WIDTHS OF THE DOUBLY EXCITED RESONANCES OF 2-ELECTRON ATOMS BELOW THE N=2 THRESHOLD

We present an alternative theoretical procedure for the positions and widths of the doubly excited resonances of a two-electron atom based on a configuration-interaction procedure for continuum by using a B-spline-based finite basis set. More specifically, by examining the energy variation of the probability density corresponding to the singly excited ionization channel, the resonant energy E(r) of the doubly excited autoionization state can be directly linked to the energy at the minimum probability density. The width of the resonance can be identified with the energy separation between two energies, which are located on the opposite side of the center of the resonance and each corresponds to a probability density twice the minimum value at E(r). The effectiveness of this procedure is demonstrated by the excellent agreement between our calculated widths of the Feshbach resonance for H- and He below the n = 2 threshold and the ones from the most accurate existing theoretical calculations.