) shows similar detection efficiency to CeBr₃ with superior energy resolution (~25.8 keV FWHM at 663 keV [55] ) although it introduces internal background due to ¹³⁸La radioactive decay. In this study, the gamma-ray flux due to the internal background of LaBr₃(Ce) was also estimated. ¹³⁸La decays with half-life of ~10¹¹ years in two decay modes; electron capture (65.5%) and beta decay (34.5%) [58]. According to Camp et al. [59] , the internal background of LaBr₃(Ce) is ~1.53 Bq/cm³. The electron capture reaction emits gamma-rays with 1.44 MeV, while the beta decay emits 789 keV gamma-rays with a Q-value of 1.05 MeV. Electron energies by the beta decay were assumed to follow a Fermi profile spectrum, extracted from the total measured spectrum by numerical deconvolution, as reported by Quarati et al. [60]. The CLYC detector has recently been studied due to its sensitivity to both gamma-ray and neutron and their discrimination by pulse shape (e.g. [61] [62] [63] [64] ). The CLYC energy resolution of ~27.1 keV FWHM at 663 keV [63] is better than CeBr₃, while the sensitivity to gamma-rays is lower because of its low density and small average atomic number. The CLYC is assumed as a dual mode detector for gamma-ray and neutron.

The detector sizes were chosen to be 2.5 inch ϕ × 2.5 inch (~200 cm³) for HPGe and 3 inch ϕ × 3 inch (~350 cm³) for the scintillators. The HPGe size was limited by the refrigerator mass.

Since neutrons have no electric charge, they are detected by interactions with detector nuclei producing charged particles. Slow (thermal and epithermal) neutrons are detected as a positive Q-value, where the Q-value is the mass difference in energy scale between the total mass of interacting particles before and after the interaction. Thermal neutrons are mainly detected through neutron absorption by nuclei followed by the emission of charged particles. The cross section of neutron absorption is, in general, a decreasing function of neutron energy, except at the resonance energies, where the cross section is appreciably large. The three isotopes of ¹⁰B, ⁶Li, and ³He have particularly large cross sections of neutron reaction and large Q -values. Therefore, they are important for thermal neutron detection. On the other hand, fast neutrons may scatter nuclei elastically with an energy ranging from zero to the energy of the neutron. The fast neutrons may be detected by measuring the energy of recoil particles.

The neutron spectrometer was defined as being composed of a lithium glass scintillator (LiG) with a boron loaded plastic scintillator (BLP) or a CLYC. A schematic drawing and the detector sensitivities as a function of the neutron energy are shown in Figure 4. The LiG typically shows high sensitivity to thermal neutron (<0.5 eV). The BLP detects separately epithermal (0.5 Ev - 500 keV) and fast (>500 keV) neutrons by delayed coincidence [8] [15]. In the BLP, neutrons undergoing nuclear capture in the 20 ns - 2.5 μs time window after the hydrogen-nuclei elastic reaction with energy over 100 keV were considered as fast neutrons here. The sensitivity of CLYC in epithermal energy range is lower than the BLP because of its lower cross section of neutron reactors. While the CLYC can separately detect gamma-ray and neutron, it cannot discriminate between fast and epithermal neutrons.

Gamma-ray emission energy spectra from our four types of target compositions are shown in Figure 6. Some typical gamma-ray lines are also assigned in Figure 6 [58] [65]. The differences in elemental compositions are evident in these spectra. Although there are some irregular features such as a gaussian at ~5.2 MeV and rectangles at ~5.5, 6.5, and 7.5 MeV, these gamma-rays are emitted by errors in the calculation mechanism of PHITS. The gaussian is derived from oxygen gamma-ray with the energy of 5.269 MeV, while the rectangles correspond to

iron gamma-ray lines at 5.921, 6.382, and 7.509 MeV, respectively [36]. These irregular gamma-rays were integrated with a linear continuum to approach the gamma-ray lines at the corresponding energies. We note that gamma-ray lines from radioactive nuclei decay are not present. The emission rates of some major gamma-ray lines are summarized in Table 5 [58] [65].

The emission rate dependences of some strong gamma-ray lines on the hydrogen concentration are shown in Figure 7. The values in this figure are normalized at those of 100 ppm hydrogen. Generally, (n, γ) plots increase with the hydrogen concentration, while (n, nγ) plots decrease with the hydrogen concentration. This trend is induced by thermal and fast neutron dependence on the hydrogen concentration, which is described in the next section. The fast neutron decrease leads to a reduction of the inelastic scattering gamma-ray production. The variation of O (n, nγ) gamma-rays is small compared with the other plots. We have evaluated the water equivalent hydrogen concentration in the sample, i.e., the number of oxygen nuclei increases in a fixed 1:2 proportion to that of hydrogen nuclei. The fast neutron decrease together with the oxygen nuclei increase induces a balancing effect on the dependence of O (n, nγ) gamma-ray. The thermal neutron dependence on the hydrogen concentration leads to an enhancement of the neutron capture gamma-rays for up to 10,000 ppm hydrogen, moderately decreasing at 20,000 ppm hydrogen. The H (n, γ) plots increase drastically, reaching over 500 at 20,000 ppm hydrogen. This is not only due to the increase of thermal neutron but also of hydrogen concentration.

Major gamma-ray emission rates from radioactive elements with different concentrations for the C-type case are shown in Table 6 [58] [65]. The emission rates with the other elemental compositions were confirmed to be similar to the C-types ones.

As shown in Figure 8, neutron fluxes in the epithermal energy show differences depending on the hydrogen concentration in each composition, while the neutron energy spectra for targets with high hydrogen compositions show peaks in the thermal energy range. The neutron emission rates in the three energy ranges are shown in Table 7. According to Naito et al. [66] , the emission rates of epithermal and fast neutrons decrease with hydrogen concentration, while that of thermal neutron becomes maximum at ~2000 ppm. Figure 9 shows the neutron emission rate dependence on hydrogen concentration. The values are normalized to the 0 ppm hydrogen case. The neutron emission rate dependence on hydrogen concentration is explained by the moderation and decrease of . The increase of hydrogen concentration induces the decrease of , which decreases the neutron yields by spallation. Effective moderation by hydrogen atoms increases the thermal neutron, but for very high hydrogen concentrations it begins to decrease due to low neutron yields. The large dynamic range of epithermal neutron flux is caused by both effective moderation and yield decrease.

Figure 10 shows the relative values of F for the four detectors obtained by the ε ( E ) / R ( E ) relation as a function of gamma-ray energy. The values of

ε ( E ) and R ( E ) were calculated by simulations and square root law of energy, respectively. The values in Figure 10 are normalized to F obtained with HPGe and 1 MeV gamma-rays. The HPGe detector shows a ~2.5 times higher value of F than LaBr³ due to its excellent energy resolution. Differences in F between CeBr³ and LaBr³ were ~10%, and those between CeBr³ and CLYC were ~15% - 40%.

The C-type asteroid gamma-ray spectra of the different detectors are shown in Figure 11. The solid angle parameter H / R was assumed to be 2.0 in this figure. Also in the following figures, H / R was fixed to 2.0 unless noted otherwise. Differences in F appear in the energy spectra. The HPGe spectrum shows sharp gamma-ray lines and low continuum level, which are results of its high energy resolution and low detection efficiency, respectively. The CeBr³ and LaBr³(Ce) spectra strongly overlap due to the similar detection efficiencies and energy resolutions. The CLYC spectrum shows a similar detection efficiency and energy resolution to HPGe and CeBr³ and LaBr³, respectively. The gamma-ray background spectrum from the spacecraft body detected by the HPGe detector is also shown as a black line in Figure 11(a). It is ~1/10 of the target gamma-ray counts for this solid angle. If the background spectrum is measured during the cruising phase, it will be effectively subtracted from the target measurements.

Nevertheless, this low background level will not affect significantly the statistical error of target measurement.

The LaBr³(Ce) internal background gamma-ray spectrum is also shown in Figure 11. Its count rate level is significantly larger than that from the target

measurement one. With this background level it is difficult to detect gamma-ray lines below 1.5 MeV. In particular, the lanthanum gamma-ray line at 1.44 MeV makes the estimation of potassium gamma-ray line at 1.46 MeV impossible. Hence, the use of this detector is not an applicable choice.

Figure 12(a) and Figure 12(b) show the count rates of BLP and CLYC with a LiG, respectively. The neutron count rates generally decrease with hydrogen concentration. This effect is related to the variation in both the neutron emission rate and detector sensitivity. The emission rate of epithermal neutrons decreases with the hydrogen concentration, while thermal neutron emission has a peak at 2000 ppm. On the other hand, the LiG is partially sensitive to epithermal neutron as shown in Figure 4(b) (~70% at 1 eV). The LiG count rate decreasing with the hydrogen concentration is explained by the energy response of detector sensitivity. Despite the similar LiG configuration between the BLP and CLYC setup, the LiG count rates in Figure 12 show differences. It is considered that some neutron events which returned to the LiG by scattering in the BLP result in higher LiG count rates in Figure 12(a). The count rate of the BLP is larger than that of the CLYC due to higher detection sensitivity (Figure 4(b)).

Comparing the count rates of C-type and Martian composition depending on hydrogen concentration, the count rates of BLP and CLYC seem to depend on the hydrogen concentration and do not distinguishing between the two compositions. This conclusion on the BLP and CLYC count rates can be extended to the S-type composition, which contains ~3300 ppm hydrogen. However, the plot corresponding to Earth’s core composition does not match these trends. The

core composition with high iron concentration may be the cause for these abnormal values. A material with large average atomic mass produces a large number of neutrons, but its moderation is not effective. Actually, high fast neutron count rates are shown in shown in Figure 12(b) as a consequence of the large average atomic mass. Moreover, the relatively large neutron capture cross section of iron results in a low thermal neutron flux. Thermal neutron absorption by iron is also visible in the LiG count rate difference between C-type and Martian compositions. Therefore, it is reasonable to conclude that the core composition does not provide sufficient moderation enough for the production of thermal and epithermal neutrons.

The CLYC count rates show larger differences depending on hydrogen concentration than the BLP count rates, especially in the range of 0 - 500 ppm. In the present simulation, the neutron count rate identification between 0 and 100 ppm of hydrogen requires ~3600 and 300 seconds for BLP and CLYC, respectively. In this respect, the CLYC has a higher potential for the hydrogen detection than the BLP although its count rates are lower. Here the value will change with the solid angle shown in Figure 2, i.e., the minimum acquisition time becomes four times longer in the case of H / R = 2.5 . However, as mentioned in Section 2.2.2, the CLYC is not usable for the discrimination between fast and epithermal neutrons.