Relativistic Correction Factors to the Magnetic Dipole and Electric Quadrupole Hyperfine Integrals Calculated with Hydrogen Wave Functions

Abstract

Relativistic correction factors to diagonal and off-diagonal dipole and electric quadrupole hyperfine integrals have been calculated for p electrons with values of the principal quantum number n in the range 2 ≤ n ≤ 10. The correction factors have been eveluated by comparing hyperfine radial integrals obtained from relativistic and non-relativistic hydrogenic wave functions. Relativistic correction factors to the mean values of r-3 for the orbital, spin-dipole and spin terms of the effective magnetic dipole Hamiltonian and to the mean values of r-3 for the electric quadrupole Hamiltonian have also been calculated. These new n-dependent correction factors are compared with earlier commonly used factors and with correction factors obtained from self-consistent-field (SCF) wave functions. It is found that improvement is obtained for p1/2 states using these new factors compared with earlier ones, while no significant improvement is obtained for p3/2 states.