  An alternative representation of the quasistatic nonradiative rates of
Gersten and Nitzan [J. Chem. Phys. 1981, 75, 1139] and Ford and Weber [Phys.
Rep. 1984, 113, 195] is derived for the respective parallel and perpendicular
dipole orientations. Given the distance d of a dipole from a sphere surface of
radius a, the representations comprise four elementary analytic functions and a
modified multipole series taking into account residual multipole contributions.
The analytic functions could be arranged hierarchically according to decreasing
singularity at the short distance limit d ---> 0, ranging from d^{-3} over
d^{-1} to ln (d/a). The alternative representations exhibit drastically
improved convergence properties. On keeping mere residual dipole contribution
of the modified multipole series, the representations agree with the converged
rates on at least 99.9% for all distances, arbitrary particle sizes and
emission wavelengths, and for a broad range of dielectric constants. The
analytic terms of the representations reveal a complex distance dependence and
could be used to interpolate between the familiar d^{-3} short-distance and
d^{-6} long-distance behaviors with an unprecedented accuracy. Therefore, the
representations could be especially useful for the qualitative and quantitative
understanding of the distance behavior of nonradiative rates of fluorophores
and semiconductor quantum dots involving nanometal surface energy transfer in
the presence of metallic nanoparticles or nanoantennas. As a byproduct, a
complete short-distance asymptotic of the quasistatic nonradiative rates is
derived. The above results for the nonradiative rates translate
straightforwardly to the so-called image enhancement factors Delta, which are
of relevance for the surface-enhanced Raman scattering.
