Collision-Induced Anisotropic Relaxation in Gases

An expression is derived for the cross sections, σⱼ⁽ˣ⁾, for the collision-induced relaxation of the multipole moments of an ensemble of excited atoms in a state of total angular momentum j. Various general sum rules are obtained for the σⱼ⁽ˣ⁾, as well as for the Λⱼ⁽ˣ⁾≡σⱼ⁽ˣ⁾-σⱼ⁽⁰⁾, the cross sections for reorienting collisions. For a $j=1$ state, one obtains Λ₁⁽¹⁾Λ₁⁽²⁾=5/3. This result implies that the cross section for collision induced |Δm|=2 transitions is always twice that for |Δm|=1 transitions, independent of the assumed interaction potential. Absolute cross sections are obtained using the van der Waals collision model. Translational motion is treated in a classical linear path approximation. It is shown that the cross sections can be written in the form σⱼ⁽ˣ⁾=Dφⱼ⁽ˣ⁾〈v3/5〉〈v〉, where v is the relative velocity between the colliding atoms, D depends on the particular atoms and states considered, and φⱼ⁽ˣ⁾ is a geometric factor which is tabulated for j values up to $j=8$. The Λⱼ⁽ˣ⁾ are related to the cross sections for transfers between magnetic sublevels. It is shown that in the present model a transfer from sublevel α to -α is forbidden for states with half-integer j values.