Electron - Alkali Atom Scattering with Spin Analysis.

P. J. O. Teubner

Philip George Burke, John F. Mitchell

An analysis of spin-polarization in low energy elastic scattering electrons by one electron s-state atoms is carried out allowing both for electron exchange and relativistic effects. First the collision matrix is written in terms of the asymptotic form of the solutions of the radial equations. Then arguments, based on the invariance of the Hamiltonian under time reversal, space rotation and space reflection are used to write down the most general form of this matrix. It is found that it can be expressed in terms of six independent amplitudes. Then expressions for the observable quantities, including the spin polarization of the electron and of the atom after the collision are derived. Finally, the analysis is specialized to the case where spin-polarization effects are caused by a spin-orbit interaction and these effects are considered in the neighbourhood of cusps and resonances in electron alkali atom scattering.

Chen-Kun Chang

C. K. Chang, R. H. Walker

Four different spin-dependent scattering cross sections are calculated by semiclassical and by partial-wave analyses for each of the five alkali atoms, Li, Na, K, Rb, and Cs, for 124 different relative kinetic energies. These cross sections are finally averaged thermally. The results agree very well with experiments.In the calculation, the interaction potential between two alkali atoms is calculated by individually considering the interaction due to the two valence $s$ electrons and to the closed electronic shells of the two atoms. The two-$s$-electron interaction is generated ad hoc phenomenologically from the known hydrogen-hydrogen interatomic potential and the closed-shell interaction from interatomic potentials of two inert atoms corresponding to the cores. The potentials so obtained are in agreement with those constructed from band spectra.

C. J. Pethick, H. Smith

From a theoretical point of view, one of the appealing features of clouds of alkali atom vapours is that particle separations, which are typically of order 10 2 nm, are large compared with the scattering length a which characterizes the strength of interactions. Scattering lengths for alkali atoms are of the order of 100 a 0 , where a 0 , is the Bohr radius, and therefore alkali atom vapours are dilute, in the sense that the dominant effects of interaction are due to two-body encounters. It is therefore possible to calculate properties of the gas reliably from a knowledge of two-body scattering at low energies, which implies that information about atomic scattering is a key ingredient in work on Bose–Einstein condensates. An alkali atom in its electronic ground state has several different hyperfine states, as we have seen in Secs. 3.1 and 3.2. Interatomic interactions give rise to transitions between these states and, as we described in Sec. 4.6, such processes are a major mechanism for loss of trapped atoms. In a scattering process, the internal states of the particles in the initial or final states are described by a set of quantum numbers, such as those for the spin, the atomic species, and their state of excitation. We shall refer to a possible choice of these quantum numbers as a channel.1 At the temperatures of interest for Bose-Einstein condensation, atoms are in their electronic ground states, and the only relevant internal states are therefore the hyperfine states. Because of the existence of several hyperfine states for a single atom, the scattering of cold alkali atoms is a multi-channel problem.

Mituo Taketani, Masayuki Nagasaki