Static multipole polarizabilites of H-atom in modified ring-shaped potentials

Abstract

The time-independent Schrödinger equation (TISE) is solved to evaluate energy eigenvalues and eigenfunctions of H-atom confined by one of the radial potentials, which is modified by a ring-shaped potential and further encaged in a spherical boundary. We have considered the following four radial potentials i.e., Debye, Exponential Cosine Screened Coulomb (ECSC), Hulthén($\alpha$), and Hulthén(2$\alpha$). Static $2^{l}$-pole polarizability of H-atom in different modified ring confinement potential is evaluated for a range of screening parameter ($\alpha$). Repulsive ring-shaped potential affects multipole polarizabilities and reduces the critical screening parameter in different modified ring confinement potentials. The confinement parameters $\alpha$ and $\beta$ considerably affect the amplitude of multipole polarizabilities. Size of the spherical boundary ($r_{0}$) crucially affects multipole polarizabilities and overweighs the effect of $\alpha$ and $\beta$. The results prove that as the screening parameter increases the polarizabilities corresponding to various radial potentials become almost equal, i.e., the response due to the different radial potentials becomes indistinguishable after a particular value of the screening parameter.

Graphic abstract