Spectral properties of non-selfadjoint extensions of the Calogero Hamiltonian

We describe all extensions of the Calogero Hamiltonian $$L=-\frac{d^2}{d{r}^2}+\frac{b}{r^2}\text{in }{L}^2({\mathbb{R}}_{+}),b<-\frac{1}{4}$$ having non empty resolvent and generating an analytic semigroup in $L^2({\mathbb{R}}_{+})$.