Semiclassical analysis of jm → j′m′ transitions in rotationally inelastic collisions in cell experiments

Recent quantum calculations of rotationally inelastic collisions of NaK (A1Σ+) with He or Ar in a cell experiment are analyzed using semiclassical approximations valid for large quantum numbers. The results suggest a physical interpretation of jm → j′m′ transitions based on the vector model and lead to expressions that explicitly involve the initial and final polar angles of the angular momentum of the target molecule. The relation between the polar angle θ and the azimuthal quantum number m links the semiclassical results for the change in polar angle (θ → θ′) to quantum results for an m → m′ transition. Analytic formulas are derived that relate the location and width of peaks in the final polar angle distribution (PAD) to the K-dependence of the coefficients dK(j, j′), which are proportional to tensor cross sections σK(j → j′). Several special cases are treated that lead to final PADs that are approximately Lorentzian or sinc functions centered at θ′ = θ. Another interesting case, “angular momentum reve...