Second-order nuclear quadrupole coupling in the Br− ion

Abstract

This paper describes a theoretical treatment of the second-order Stark effect on the nuclear quadrupole interaction of a closed-shell atomic system. A method of calculation is presented which applies a dipolar perturbation in the uncoupled Hartree approximation. It is suggested in the context of ionic solids that the unperturbed anion be represented by Hartree–Fock wavefunctions appropriate to the free neutral atom rather than by the more extended free-ion functions. The first-order perturbation to the wavefunction is obtained by numerical solution of a differential equation (the method of Kotani and Sternheimer), and the second-order perturbation is approximated by projecting it onto the unperturbed wavefunction. The Br− ion is considered in detail and it is shown that, in the strong electrostatic fields to be found in ionic solids, the second-order nuclear quadrupole coupling can be considerable. The calculation yields a dipolarizability of 6.19 Å3, a dipole shielding factor of 4.45, a second-order Stark quadrupolarizability of 0.544 Å5 V−1, and a second-order Stark effect on the field gradient of γ24=−3.23 V−1. The second-order response is smaller in this case than in the free Cl− ion of earlier, variational calculations.