Many-body calculation of the electric field gradient in the aluminum atom

Abstract

The electric field gradient for the lowest ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state in the aluminum atom has been calculated by many-body perturbation theory. We find that the quadrupole shielding factor has a much larger antishielding contribution coming from the radial excitations of the $2p$ core than previously estimated. This substantially larger contribution has not been considered in earlier work. It arises from the fact that only one of the $2p$-core electrons undergoes a monopole ($K=0$) exchange interaction with the valence $3p$ electron, breaking the spherical symmetry of the $2p$ core. Two-particle excitations consisting of correlation and consistency effects lead to a significant shielding contribution. The total quadrupole shielding factor is found to be antishielding in nature and has a value of $R = -11.8\mathrm{}\pm 1\%$. The net field gradient at the nucleus is $q=0.487\mathrm{}\pm 0.004$ a.u. From the measured quadrupole coupling constant we deduce the nuclear moment ${\mathrm{of}}^{27}$ Al as $Q=0.165\mathrm{}\pm 0.002$ b.