Line-shape parameters forP1Feshbach resonances in He andLi+

Abstract

The line-shape parameter ($q$) for the three lowest ${}_{}{}^1{}_{}{}^{}P$ autoionization states of He and ${\mathrm{Li}}^{+}$ below the first excited target (${\mathrm{He}}^{+}$, ${\mathrm{Li}}^{2+}$) level are accurately calculated. In order to do this we rederive a rigorous expression for $q$ in terms of the Feshbach formalism; the formula contains additional terms representing the effect of other resonances on the resonance being calculated. Hylleraas functions are used to calculate $Q\Phi$, and the exchange approximation is used for the nonresonant continuum. Results agree well with the experiment where available. Our previous calculations of positions and widths are not affected; however, it is noted that the energy of the newest experiment of Morgan and Ederer for the lowest ${}_{}{}^1{}_{}{}^{}P$ autoionization state of He (60.151 ± 0.01 eV) is such that when it is combined with the older experimental value of Madden and Codling (60.133 ± 0.015 eV), the weighted mean of the two measurements (60.145 ± 0.008 eV) is in exceptional agreement with our previous value (60.145 eV).