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

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= √${\mathit{r}}_1^2$+${\mathit{r}}_2^2$ . This method, combined with quantum-defect theory, produces an R-dependent phase shift πτ(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.