Resonances for Coulombic potentials by complex scaling and free-reflection complex-absorbing potentials

Abstract

Analytical expressions for the resonances of the long-range potential (LRP), V(r)=a/r-b/r{sup 2}, as a function of the Hamiltonian parameters were derived by Doolen a long time ago [Int. J. Quant. Chem. 14, 523 (1979)]. Here we show that converged numerical results are obtained by applying the shifted complex scaling and the smooth-exterior scaling (SES) methods rather than the usual complex coordinate method (i.e., complex scaling). The narrow and broad shape-type resonances are shown to be localized inside or over the potential barrier and not inside the potential well. Therefore, the resonances for Doolen LRP's are not associated with the tunneling through the potential barrier as one might expect. The fact that the SES provides a universal reflection-free absorbing potential is, in particular, important in view of future applications. In particular, it is most convenient to calculate the molecular autoionizing resonances by adding one-electron complex absorbing potentials into the codes of the available quantum molecular electronic packages.