Direct Urca process in a neutron star mantle

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.