Exploring changes in the static multipole polarizabilities of hydrogen atoms in Coulomb plus inverse square root potential

Abstract Polarizability is an important physical quantity that measures the electronic structure of an atomic molecule under the influence of an external electric field. Inspired by the work of A.M. Ishkhanyan and Pablo Serra, the authors have proposed to probe the atomic properties in the 1-5s state of free hydrogen atoms at criticality in Coulomb plus inverse square root potential. We have numerically calculated the polarizability with high accuracy in this work with the generalized pseudospectral method, which is a globally based configuration method with strong superiority in calculating the one-electron system. It allows numerical results to be obtained with high accuracy while ensuring the convergence of the results. Currently, the results of calculations of multipole polarizabilities of free hydrogen atoms in Coulomb plus inverse square root potential are all scarce, and most of them suffer from insufficient calculation accuracy. Therefore, it is expected that the results of this work could provide some accurate numerical results to fill the current data gap.