  We examine the isotope effect of superconductivity in systems with coexisting
interactions of phonon and nonphonon mechanisms in addition to the direct
Coulomb interaction. The interaction mediated by the spin fluctuations is
discussed as an example of the nonphonon interaction. Extended formulas for the
transition temperature Tc and the isotope-effect coefficient alpha are derived
for cases (a) omega_np < omega_D and (b) omega_np > omega_D, where omega_np is
an effective cutoff frequency of the nonphonon interaction that corresponds to
the Debye frequency omega_D in the phonon interaction. In case (a), it is found
that the nonphonon interaction does not change the condition for the inverse
isotope effect, i.e., mu^* > lambda_ph/2, but it modifies the magnitude of
alpha markedly. In particular, it is found that a giant isotope shift occurs
when the phonon and nonphonon interactions cancel each other largely. For
instance, strong critical spin fluctuations may give rise to the giant isotope
effect. In case (b), it is found that the inverse isotope effect occurs only
when the nonphonon interaction and the repulsive Coulomb interaction, in total
effect, work as repulsive interactions against the superconductivity. We
discuss the relevance of the present result to some organic superconductors,
such as kappa-(ET)2Cu(NCS)2 and Sr2RuO4 superconductors, in which inverse
isotope effects have been observed, and briefly to high-Tc cuprates, in which
giant isotope effects have been observed.
