Quasiclassical estimates of resonance energies

Quasiclassical estimates of nonrelativistic s-wave resonance energies for penetrable barriers like $C_2$/$r^2$+$C_n$/$r^n$ are presented and discussed. Such barriers are considered for the case $C_2$$C_n$>0, and 0<n<2 as well as for the case $C_2$>0, $C_n$n>2. One starts from the typical analytical forms characterizing the quasiclassical extremal values of the corresponding Schrödinger Hamiltonian. Then one proceeds by use of the analytic continuation of the underlying phase-space quantum towards complex values.