Energies and electron correlation effects in two-electron doubly excited (nl)2 states

Resonance energies and autoionization widths of the , and doubly excited states of the helium isoelectronic sequence

“…The present results are in very good agreement with those reported by other researchers (for data of Ref. [13] see below). The autoionizing widths of the 1 G e and 1 I e states are relatively large and increasing with Z .…”

“…However, if one uses projection operators as in O'Malley and Geltman's approach [9] bounds can be obtained for the eigenvalues of the projected Hamiltonian. The results of [13] show a variational collapse and particularly for high-Z states. These authors did not use any kind of projection operation to prevent a variational collapse, by projecting-out the continuum.…”

“…There is a point worth noting with regards to the results reported in Ref. [13]. The Hylleraas-Undheim-McDonald theorem [18,19] provides a theoretical basis for the relation between exact and approximate energies.…”

“…The major difficulty of the stabilization methods is that it is necessary to do numerous calculations for any problem of interest. In [13] a very small basis set was used and, as a consequence, the obtained results are actually pseudo resonances or local minima of the energy.…”

Chemical-Vapor-Deposited Diamond Overgrowth on Platinum Thin Films Deposited on Diamond Substrates

“…Since the first experiment by Madden and Colding [1] doubly excited states (DES) of helium-like ions have been the subject of many theoretical and experimental investigations [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The main problem in the theoretical study of DES is connected with the correlated motion of excited electrons in the field of a nuclear charge Z .…”