Quantum Statistical Corrections to Astrophysical Photodisintegration
  Rates
  Tabulated rates for astrophysical photodisintegration reactions make use of
Boltzmann statistics for the photons involved as well as the interacting
nuclei. Here we derive analytic corrections for the Planck-spectrum quantum
statistics of the photon energy distribution. These corrections can be deduced
directly from the detailed-balance condition without the assumption of
equilibrium as long as the photons are represented by a Planck spectrum.
Moreover we show that these corrections affect not only the photodisintegration
rates but also modify the conditions of nuclear statistical equilibrium as
represented in the Saha equation. We deduce new analytic corrections to the
classical Maxwell-Boltzmann statistics which can easily be added to the reverse
reaction rates of existing reaction network tabulations. We show that the
effects of quantum statistics, though generally quite small, always tend to
speed up photodisintegration rates and are largest for nuclei and environments
for which Q/kT ~ 1. As an illustration, we examine possible effects of these
corrections on the r-process, the rp-process, explosive silicon burning, the
$\gamma$-process and big bang nucleosynthesis. We find that in most cases one
is quite justified in neglecting these corrections. The correction is largest
for reactions near the drip line for an r-process with very high neutron
density, or an rp-process at high-temperature.
