Pycnonuclear burning of 34Ne in accreting neutron stars

We study the pycnonuclear burning of 34Ne in the inner crust of an accreting neutron star. We show that the associated energy production rate can be calculated analytically for any arbitrary temporal variability of the mass accretion rate. We argue that the theoretical time-scale for 34Ne burning is currently very uncertain and ranges from a fraction of a millisecond to a few years. The fastest allowable burning may change the composition of the accreted crust while the slowest burning leads to a time-independent nuclear energy generation rate for a variable accretion. The results are important for constructing self-consistent models of the accreted crust and deep crustal heating in neutron stars which enter soft X-ray transients.