Fermi's golden rule (FGR) serves as the basis for many expressions of
spectroscopic observables and quantum transition rates. The utility of FGR has
been demonstrated through decades of experimental confirmation. However, there
still remain important cases where the evaluation of a FGR rate is ambiguous or
ill-defined. Examples are cases where the rate has divergent terms due to the
sparsity in the density of final states or time dependent fluctuations of
system Hamiltonians. Strictly speaking, assumptions of FGR are no longer valid
for such cases. However, it is still possible to define modified FGR rate
expressions that are useful as effective rates. The resulting modified FGR rate
expressions resolve a long standing ambiguity often encountered in using FGR
and offer more reliable ways to model general rate processes. Simple model
calculations illustrate the utility and implications of new rate expressions.Comment: 11 pages, 4 figure