  We show that the direct Urca process of neutrino emission is allowed in two
possible phases of nonspherical nuclei (inverse cylinders and inverse spheres)
in the mantle of a neutron star near the crust-core interface. The process is
open because neutrons and protons move in a periodic potential created by
inhomogeneous nuclear structures. In this way the nucleons acquire large
quasimomenta needed to satisfy momentum-conservation in the neutrino reaction.
The appropriate neutrino emissivity in a nonsuperfluid matter is about 2--3
orders of magnitude higher than the emissivity of the modified Urca process in
the stellar core. The process may noticeably accelerate the cooling of low-mass
neutron stars.
