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Using a Wigner-Seitz approximation with spherical cells, we re-analyze awidely used single nucleus model of accreting neutron star crust. We calculatebeta disequilibrium within the crust, which is sizable, and implies thatneutron and baryon chemical potentials, $\mu_n$ and $\mu_{\rm b}$, are notequal. We include also non-equilibrium reactions, driven by matter compression,and proceeding in the reaction layers. The constancy of $e^{\Phi}\mu_n$, wherethe spacetime metric component $g_{00}=e^{2\Phi}$, in the shells between thereaction layers is not applicable, because single electron captures areblocked, so that the neutron fraction is fixed, and therefore neutrons are notan independent component of the crust matter. The absence of neutron diffusionin the shells between the reaction layers, stems from the constancy of theneutron fraction (concentration) in these shells. In the reaction layers, theoutward force resulting from neutron fraction gradient is balanced by theinward gravitational force acting on unbound neutrons. Neglecting the thicknessof the reaction layers compared to the shell thickness, we obtain condition$e^{\Phi(r)}f_Q(r)g(r)=$constant, where $g$ is Gibbs energy per nucleon,undergoing discontinuous drops on the reaction surfaces, and$f_Q(r)g(r)={\widetilde{g}}(r)$ is a continuous function, due to the factor$f_Q(r)$ canceling the discontinuities (drops) in $g(r)$. The function $f_Q(r)$is calculated using the Tolman-Oppenheimer-Volkov equations from $f_Q(P)$ and$g(P)$ obtained from the equation of state (EOS) with discontinuites. Theconstancy of of $e^{\Phi(r)}{\widetilde{g}}(r)$ is an extension of the standardrelation $e^{\Phi(r)}{{\mu}}_{\rm b}(r)=$constant, valid in hydrostaticequilibrium for catalyzed crust.

Redshift factor and diffusive equilibrium of unbound neutrons in the single nucleus model of accreting neutron star crust