Effect of spin-orbit coupling on2p12−2p32rotational transitions in heavy-ion collisions

We consider the effect of spin-orbit coupling between the molecular orbitals correlated to the united-atom $2p_{\frac{1}{2}}$ and $2p_{\frac{3}{2}}$ states on rotational-coupling transition probabilities in heavy-ion collisions. In low-$Z$, lowvelocity encounters, where the splitting is small, calculations of the rotational-coupling cross section have been shown to be in agreement with experiment. We compute a correction factor to the previous calculations in terms of a general scaling parameter $\xi =\frac{\Delta E}{{\left(k{v}_1^2\right)}^{\frac{1}{3}}}$, where $\Delta E$ is the spin-orbit splitting in the united atom, $v_1$ is the ion velocity, and $k=\frac{Z_1{Z}_2{(Z_1+Z_2)}^2}{40}$ a.u. The correction is generally small, but is observed in high-$Z$ encounters at low velocities.