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Observations of soft X-ray transients in quiescence suggest the existence ofheat sources in the crust of accreting neutron stars. Heat is thought to bereleased by electroweak and nuclear processes triggered by the burying of ashesof X-ray bursts. The heating is studied using a fully quantum approach takingconsistently into account nuclear shell effects. We have followed the evolutionof ashes made of $^{56}$Fe employing the nuclear energy-density functionaltheory. Both the outer and inner crusts are described using the samefunctional, thus ensuring a unified and thermodynamically consistent treatment.To assess the role of the neutron-matter constraint, we have employed the setof accurately calibrated Brussels-Montreal functionals BSk19, BSk20, and BSk21and for comparison the SLy4 functional. Due to nuclear shell effects, the fullyaccreted crust is found to be much less stratified than in previous studies. Inparticular, large regions of the inner crust contain clusters with the magicnumber $Z=14$. The heat deposited in the outer crust is tightly constrained byexperimental atomic mass data. The shallow heating we obtain does not exceed$0.2$~MeV and is therefore not enough to explain the cooling of some soft X-raytransients. The total heat released in the crust is very sensitive to detailsof the nuclear structure and is predicted to lie in the range from $1.5$~MeV to$1.7$~MeV. The evolution of an accreted matter element and therefore thelocation of heat sources are governed to a large extent by the existence ofnuclear shell closures. Ignoring these effects in the inner crust, the totalheat falls to $\sim 0.6$~MeV. The neutron-matter constraint is also found toplay a key role. The large amount of heat obtained by Steiner et al. (2012)could thus be traced back to unrealistic neutron-matter equations of state.

Crustal heating in accreting neutron stars from the nuclear energy-density functional theory. I. Proton shell effects and neutron-matter constraint