Wigner Distribution Functions as a Tool for Studying Gas Phase Alkali Metal Plus Noble Gas Collisions

Wave packet propagation methods are used to compute scattering Wigner Distribution Functions WDF for the square well potential, square barrier potential, and the HH2 and OHCO, and several MNg collisions. The scattering WDF are used to interpret how probabilities flow among various potential energy surfaces as a function of time during a collision. Positive values of the scattering WDF correspond to the addition of probability to scatter into the state that corresponds to the asymptotic limit of the potential energy surface of interest. Negative values correspond to the loss of probability to scatter into the state that corresponds to the asymptotic limit of the surface of interest, and zero values correspond to probability associated with the wave packet that is still in the interaction region. The loss of probability on one surface corresponds to the addition of probability on another surface at different times. Bands of oscillating peaks and valleys that form in the structure of the scattering WDF correspond to presence of secondary transmission or reflection with significant probability. The square well frequencies at which probability arrive in a scattering channel corresponds to the depth and width of the well. Scattering WDF were computed for the following combinations KHe, KNe, KAr, RbHe, RbNe, RbAr, CsNe, and CsAr. The scattering WDF revealed that as the mass of the noble gas increased, a significant proportion of probability was transferred from the 2P32 pump state to the 2P12 lasing state for a larger number of total angular momentum values. Similarily, as the mass of the alkali metal decreased, there was a reduced transfer of probability to make a transition from the 2P32 state to the 2P12 state. The reduced probability to make a transition from the 2P32 to the 2P12 manifolds for the MHe collisions is compensated by the large average velocity of He.