Nuclear Quadrupole Coupling in theLi2Molecule

Abstract

The effect of the quadrupole moment induced in the $1s$ shell on the nuclear quadrupole coupling $q$ in the ${\mathrm{Li}}_2$ molecule has been investigated for several wave functions. For the most accurate variational wave function of James, the inclusion of the induced moment gives $\frac{q}{2e}=-0.00106\mathrm{}{a_{\mathrm{H}}}^{-3\mathrm{}}$. This result, together with the quadrupole coupling $eqQ=+0.060\mathrm{}$ Mc/sec for ${\mathrm{Li}}^7$, leads to a negative value of the quadrupole moment $Q\left({\mathrm{Li}}^7\right)$. However the value of $q$ is so close to zero that the magnitude and even the sign of $Q$ is uncertain. The value of $\frac{1}{q}$ which determines $Q$ is very sensitive to changes in the molecular wave function, and it is shown that a small modification of the James wave function would lead to a negative $Q\left({\mathrm{Li}}^7\right)$ which agrees in order of magnitude with the prediction of the nuclear shell model. Calculations of $q$ were also carried out for the Heitler-London and Coulson-Duncanson wave functions for the ${\mathrm{Li}}_2$ molecule.