Phase-amplitude method applied to doubly excited states of He (1Se).

Abstract

We present a phase-amplitude (PA) procedure, which emphasizes the evolution of the ${\mathrm{He}}^{\mathrm{*}\mathrm{*}}$ wave function from the origin of the hyper-radius R= \ensuremath{\surd}${\mathit{r}}_{1}^{2}$+${\mathit{r}}_{2}^{2}$ . This method, combined with quantum-defect theory, produces an R-dependent phase shift \ensuremath{\pi}\ensuremath{\tau}(R) of the ionized channel, whose variation with R illustrates explicitly its coupling with the closed resonant channels. Previous calculations (e.g., of the R-matrix type) whose dynamical information remains hidden within a core region are thus complemented and extended by displaying the R dependence of phase shifts for several low doubly excited resonances of He${(}^{1}$${\mathit{S}}^{\mathit{e}}$). The large R limit yields the familiar scattering phase shift, in fair agreement with experimental data. The results illustrate the dominant role of short-range channel coupling in the formation of resonances.