  Cyclotron decay and absorption rates have been well studied in the
literature, focusing primarily on spectral, angular and polarization
dependence. Astrophysical applications usually do not require retention of
information on the electron spin state, and these are normally averaged in
obtaining the requisite rates. In magnetic fields, higher order quantum
processes such as Compton scattering become resonant at the cyclotron frequency
and its harmonics, with the resonances being formally divergent. Such
divergences are usually eliminated by accounting for the finite lifetimes of
excited Landau states. This practice requires the use of spin-dependent
cyclotron rates in order to obtain accurate determinations of process rates
very near cyclotronic resonances, the phase space domain most relevant for
certain applications to pulsar models. This paper develops previous results in
the literature to obtain compact analytic expressions for cyclotron decay
rates/widths in terms of a series of Legendre functions of the second kind;
these expressions can be expediently used in astrophysical models. The rates
are derived using two popular eigenstate formalisms, namely that due to Sokolov
and Ternov, and that due to Johnson and Lippmann. These constitute two sets of
eigenfunctions of the Dirac equation that diagonalize different operators, and
accordingly yield different spin-dependent cyclotron rates. This paper
illustrates the attractive Lorentz transformation characteristics of the
Sokolov and Ternov formulation, which is another reason why it is preferable
when electron spin information must be explicitly retained.
