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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.

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