Multipole polarizabilities for hydrogen-like atoms in Hulthen potential with and without spherical confinement

The multipole polarizabilities for hydrogen-like atoms with Hulthen potential are calculated with the sum-over-states formalism where the system bound and pseudocontinuum states are produced by employing the generalized pseudospectral method. Energies for nonzero angular momentum states, transition oscillator strengths, and dipole polarizabilities for the ground state of H atom with HP are calculated with high accuracy and compared with previous calculations. Quadrupole, octupole, and hexadecapole polarizabilities for both the ground and excited states are reported for the first time. The combined effect of Hulthen potential and impenetrable sphere on the polarizabilities is investigated, and the relation of such system with the confined H atom and particle in a box is discussed. Further comparison among Hulthen, screened Coulomb, and exponential cosine screened Coulomb potentials reveals that although the ground state energies follow the comparison theorem very well, their first-order energy corrections show complicated variations.

Automated summary

In this study, the multipole polarizabilities for hydrogen-like atoms with Hulthen potential were calculated using the generalized pseudospectral method, producing precise results for energy states, transition oscillator strengths, and dipole polarizabilities. Additionally, quadrupole, octupole, and hexadecapole polarizabilities for both ground and excited states were reported for the first time, along with an investigation into the combined effect of Hulthen potential and an impenetrable sphere on polarizabilities. Comparison among different potential models revealed complex variations in energy corrections despite good agreement in ground state energies with the comparison theorem.