Effect of the distorted core on the electric field gradient of conduction electrons in noncubic metals

Abstract

In calculations of the electric field gradient (EFG) of conduction electrons in noncubic metals, it is a normal practice for the conduction-electron states to be determined by the lattice of ions and other electrons. However, in reality, these conduction-electron states are also perturbed directly by the nuclear quadrupole moment and indirectly by the distorted core, the distortion here being due to the EFG of the external lattice ions and the nuclear quadrupole moment. Such perturbations of the conventional conduction-electron states can give an additional EFG. It is the latter quantity that is calculated in the present work both for Be and Mg metals. Model potential theory is used to represent the conduction-electron distribution external to the ion core at whose nucleus the EFG is calculated. Corrections to the model wave functions to first order both in nuclear quadrupole and distorted core perturbations are calculated. With the use of the latter wave functions, the radial densities of the induced EFG and quadrupole moment in the conduction-electron states are computed. These radial densities, along with the available radially dependent antishielding factors, are then used in the general expression of Lodge for the field gradient to evaluate the additional EFG of the conduction electrons. The model wave functions are also used to represent the conduction electrons in the core region, for which this representation is not exact. Corrections to EFG arising from this effect are estimated. The calculated results show that additional EFG's from the perturbations of the conventional conduction-electron states are, respectively, 1% and 20% of the traditional values obtained by Lodge for Be and Mg. Furthermore, these additional EFG's are roughly -1.5% and 12.8% of the respective electronic contributions of the conventional conduction-electron states obtained in the calculations of Mohapatra et al. for Be and of Jena et al. for Mg, where more accurate wave functions than those of Lodge were used. The increasing trend in the magnitudes of the additional EFG with the increasing size of the atomic core suggests that the effect of the distorted core on the conventional conduction-electron states may become more important for other noncubic metals with larger atomic cores.