1. Study of high energy cosmic rays by different components of back scattered radiation generated in the lunar regolith N. N. Kalmykov 1, A. A. Konstantinov 1, R. A. Mukhamedshin 2, D. M. Podorozhnyi 1, L. G. Sveshnikova 1, A. N. Turundaevskiy 1, L. G. Tkachev 3, A. P. Chubenko 4 1 Scobel’tsyn Research Institute of Nuclear Physics, Moscow State University, Moscow, Russia 2 Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia 3 Joint Institute for Nuclear Research, Dubna, Russia 4 Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia

2. Possible experiments aimed at studying the primary cosmic rays on the Moon’s surface considered. Monte-Carlo simulation was used. Three components (secondary neutrons, gamma rays, and radio waves) of back scattered radiation can be simultaneously registered. These components of radiation are generated by showers developing in the lunar regolith. Primary particle parameters can be reconstructed.

3. The chemical composition of PCRs must be studied to discover the origin of peculiarities in the PCR energy spectrum, investigate the ratio of secondary_to_primary nuclei in the high energy range, and search for exotic particles. The Moon surface We analyze using three components to measure the parameters of PCR particles incident on the lunar surface: secondary neutrons, gamma quanta (particles of back current), and radio waves. The signals for each component are evaluated using a Monte Carlo (MC) simulation of showers.

4. Neutron albedo Neutron background is for 600 μs. 100 (solid) and 8 (dashed) m 2 registration area. It was found during simulations that for PCR particles incident at angles of ~ 50° to the vertical, the total number of neutrons reaching the surface is ~10 4 at 100 TeV, or approximately 10% of the total number of neutrons generated in the regolith.

5. Neutron energy spectra (protons, helium, iron) We considered energy spectra (in figure), fluctuations and spatial characteristics of a neutron spot on the Moon’s surface. It was found that at PCR energies E 0 ~ 10 14 eV, the fluctuations in the neutron flux of primary nuclei are ~20% for the case of iron and ~30% for carbon, while for protons they are ~70%. The last effect is due to the higher penetrability of protons.

6. Albedo of gamma-rays Many secondary particles are generated by showers in matter. The part of these particles is emitted at big angles relative to the primary particle direction. The gamma quanta contribution into back current is sufficient due to decay of low energy secondary neutral pions. We considered primary protons with energies of 10 12 to 10 15 eV to estimate the albedo gamma ray yield. By means of MC simulation (using the GEANTcode) we studied some characteristics of back scattered particles (with energies >15 keV) included the total number of albedo gamma quanta n g and their spatial distribution. The main part of albedo gamma quanta is concentrated is some meters area near the track of the primary particle.

7. Gamma albedo spatial distribution (all trajectories). The background is shown for 100 (solid) and 10 (dashed) μs registration

8. Albedo gamma quanta energy spectra

9. Gamma albedo energy dependence. The background is shown for 100 (solid) and 10 (dashed) μs registration

11. The total back current depends on the angle of the cascade axis’s inclination θ, which can be determined using the asymmetry of the back scattered particles spatial distribution. This distribution is more asymmetrical for large inclination angles. We used as asymmetry parameter the ratio of spatial distribution dispersions R ct =σ 2 (X l )/σ 2 (X t ). Here X l, X t are longitudinal and transverse axes of dispersion ellipse. The cosθ asymmetry dependence is close to logarithmical cosθ=0.505 log(7.25/R ct ). The RMS errors of cosθ are equal 0.16 at 10 13 eV and 0.12 at 10 15 eV.

12. We used total number of back scattered gamma quanta and asymmetry data to reconstruct primary particles energies. As energy E increases, the error of its determination decreases from ~200% (at E~10 12 eV) to ~100% (at E~10 14 –10 15 eV).

13. Albedo of radio emission MC simulations were conducted for different showers (using the GEANT code). The field of radio emission was calculated from every particle of the shower. The radio wave absorption and refraction in the regolith were taken into account. Refraction factor n was set at 1.7 for density ρ=1.7 g/cm 3, and was scaled for other values according to the Clausius–Mossotti formula.

14. Frequency spectrum of the field intensity of radio waves (total field) (proton, 10 13 eV) at different angles of observation θ (θ=60° corresponds to the Cherenkov angle). As can be seen, frequencies ≈1– 10 GHz are the best for observations. These frequencies can be used for energy measurements.

15. Spatial distribution of radio emission We took into account the absorption and refraction of radio waves and their reflection from regolith layers of different densities. Only in inclined showers the emission from a Cherenkov peak can emerge from the regolith into the vacuum of space. For vertical showers total reflection diminishes radio emission. At the top layer of regolith the total reflection angle is equal to θ R =35°. The Cherenkov angle is equal to θ C =55°. Thus a Cherenkov peak registration can be used only for showers with zenith angle θ> θ C - θ R =20°.

16. The reconstructed energy distribution (proton, 10 13 eV) For a Cherenkov peak the energy dependence of the intensity of the radio emission field is close to linear: E ν max  9·10 –5 (E 0 /1 TeV) 1.03 μV/m·MHz (at 45°). This dependence can be used to reconstruct primary energy. The RMS errors are equal to 30% (at 10 12 eV), 20% (at 10 13 eV), 15% (at 10 14 eV). If we assume that the noise level is 1 μV m –1 MHz –1 at 1 GHz, then the lower threshold of radio emission field recording is ~10 16 -10 17 eV; it is more efficient to arrange the receiving antennas above the ionization neutron calorimeter.

17. Conclusion Our simulations demonstrate the feasibility to registrate PCR particles in three components (neutrons, gamma rays, and radio waves) of the back current from showers developing in the lunar regolith. The lower thresholds for recording the PCR particles is ~10 14 eV (for gamma albedo), ~10 16 eV (for radio emission), and the error of primary energy determination is sufficiently low to reconstruct primary energy spectra.