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Accurate understanding of the subsurface production rate of the radionuclide$^{39}$Ar is necessary for argon dating techniques and noble gas geochemistryof the shallow and the deep Earth, and is also of interest to the WIMP darkmatter experimental particle physics community. Our new calculations ofsubsurface production of neutrons, $^{21}$Ne, and $^{39}$Ar take advantage ofthe state-of-the-art reliable tools of nuclear physics to obtain reaction crosssections and spectra (TALYS) and to evaluate neutron propagation in rock(MCNP6). We discuss our method and results in relation to previous studies andshow the relative importance of various neutron, $^{21}$Ne, and $^{39}$Arnucleogenic production channels. Uncertainty in nuclear reaction crosssections, which is the major contributor to overall calculation uncertainty, isestimated from variability in existing experimental and library data. Dependingon selected rock composition, on the order of $10^7$-$10^{10}$ {\alpha}particles are produced in one kilogram of rock per year (order of 1-$10^3$kg$^{-1}$ s$^{-1}$); the number of produced neutrons is lower by $\sim6$ ordersof magnitude, $^{21}$Ne production rate drops by an additional factor of 15-20,and another one order of magnitude or more is dropped in production of$^{39}$Ar. Our calculation yields a nucleogenic $^{21}$Ne/$^4$He productionratio of $(4.6\pm0.6) \times 10^{-8}$ in Continental Crust and $(4.2\pm0.5)\times 10^{-8}$ in Oceanic Crust and Depleted Mantle. Calculated $^{39}$Arproduction rates span a great range from $29\pm9$ atoms kg-rock$^{-1}$yr$^{-1}$ in the K-Th-U-enriched Upper Continental Crust to $(2.6\pm0.8) \times10^{-4}$ atoms kg-rock$^{-1}$ yr$^{-1}$ in Depleted Upper Mantle. Nucleogenic$^{39}$Ar production exceeds the cosmogenic production below $\sim700$ metersdepth and thus, affects radiometric ages of groundwater.

Subterranean production of neutrons, $^{39}$Ar and $^{21}$Ne: Rates and uncertainties