Coupled continuum perturbative Feshbach approach to calculate total and partial widths: 1,3Se(3lnl) resonant states of He, C4+, N5+, and O6+

Abstract

We apply a perturbative method, which takes into account the interaction between different open channels, to calculate total and partial widths of atomic resonances in the framework of the Feshbach formalism. The method requires the calculation of elastic, e.g., noncoupled open-channel wave functions, as in the case in which only one channel is open, thus avoiding the solution of complicated systems of coupled differential equations. As an illustration we have calculated energy positions, total and partial widths of $^{1}$,3${\mathrm{S}}^{\mathrm{e}}$(3lnl) resonant states of He, ${\mathrm{C}}^{4+}$, ${\mathrm{N}}^{5+}$, and ${\mathrm{O}}^{6+}$. Our results show that the accuracy reached with this simple approach is comparable to other different non-Feshbach methods and that neglect of the coupling between different open channels can be considered as a reasonable approximation to obtain total and partial widths.