The temperature in the crust of an accreting neutron star, which comprises its outermost kilometre, is set by heating from nuclear reactions at large densities, neutrino cooling and heat transport from the interior. The heated crust has been thought to affect observable phenomena at shallower depths, such as thermonuclear bursts in the accreted envelope. Here we report that cycles of electron capture and its inverse, β(-) decay, involving neutron-rich nuclei at a typical depth of about 150 metres, cool the outer neutron star crust by emitting neutrinos while also thermally decoupling the surface layers from the deeper crust. This 'Urca' mechanism has been studied in the context of white dwarfs and type Ia supernovae, but hitherto was not considered in neutron stars, because previous models computed the crust reactions using a zero-temperature approximation and assumed that only a single nuclear species was present at any given depth. The thermal decoupling means that X-ray bursts and other surface phenomena are largely independent of the strength of deep crustal heating. The unexpectedly short recurrence times, of the order of years, observed for very energetic thermonuclear superbursts are therefore not an indicator of a hot crust, but may point instead to an unknown local heating mechanism near the neutron star surface.

X-ray observations of transiently accreting neutron stars during quiescence provide information about the structure of neutron star crusts and the properties of dense matter. Interpretation of the observational data requires an understanding of the nuclear reactions that heat and cool the crust during accretion, and define its nonequilibrium composition. We identify here in detail the typical nuclear reaction sequences down to a depth in the inner crust where the mass density is ρ = 2 × 10 12 g cm −3 using a full nuclear reaction network for a range of initial compositions. The reaction sequences differ substantially from previous work. We find a robust reduction of crust impurity at the transition to the inner crust regardless of initial composition, though shell effects can delay the formation of a pure crust somewhat to densities beyond ρ = 2 × 10 12 g cm −3 . This naturally explains the small inner crust impurity inferred from observations of a broad range of systems. The exception are initial compositions with A ≥ 102 nuclei, where the inner crust remains impure with an impurity parameter of Q imp ≈ 20 due to the N = 82 shell closure. In agreement with previous work we find that nuclear heating is relatively robust and independent of initial composition, while cooling via nuclear Urca cycles in the outer crust depends strongly on initial composition. This work forms a basis for future studies of the sensitivity of crust models to nuclear physics and provides profiles of composition for realistic crust models.