Multipole nuclear shielding factors of hydrogen-like ions in plasmas modeled by screened-type Coulomb potentials

The multipole (dipole, quadrupole, octupole, and hexadecapole) nuclear shielding factors of hydrogen-like ions embedded in plasma environments are investigated to elucidate the shielding effect of atomic electrons on the external nuclear charge. The plasma screening effect on the embedded atom is modeled by screened-type Coulomb potentials, which include the static Debye–Hückel potential for weakly coupled plasmas, the exponential cosine screened Coulomb potential for dense quantum plasmas, and the Hulthén potential for astrophysical plasmas. Utilizing the sum-over-states formalism together with the generalized pseudospectral method, accurate values of multipole nuclear shielding factors are obtained over the entire range of screening parameters where the system ground state exists as a bound state. It is shown that the dipole shielding factor depends only on the nuclear charge and total number of electrons of the atom, while the higher-pole results increase monotonically as the plasma screening effect becomes stronger. The limiting values of nuclear shielding factors at the system critical bound limits are discussed, and discrepancies among different plasma models are shown to be closely related to the quantum phase transitions of systems at corresponding critical screening parameters. Hylleraas variational perturbation theory is employed to analyze the asymptotic behavior of nuclear shielding factors in weak plasma screening environments. It is found that only the third- and higher-order approximations can properly reproduce the quadratic scaling laws of nuclear shielding factors at small screening parameters.