Mapping of the lunar surface by average atomic number based on positron annihilation radiation from Chang’e‐1

A map of the average atomic number of lunar rock and soil can be used to differentiate lithology and soil type on the lunar surface. This paper establishes a linear relationship between the average atomic number of lunar rock or soil and the flux of position annihilation radiation (0.512‐MeV gamma‐ray) from the lunar surface. The relationship is confirmed by Monte Carlo simulation with data from lunar rock or soil samples collected by Luna (Russia) and Apollo (USA) missions. A map of the average atomic number of the lunar rock and soil on the lunar surface has been derived from the Gamma‐Ray Spectrometer data collected by Chang’e‐1, an unmanned Chinese lunar‐orbiting spacecraft. In the map, the higher average atomic numbers (ZA > 12.5), which are related to different types of basalt, are in the maria region; the highest ZA (13.2) readings are associated with Sinus Aestuum. The middle ZA (~12.1) regions, in the shape of irregular oval rings, are in West Oceanus Procellarum and Mare Frigoris, which seems to be consistent with the distribution of potassium, rare earth elements, and phosphorus as a unique feature on the lunar surface. The lower average atomic numbers (ZA < 11.5) are found to be correlated with the anorthosite on the far side of the Moon.


Introduction
The average atomic number of lunar rock and soil is an important geophysical and geochemical parameter. A map of the average atomic number of lunar rock and soil can be used to differentiate lunar surface lithology and soil types. The relationship between fast neutron flux from the lunar surface and the average atomic mass of lunar soil was found by Gasnault (Gasnault et al., 2001), which confirmed that fast neutron leakage flux in the energy range of 0.6 to 8 MeV was proportional to average soil atomic mass. Accordingly, from the fast neutron spectra collected by the Lunar Prospector Fast Neutron Spectrometer (LPFNS), a map of the average atomic mass of lunar rock and soil was obtained with a precision of ~20%.
The Gamma-Ray Spectrometer (GRS) aboard the Chinese lunar-orbiting spacecraft Chang'e-1 provides the distribution of major elements O, Si, Mg, Al, Ca, Na, and Fe (Hasebe et al., 2009;Kobayashi et al., 2012) and natural radioactive elements U, Th, and K on the lunar surface (Hasebe et al., 2009;Ouyang ZY et al., 2011;Zhu MH et al., 2013. During the Chang'e-1 mission, the spacecraft stayed in a circular polar orbit with a period of 127 minutes at a nominal altitude of 200 km. Global GRS data over intervals of 3 seconds were obtained from the in-flight gamma spectra in the energy range of 0.1 to 9 MeV (Hasebe et al., 2009;Ma T et al., 2008;Yang J et al., 2013;Zhu MH et al., 2010).
The high-energy gamma rays from the lunar surface originate predominantly from cosmic neutron and proton interactions with lunar rocks and soil (Reedy, 1978). Some characteristic gamma rays are identified from GRS data (Hasebe et al., 2009;Yang J et al., 2013;Zhu MH et al., 2010). GRS peaks at or near 0.512, 0.58-0. 61, 1.46, 1.80, 2.20-2.62, 6.1, 6.76, and 7.1-7.6 MeV are associated with position annihilation radiation (PAR) and natural or induced radiation from the elements U, Th, K, Al, Si, O, Ti, and Fe (Yang J et al., 2013;Zhu MH et al., 2011). This paper investigates the relationship between 0.512-MeV PAR intensities and the average atomic number of lunar rock and soil. First, an analytical model suggests a linear relationship between the PAR flux from the lunar surface and the average atomic mass of surface rock and soil. Second, the analytical model is found to agree well with results of the Monte Carlo simulation. Finally, a map of the average atomic number, obtained by the model with data from the Chang'e-1 GRS, is constructed.

Theory
The 0.512-MeV gamma rays are generated from PAR, in which the positron is from pair production (Knoll, 2000). In Figure 1, we consider a simplified physical model for calculating the flux of 0.512-MeV gamma rays emitted from the lunar surface as a semi-infinite homogeneous medium. In the model it is assumed that the yield of gamma rays induced by the cosmic rays is a constant over the depth of interest.
The flux of annihilation photons produced in a thin layer of thickness dx is given by

I Ei
where A j is the atomic mass of the jth element in layer dx, C j is the mass fraction of the jth element in layer dx in percent, ρ is the density of lunar soil or rock in grams per cubic centimeter, is the flux of excitation gamma rays in the layer with energy E i , in cm -2 s -1 , N A is the Avogadro's constant, 6.02×10 23 , the coefficient of 2 indicates that two annihilation photons are generated per pair-production interaction, and K ij is the probability of pair-production interaction between a photon of energy E i and an atom of element Z j , which can be given by (Knoll, 2000) where k is a constant, and E i , in MeV, is the ith energy above 1.02 MeV.
Equation (1) can be rewritten as Because the lunar rock and soil mainly consists of petrogenetic elements, the ratio of Z j to A j approximates to 0.5. Therefore, Equation (3) transforms to The flux of 0.512-MeV gamma rays emitted from layer dx will attenuate through upper layers to the lunar surface (see Figure 1). The flux of 0.512-MeV gamma rays from layer dx to the lunar surface can be given by where is the linear attenuation coefficient of 0.512-MeV gamma rays for the lunar medium in cm -1 .
The flux of 0.512-MeV gamma rays leaking out the lunar surface, I 0.512 , is an integral over the semi-infinite layer.
where is the average atomic number of the rock and soil on the lunar surface.

Ei
The flux of gamma rays with energy E i induced by cosmic rays striking the lunar surface, , is given as following where is the yield of gamma rays in the thin layer and is assumed as a constant, is the linear attenuation coefficient of the lunar rock and soil for gamma rays with energy E i , in in cm -1 . can be calculated by XCOM software, which is developed by the National Institute of Standards and Technology.

Ei
From Equation (6), the average atomic number of the lunar rock and soil can be expressed as a function of and I 0.512 , where is a coefficient that could be obtained by Monte Carlo simulation, as described in Section 3. The net peak area, , is as ε i E i where is the peak efficiency of the gamma-ray spectrometer at energy .
From Equations (8) and (9), we get where and are the net peak areas with 0.512-MeV and . In this equation the net peak areas are obtained from Chang'e-1 GRS data, and the peak efficiency of and can be obtained by Monte Carlo simulations.

Simulation of the PAR Flux Emitted from the Lunar Surface
The Geant4 Monte Carlo code has been used to simulate the gamma ray spectra from the lunar surface (Gurtner et al., 2006;Ohishi et al., 2004;Yamashita et al., 2008). The model consists of a cylinder which is filled with the lunar rock and soil with a density of 2.0 g/cm 3 and a 40cm-diameter sphere current detector, as shown in Figure 2. The detector is placed on the axis of the cylinder, 0.5 m above the cylinder's upper surface. Six types of lunar rock, including KREEP, anorthosite, dunite, high alumina basalt, low titanium basalt, and high titanium basalt, are used to study the relationship between the average atomic number and the flux of 0.512-MeV gamma rays. The compositions and average atomic numbers of the six lunar rocks are given in Table 1 (Heiken et al., 1991).
The primary source beam injected into the lunar rock and soil is 100-MeV protons. The energy range of gamma ray spectra is from 0.01 to 10 MeV and the energy interval is 4.89 keV. The number of history events is set as 2.0×10 9 and the statistical error of results is <5% in any energy bin. MeV), produced from neutron inelastic scattering, can be acquired. In addition, a fraction of the gamma rays in the spectrum are produced by neutron capture (e.g., 4.93 MeV ( 28 Si), 6.76 MeV ( 48 Ti), and 7.64 MeV ( 56 Fe)) (Reedy, 1978(Reedy, , 2000(Reedy, , 2013. The simulation results for the PAR flux and higher flux gamma lines for the six lunar rocks are given by Table 2.
The flux of PAR and induced gamma rays in the six lunar rocks, calculated by Geant4 Monte Carlo code, are listed in Table 2. The is calculated in table, which the average value used is list in Table 3.

Simulation of the Linear Attenuation Coefficients and Constant a µ
Ei µ

Ei
The of KREEP, anorthosite, dunite, high alumina basalt, low titanium basalt, and high titanium basalt are listed in Table 3. The relative errors of between the average value and each lithology are <±2%.
The relationship between the ratio of I 0.512 to and Z A is shown in Figure 4. The a in Equation (10) for calculating the average atomic number of the lunar rock and soil is obtained by linear fitting. The a values for the six lunar rocks are listed in Table 2 and the average a for lunar rocks and soils is 1.10.   Notes: * The values in parentheses present the relative errors for in unit of millesimals, provided by the Geant4 Monte Carlo code, and the others are the transfer relative errors. In particular, the relative errors for the average atomic number "Z A " cannot be acquired. Consequently, the transfer relative errors for "a" are instead that of .

Simulation of Peak Efficiency of the GRS ε i
To calculate the average atomic number of the lunar rock and soil from Chang'e-1 GRS data, the peak efficiency of the Chang'e-1 GRS is determined at 0.512 MeV and other high energies by Geant4 Monte Carlo code simulation. The gamma-ray source used in simulation uniformly distributes on a surface. The relative peak efficiency to that at 0.512 MeV, are given in Table 4.

Average Atomic Number of Rock and Soil on Lunar
Surface 4.1 Gamma-ray Spectra from Chang'e-1 2467169 spectra recorded by Chang'e-1 GRS (Ma T et al., 2008) are used to map the average atomic number of rock and soil on lunar surface. A map with grid of 150 km×150 km is applied to cover the Moon.
The spectrum, as shown in Figure 5, is the sum of all the available spectra in different flight cycles of Chang'e-1 GRS in the same grid. The background, estimated by a fast-Fourier-transform numerical µ Ei Notes: *Values in parentheses present the relative transfer errors for . Figure 4. Relationship between average atomic number and method (Zhang QX et al., 2012), and net spectrum are also shown in Figure 5. As seen in the figure, the 0.512 MeV peak from the PAR is obvious. Other peaks corresponding to isotopes in the lunar rock and soil also can be easily identified: e.g., at 0.  Table 5. , a and are obtained in section 3.
The peak at ~6.0 MeV, from the inelastic scattering of fast neutrons on oxygen, is not used to evaluate the average atomic number of lunar rock and soil, because the fuel tank is near the GRS and the residual oxygen cannot be quantified during the Chang'e-1 mission.
To acquire the net counts directly from PAR at 0.512 MeV, the overlapping portion from the 0.511-MeV gamma rays of 208 Tl should be removed since the relative emission fraction of the 0.511-MeV gamma ray from 208 Tl is 25% of its 2.62-MeV gamma ray. The relative efficiency to 208 Tl is 39.44% (to PAR). So when calculating the net peak area of the 0.511-MeV, the contribution from 208 Tl, amounting to 63.38% of the area of the 2.62-MeV gamma ray, should be removed.

Map of Average Atomic Number of the Lunar Surface µ Ei
To verify the results of Figure 6, average atomic numbers of the lunar rock and soil at points where Apollo and Luna rovers landed and took samples are recorded. The scatter diagram of the atomic mass of samples from the A11, A12, A15, A16, A17, L16, L20, and L24 mission (Gasnault et al., 2001) and the average atomic numbers are plotted in Figure 7. The error bars on average atomic number are the transferred relative errors of "a", " " and the GRS measurement statistical errors. As seen in Figure 7, the correlation coefficient is 0.7176 between average atomic number and average atomic mass.
As seen in Figure 6, the higher Z A value region corresponds to lunar maria, such as Mare Frigoris (56.0°N, 1.4°E), Mare Vaporum (13.3°N, 3.6°E), Mare Australe (38.9°S, 93.0°E), and Mare Imbrium (32.8°N, 15.6°W) (Jolliff et al., 2000). This result is in agreement with the results of average atomic mass mapping by the Lunar Prospector Neutron System (LP-NS) Gasnault et al., 2001), especially on the edge of Mare Vaporum and Mare Insularum (7.5°N, 30°W), close to Sinus Aestuum (10.9°N, 8.8°W), with a Z A value up to 13.2. Its regional strike tends southwest throughout the Mare Imbrium and Mare Vaporum, corresponding to the Apollo gamma-ray system data: A majority of maria are covered by different types of basalt, all of which have a higher average atomic number than other lunabase (Hasebe et al., 2009;Haskin, 1998;Zhu MH et al., 2010). In addition, some craters, such as Schwarzshild (70.1°N, 121.2°E), have a higher Z A value. As a consequence of meteorite collision impact, dark basalt, including some heavier elements, is deposited in the bottoms of craters. Therefore, these regions display a notable characteristic in the map of average atomic number.
A couple of medium Z A value (~12.5) regions can be identified on the Z A map. Two of them, surrounded by irregular oval rings, are West Oceanus Procellarum and Mare Frigoris. Others are around some large craters, such as Sinus Iridum (44.1°N, 31.5°W). These regions seem to be consistent with the distribution of KREEP as a unique feature on the lunar surface. Although the reason for the unique shape of average atomic number areas is still an open issue, petrogenesis, impact melting (Delano and Ringwood, 1978), or magma upwelling (Dymek, 1986;McKay, 1986;Taylor, 1982) are considered possibilities. Diagenesis certainly played a significant role in compositional differentiation. Therefore, the regionalized medium Z A value concentration is affected by the course of magmatism beneath the KREEP terrane (Taylor, 2014;Taylor et al., 2006).
Other than the above high and medium Z A regions, the majority of the lunar surface has lower average atomic numbers. This is because the region is widely covered with lunabase, which basically  Figure 5. Gamma-ray spectrum recorded by Chang'e-1 GRS in the region of Mare Imbrium.

Earth and Planetary Physics
doi: 10.26464/epp2018023 243 consists of mafic anorthosite (Korotev et al., 2003) and bytownite anorthosite (Norman and Ryder, 1980;Warren, 1993Warren, , 2005, both of which are rich in light elements, such as Mg, Ca, Na, and Ti. From the above discussion, a couple of significant points can be summarized. First, there is a strong correlation between the average atomic number and the concentration of iron in maria regions, which is confirmed by gamma-ray spectra Lawrence et al., 2002), neutron spectra (Elphic et al., , 2000, and multispectral analysis (Ling ZC et al., 2011;Yan BX et al., 2012). Second, there some high Z A value spots surrounding the maria and scattered throughout the Moon. In the terrane, these spots typically appear in crater areas. Lunar craters are a result of meteorite impact. Their structure allows the mantle below the impact basin to upwell into the crater bottom and deposit basalt (with a high Z A value) that easily permeates into the lithosphere (Phillips and Lambeck, 1980;Wise and Yates, 1970). This phenomenon is referred to as a mascon in geodetic gravimetry (Byrne et al., 2015;Freed et al., 2014;Melosh et al., 2013;Miljković et al., 2015;Montesi, 2013;Thorey et al., 2015). Third, the average atomic number in sinus areas is found on the gradient features (from 12 to 13). As an extended part from the highlands to maria, sinus have both characteristics. Therefore, in Figure 6 some sinus are filled with gradient color, such as Sinus Aestuum and Sinus Iridum.

Conclusions
A linear approximation for the relationship between position annihilation radiation gamma flux from the lunar surface and the average atomic number of lunar rocks or soil has been established. A simplified Monte Carlo model has been developed to confirm this method for evaluating average atomic number of the rock and soil on the lunar surface. The method has been used to construct a map of average atomic number on a 150 km×150 km grid from the Chang'e-1 GRS. The global map of average atomic number can differentiate the various types of lithology. The higher average atomic number (Z A >12.5) located in the maria regions is closely related to different types of basalt, with the highest Z A value of 13.2 found near Sinus Aestuum (10.9°N, 8.8°W). The West Oceanus Procellarum and Mare Frigoris regions surrounded by irregular oval rings are found to have medium Z A values (~12.1), which seems to be consistent with the distribution of KREEP as a unique feature on the lunar surface. The lower average atomic number (Z A <11.5) regions cover the majority of the lunar surface that is relatively dominated by anorthosite.