Doubly excited¹S^estates of H^-and He below the N hydrogenic thresholds with N⩽6

Abstract

The doubly excited 1Se states of H- and He are studied by using the hyperspherical coordinate representation and the adiabatic approximation. The adiabatic potentials below the N<or=6 hydrogenic thresholds are calculated by means of the trial functions which are constructed from the hyperspherical harmonics and the analytical channel functions proposed by Lin (1981, 1982). The lowest few adiabatic potentials belonging to the Nth threshold have close avoided crossings with higher ones belonging to the (N-1)th threshold. It is shown that the potentials can be connected diabatically at these crossing points. According to this prescription, the energy levels of the doubly excited states below the N<or=6 thresholds are calculated.