# S-wave reonances of $V(r)=-c^2(r+1/r)^2, c \in \Re$

I need to know the s-wave resonances of the central potential $$V(r)=-c^2(r+1/r)^2, c\in \Re$$. Here we have a well attached to a barrier so we expect quantized quasibound/ metastable/ resonant states (Gamov's states). The reduced radial Schoedinger equation $$u''(r)+(k^2+ c^2(r+1/r)^2] u(r)=0,~ r \in (0,\infty)$$ ($$2m=1=\hbar^2$$) for this potential is solvable in terms of confluent hypergeometric and Laguarre functions. However, finding a solution which vanishes at $$r=0$$ and behaves as (Gamov's) out-going wave asymptotically could be challenging. I wonder, if the analytic complex eigenvalues of the type $$E_n-i\Gamma_n/2$$ are already known for this potential. Any information or Ref. is welcome.