The transition operator for depolarizing collisions

The transition operator accounting for changes of the Zeeman sublevels of a¹ P-state or closely spaced² P-states has been derived using the classical-path approximation. In a first order approach to the problem thep-state atom is assumed to enter the range of a foreign atom non-adiabatically fast until reaching the point of the closest distance. There it is assumed to stop for the entire collision time. During this time the molecular σ and π states suffer phase-shifts due to the interaction with the molecular electric field. Subsequently thep-state atom leaves the range of the foreign atom again non-adiabatically fast. TheT-operator hence derived gives rise to the so-calledm _j-selection rule. In a better approach thep-state atom is assumed to stop twice when passing the range of the foreign atom. From this approximation additional terms to theT-operator arise which characteristically account for ‘molecular coupling’ phenomena during the collision. Consequently, these terms violate the afore-mentionedm _j-selection rule.