Structural analysis of the ro-vibrational states of screened hydrogen molecular ion in the regime of Borromean binding

Abstract

A detailed analysis on the structural properties of first three ro-vibrational (J = 0, ν = 0, 1, 2; J and ν being the rotational and vibrational quantum numbers, respectively) states of ion bound via screened Coulomb interaction has been reported. Generalized Hylleraas type basis set has been considered to construct the trial wave function under the Ritz variational framework. In order to incorporate the localized relative motion of the protons (or nuclei), we have used high powers of the interprotonic (or internuclear) distance in the basis set. The Borromean binding regime or the Borromean window (BW) has been identified for the said three states of ion. The energy components contributing to the total energy are estimated as a parametric function of the screening parameter. Different geometrical entities e.g. radial moments (p = − 1, 1 and 2), angular moments [(i) = (1) or (12)], expectation value of the delta function as well as the one-particle density are determined to get a clear view of the structural behaviour of ion in its ground state as well as in the excited states, specially within the BW.