# Spin-exchange cross sections of alkali-atoms

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## Abstract

In the collision of atoms with one valence S electron outside closed shells (alkali-like atoms), an important feature of the process is the indistinguishability of electrons. This can give rise to an exchange of electrons between the colliding atoms. This process has come to be called spin-exchange scattering. These spin-exchange effects may be calculated using the usual scattering theories. This process is the subject of this paper. To calculate numerically spin-exchange cross sections, the spin-dependent interaction characterizing the scattering is required. This interaction for two alkaline atoms is calculated by individually considering the interactions due to the valence S electrons and to the closed electronic shells of the two atoms. The two S electron interaction is generated phenomenonologically from the known hydrogen-hydrogen interatomic potential and the closed shell interaction from interatomic potentials of two inert atoms. Two undetermined parameters characterizing the scale of the interaction are introduced in this generation. These parameters are determined from experimentally known values of the equilibrium distance and the dissociation energy appropriate for the molecular state of the atomic system of interest. These theoretical potentials so obtained are in agreement with those constructed from band spectra. Unfortunately, these direct observations yield spin-dependent interaction potentials only for the singlet state of the alkaline atoms. This technique is extended to obtain the interaction potentials for cases for which there is at the present time inadequate experimental information for their construction, and for those cases in which no stable molecule is formed. It is hoped that the good agreement of our phenomenonological calculation of potentials can be extrapolated to those cases for which no experimental check is possible. These interaction potentials are also used to calculate the second virial coefficients. The present theories of spin-dependent scattering of alkali-like atoms are introduced, and our potentials are used to calculate various cross sections by semi-classical techniques and by partial wave analysis. The results of the semi-classical method compare fairly well with experimental ones. Six different scattering cross sections are calculated by partial wave analysis for each of the six alkaline atoms, H, Li, Na, K, Rb and Cs, for 124 different relative kinetic energies. These cross sections are finally averaged with Maxwellian distribution for temperature of range from 10Â°k to 9500Â°k, and the partial results are shown in the following table...