A coupled channel quantum scattering study of alignment effects in Na(2P3/2)+He→Na(2P1/2)+He collisions

Abstract

In this paper we present results of coupled channel quantum scattering calculations of the alignment selected j=3/2→ j=1/2 fine structure changing integral cross section for Na(2P)+He. This cross section has in the past been written in terms of a coherent sum of partial wave amplitudes, but we have found that it can be expressed in terms of an incoherent sum of partial cross sections, each labeled by the total angular momentum J and by parity. It is also possible to define an alignment selected wave function for each J such that the azimuthal average of the square of this wave function projected onto each final state is proportional to the magnitude of the partial cross section into that state. This J labeled wave function is thus clearly related to the physical measurables, and we have used it to determine propensities for preservation of asymptotically prepared alignment during collisions. Using a potential surface based on Pascale’s ab initio calculations, we find that the alignment ratio σ⊥/σ∥ is an increasing function of energy, with a value less than unity at low energy (<0.01 eV), but increasing quickly to a value of about 2.0 at 0.04 eV and then more slowly at higher energy, up to a value of 2.7 at 0.2 eV (the highest energy considered). Above 0.02 eV, both the alignment ratio and the alignment selected integral cross sections are in good agreement with values calculated in an accompanying semiclassical study (Kovalenko, Leone, and Delos). An examination of the J labeled alignment selected scattering wave functions and of the expectation values of 〈Ω〉, 〈Λ〉, and 〈Σ〉 indicates that at low J when the initial state is prepared with ∥ polarization, the dominant state at short range is Σ while with ⊥ polarization the dominant state is Π (i.e., asymptotic alignment is preserved). By way of contrast, this propensity for alignment preservation is not seen if fluxes or probability densities associated with alignment selected wave functions labeled by the initial orbital quantum number l (rather than J) are considered. This l labeled result is in accord with recent work by Pouilly and Alexander, but the lack of alignment preservation in this case has no relationship with the alignment cross sections, or with the alignment selected plane wave scattering wave function, since the l labeled wave functions must be coherently combined to generate this information. The orbital scrambling found for the l labeled solutions thus is not related to measurable properties, and instead the correct picture is provided by the J labeled solutions, which do show preservation of alignment. We find that even in the J labeled picture, alignment preservation does not by itself guarantee any specific trend in the alignment ratio for the fine structure transition.