Partial widths and interchannel coupling in autoionizing states in terms of complex eigenvalues and complex coordinates

The use of complex coordinates allows the possibility of treating resonances of many-electron systems based on a complex eigenvalue Schrödinger equation. A many-body analysis of this equation has led to the establishment of convenient and systematic procedures for including electron correlation and for computing partial and total widths, without and with interchannel coupling, in multichannel autoionization. This is done by computing the asymptotic-pair (AP) correlation functions from an independent asymptotic-pair approximation (IAPA) and then mixing them (MAP, i.e., the mixing of asymptotic pairs) from a diagonalization of the total non-Hermitian Hamiltonian matrix. Nonorthonormality complications are resolved by straightforward computation. We report results for ${\mathrm{Ne}}^{+}$ 1s2$s^2$2$p^6$ ${}^2$S, which decays into five one-electron channels: 1s-2$p^2$ ${}^1$D, 1s-2$p^2$ ${}^1$S, 1s-2s2p ${}^3$ $P^o$, 1s-2s2p ${}^1$ $P^o$, and 1s-2$s^2$ ${}^1$S. The corresponding partial-width values from MAP are (in ${10}^{\mathrm{-}2}$ a.u.): 0.565, 0.040, 0.032, 0.165, and 0.043. The proximity of these results to the available experimental information as well as that to previous results from many-body calculations with real coordinates offers a practical verification of this theory.