Scattering by the Singular Potential−gr−4lnr

In connection with higher order leptonic weak interactions, divergent series containing an infinite number of logarithmic factors are encountered. In order to have some understanding of series of this type, the problem of scattering by the singular potential $-g{r}^{-4\mathrm{}}\ln r$ is examined for the special case of zero energy. This problem has the advantage that the correct answer can be obtained by other means. Generalization to the potential $-g{r}^{-\lambda }\ln r$ with $\lambda >3\mathrm{}$ is also considered.