Phenomenology of muon-induced neutron yield

The cosmogenic neutron yield $Y_n$ characterizes the ability of matter to produce neutrons under the effect of cosmic ray muons with spectrum and average energy corresponding to an observation depth. The yield is the basic characteristic of cosmogenic neutrons. The neutron production rate and neutron flux both are derivatives of the yield. The constancy of the exponents $\alpha$ and $\beta$ in the known dependencies of the yield on energy $Y_n\propto E_{\mu }^{\alpha }$ and the atomic weight $Y_n\propto A^{\beta }$ allows one to combine these dependencies in a single formula and to connect the yield with muon energy loss in matter. As a result, the phenomenological formulas for the yields of muon-induced charged pions and neutrons can be obtained. These expressions both are associated with nuclear loss of the ultrarelativistic muons, which provides the main contribution to the total neutron yield. The total yield can be described by a universal formula, which is the best fit of the experimental data.

Figure 1

Correspondence of the measured neutron yield ${}^{\mathrm{ex}}Y_n$ and the values calculated using the UF.