  Flavor-changing charged current ("Urca") processes are of central importance
in the astrophysics of neutron stars. Standard calculations approximate the
Urca rate as the sum of two contributions, direct Urca and modified Urca.
Attempts to make modified Urca calculations more accurate have been impeded by
an unphysical divergence at the direct Urca threshold density. In this paper we
describe a systematically improvable approach where, in the simplest
approximation, instead of modified Urca we include an imaginary part of the
nucleon mass (nucleon width). The total Urca rate is then obtained via a
straightforward generalization of the direct Urca calculation, yielding results
that agree with both direct and modified Urca at the densities where those
approximations are valid. At low densities, we observe an enhancement of the
rate by more than an order of magnitude, with important ramifications for
neutron star cooling and other transport properties.
