n}$) denotes the number density of electrons (neutrons). It was shown [@Sha-Teu:1983:BHWDNS:] that $$\lambda_\mathrm{e}\sim 9\times 10^7\left(\frac{\rho_\mathrm{nucl}}{\rho}    \right)^{4/3}\left(\frac{100~\mathrm{keV}}{E_\nu}\right)^{3}~\mathrm{km},$$ while $$\lambda_\mathrm{n}\sim 300\frac{\rho_\mathrm{nucl}}{\rho}    \left(\frac{100\mathrm{keV}}{E_\nu}\right)^{2}~\mathrm{km}.$$ There is $\lambda_\mathrm{e} \gtrsim  10$ km for $E_\nu \lesssim 20$ MeV and $\lambda_\mathrm{n} \gtrsim 10$ km for $E_\nu \lesssim 500$ keV. Therefore, in a few hours old neutron star, see [@Lat-Pra:2007:PhysRep:; @Sha-Teu:1983:BHWDNS:], at temperatures $T \lesssim 10^9$ K ($E_\nu \sim 100$ keV), the neutrino motion could be considered geodetical through whole the internal spacetime.

Bound neutrinos with mean free path${}\gg R$ will slow down the cooling. Of course, they will be re-scattered due to finiteness of the mean free path. An eventual scattering of trapped neutrinos will cause change of their impact parameter, therefore, some of them will escape the ECS, suppressing thus the slow down of the cooling process in the region of neutrino trapping. Clearly, the scattering effect of the trapped neutrinos is a complex process deserving sophisticated numerical code based on the Monte Carlo method (we expect modelling of this effect in future).

The cooling process deserves sophisticated analytical estimates and detailed numerical simulations. As a first step in considering the role of trapped neutrinos in ECS, efficiency of the neutrino trapping effect was studied in 