Helium atom embedded in dense semi-classical plasmas: Ground state and doubly excited singlet S states

Abstract

The properties of the ground state and the doubly excited singlet S states of the helium atom embedded in dense semi-classical plasma have been investigated theoretically. The organized effect of the plasma is described by a pseudopotential which takes care of the collective screening effect and quantum mechanical effect of diffraction through the screening parameter and the de Broglie wavelength. The ground state energy has been determined variationally by employing an extensive square-summable wavefunction, whereas the stabilization method is utilized to identify the doubly excited states (DES). The energies and widths of the DESs are extracted from the Lorentzian fittings of the density of the states. Six doubly excited singlet S states are seen to emerge in the stabilization diagram. Convergence of the results thus obtained are corroborated by gradually expanding the wavefunction. A comprehensive study is performed to examine the effects of increasing de Broglie wavelength at a fixed plasma screening strength on the energies and widths of the states. It is found that the energies of the states are gradually lifted due to an increase in the de Broglie wavelength. The increase in the ground state energy gradually makes the atom unstable. Special emphasis is given to accurately determine the critical values of the de Broglie wavelength (for a given plasma screening strength) which lead to the instability. However, it is observed that the widths of the states show distinctive behaviour. Attempts are made to analyse the behaviour of the energies and widths in a qualitative fashion.