Excitation Transfer and Diffusion Property in a very Weakly Excited Lithium Gas

The aim of this study is a quantal computation of the diffusion coefficient $D$ of excited lithium atoms Li(2p) in their parent gas Li(2s). The variation law of $D$ with temperature $T$ is also treated. The calculations are further extended to the determination of the excitation transfer cross section correlated with the process Li(2p)+Li(2s) $\rightarrow$ Li(2s)+Li (2p). To do so, we have constructed from recent RKR and/or ab initio data points the eight singlet and triplet potential energy curves through which an atom Li(2p) approaches Li(2s). In the short- and long-range regions, the data points are smoothly connected to the forms $\exp(-bR)$ and $1/R^{n},$ respectively. The phase shifts, obtained for each energy $E$ and angular momentum $l$ from the numerical integration of the radial wave equation, allow the calculation of the diffusion and excitation transfer cross sections $Q_{D}$ and $Q_{tr}$. Our results show that the weighted cross sections vary with energy like $E^{-1/2} $ and the diffusion coefficient is found of the form $D \sim AT/n$, with $n$ being the number density and $A$ a constant. A semi-classical method shows $Q_{D} \simeq 2Q_{tr}$ and points out that the long-range $R^{-3}$ forces are prominent in the diffusion of excited atoms in their parent gas.