Doubly excited states 1De and 3De of He below the N = 2 threshold of He+

The positions and widths of the three series of doubly excited-state singlet and triplet resonances 1De and 3De of He at energies below the N = 2 excitation threshold of He+ were determined through an accurate calculation of phase shifts employing a numerical procedure developed earlier by us for electron-hydrogenlike-ion scattering within the Harris-Nesbet variational method. Our results can be used to resolve the discrepancy existing among those obtained by various research groups for the middle-lying resonances of these series. Due to the high accuracy of our method, we were able to determine, for the first time, the positions and widths of several high-lying resonances very close to the threshold, and hence to confirm the definite existence of the c series of doubly excited states of the extremely narrow width for both singlet and triplet D waves as predicted by theory for He. We discuss our results in comparison with those obtained by other groups who employed completely different numerical methods for their calculations, stressing the significant accuracy of our method and its possible relevant future research perspective