Velocity-Dependent Potentials and the Shell Model of Oxygen-18

An expansion of the shell-model matrix elements of the velocity-dependent potential $m^{-1\mathrm{}}\left[p^{2}V\right(r)+V(r\left)\mathrm{}{p}^2\right]$ in the Talmi integrals of $V$ is derived and applied to calculate the energy levels of ${\mathrm{O}}^{18}$ using the nucleon-nucleon potential of Green. It is found that the correct ordering of the levels is obtained but the potential must be altered slightly to obtain agreement comparable with that given by Dawson, Talmi, and Walecka using the Brueckner-Gammel-Thaler potential.