  We consider the astrophysical reaction rates for radiative neutron capture
reactions ($n,\gamma$) in the crust of a neutron star. The presence of
degenerate neutrons at high densities (mainly in the inner crust) can
drastically affect the reaction rates. Standard rates assuming a
Maxwell-Boltzmann distribution for neutrons can underestimate the rates by
several orders of magnitude. We derive simple analytical expressions for
reaction rates at a variety of conditions with account for neutron degeneracy.
We also discuss the plasma effects on the outgoing radiative transition channel
in neutron radiative capture reactions and show that these effects can also
increase the reaction rates by a few orders of magnitude. In addition, using
detailed balance, we analyze the effects of neutron degeneracy and plasma
physics on reverse ($\gamma,n$) photodisintegration. We discuss the dependence
of the reaction rates on temperature and neutron chemical potential and outline
the efficiency of these reactions in the neutron star crust.
