Scaling and asymptotic properties of evaporated neutron inclusive cross sections in high energy hadron-nucleus and nucleus-nucleus interactions

New properties of the evaporated neutron ($E< 30$ MeV) energy spectra in hadron-nucleus interactions are found which have not been marked before. Particularly, the spectra approach the asymptotic regime, namely, they weakly depend on the collision energy at momenta of projectile protons larger than $5$–$6$ GeV/c; the spectra for various nuclei are similar, and can be approximately described by the function $A^n f(E)$. Experimental data on neutron spectra in the case of projectile $\pi$-mesons show analogous behaviour, but the statistics of the data do not allow one to draw clear conclusions. In our analysis we used ITEP experimental data on inclusive cross sections of neutrons produced in interactions of $\pi$-mesons and protons with various nuclei in the energy range from $747$ MeV up to $8.1$ GeV. The observed properties allow one to predict neutron yields in the nucleus-nucleus interactions at high and super high energies. Predictions for the NICA/MPD experiment at JINR are presented. It is shown that the FTF (Fritiof)-model of the Geant4 toolkit qualitatively reproduces the observed regularities. For the first time estimates of the neutron energy flows are obtained at both RHIC and LHC energies.