Gravitational eigenstates in weak gravity I: dipole decay rates of
  charged particles
  The experimental demonstration that neutrons can reside in gravitational
quantum stationary states formed in the gravitational field of the Earth
indicates a need to examine in more detail the general theoretical properties
of gravitational eigenstates. Despite the almost universal study of quantum
theory applied to atomic and molecular states very little work has been done to
investigate the properties of the hypothetical stationary states that should
exist in similar types of gravitational central potential wells, particularly
those with large quantum numbers. In this first of a series of papers, we
attempt to address this shortfall by developing analytic, non-integral
expressions for the electromagnetic dipole state-to-state transition rates of
charged particles for any given initial and final gravitational quantum states.
The expressions are non-relativistic and hence valid provided the eigenstate
wavefunctions do not extend significantly into regions of strong gravity. The
formulae may be used to obtain tractable approximations to the transition rates
that can be used to give general trends associated with certain types of
transitions. Surprisingly, we find that some of the high angular momentum
eigenstates have extremely long lifetimes and a resulting stability that belies
the multitude of channels available for state decay.
