The project of ultracold neutron sources at the PIK reactor with superfluid helium as a moderator

The project of ultracold neutron sources at the PIK reactor with superfluid helium as a moderator is presented. The rate of producing ultracold neutrons in superfluid helium is 100 cm$^{-3}$ s$^{-1}$ at neutron flux density $\Phi$($\lambda$ = 9 $\mathring{\mathrm{A}}$)=10$^9$ cm$^{-2}$ s$^{-1}$ $\mathring{\mathrm{A}}^{-1}$. At a moderator temperature of 1 K within the experimental volume of 351, the density of ultracold neutrons may be equal to 1.3 $\times$ 10$^3$ cm$^{-3}$, which is two orders of magnitude exceeds that the currently existing ultracold neutron sources.