Gravitational potential of a truncated singular isothermal sphere ($\Phi (r)=-2k[1+\ln (r_0/r)]$)

With potential zero at infinity, a truncated profile $\rho =k/(2\pi G{r}^2)$ has $\Phi (r)=-2k[1+\ln (r_0/r)]$ inside the truncation. Exterior spherical shells have zero force inside but contribute a nonzero constant potential there; omitting them changes escape work.