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Physical Review

Calculations of Spin-Exchange Cross Sections of Alkali Atoms by Partial-Wave Analysis

C. K. Chang, R. H. Walker

Published Feb 5, 1969• 12 citations

Abstract

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.

DOI: 10.1103/physrev.178.198

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Application of the Pseudopotential Method to Atomic Scattering

J. Callaway, P. S. Laghos

The empirical pseudopotential method is discussed and applied to a calculation of the spin-exchange cross section in collisions of Na and Cs atoms. The difference between potential energy curves for the lowest singlet and triplet states of the Na-Cs system is calculated by the Heitler-London method, using a Hamiltonian in which the effects of tightly bound electrons are replaced by a pseudopotential. Wave functions for the free atoms are found by numerical integration using the pseudopotential, and agree well with the exact valence-electron functions at large distances. The scattering phase shifts are calculated in the WKB approximation, and the cross section computed from them is averaged over a Boltzmann distribution of relative velocities. At a temperature of 500\ifmmode^\circ\else\textdegree\fi{}K, the averaged reduced spin-exchange cross section is 1.5 \ifmmode\times\else\texttimes\fi{} 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$.

Physical Review•Nov 5, 1969•46 citations

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.

Abstract We study theoretically interaction potentials and low-energy collisions between different alkali atoms and alkali ions. Specifically, we consider systems such as X + Y + , where X( Y + ) is either Li(Cs + ) or Cs(Li + ), Na(Cs + ) or Cs(Na + ) and Li(Rb + ) or Rb(Li + ). We calculate the molecular potentials of the ground and first two excited states of these three systems using a pseudopotential method and compare our results with those obtained by others. We derive ground-state scattering wave functions and analyze the cold collisional properties of these systems for a wide range of energies. We find that, in order to get convergent results for the total scattering cross sections for energies of the order 1 K, one needs to take into account at least 60 partial waves. The low-energy scattering properties calculated in this paper may serve as a precursor for experimental exploration of quantum collisions between an alkali atom and an alkali ion of a different nucleus.

Collisions of alkali-metal atoms in the ground state with the electron spin S = 1/2 are accompanied by exchange of electron coordinates between colliding particles, which leads to polarization transfer between them (i.e., to the well-known phenomenon of spin exchange). In addition, along with the polarization transfer from one partner to another, the magnetic resonance lines of colliding atoms are broadened and shifted in spin-exchange collisions. In particular the last two processes depend on the complex spin-exchange cross section. The real part of the cross section determines the so-called "spin-exchange cross section," which is responsible for the broadening of magnetic resonance lines, while the imaginary part determines the shift cross section, which governs the frequency shift of magnetic resonance. In order to describe the spin-exchange process one have to know complex spin-exchange cross sections. Complex spin-exchange cross sections are calculated on the basis of the data on the singlet (X 1 Σ + ) and triplet (a 3 Σ + ) potentials describing the interaction alkali-metal atoms in the ground state. Collisions of alkali-metal atoms Cs, Rb, K, Na in the ground state are considered in the energy interval of 10 −4 −10 −2 au.

The empirical pseudopotential method is discussed and applied to a calculation of the spin-exchange cross section in collisions of Na and Cs atoms. The difference between potential energy curves for the lowest singlet and triplet states of the Na-Cs system is calculated by the Heitler-London method, using a Hamiltonian in which the effects of tightly bound electrons are replaced by a pseudopotential. Wave functions for the free atoms are found by numerical integration using the pseudopotential, and agree well with the exact valence-electron functions at large distances. The scattering phase shifts are calculated in the WKB approximation, and the cross section computed from them is averaged over a Boltzmann distribution of relative velocities. At a temperature of 500\ifmmode^\circ\else\textdegree\fi{}K, the averaged reduced spin-exchange cross section is 1.5 \ifmmode\times\else\texttimes\fi{} 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}14}$

{\mathrm{cm}}^{2}

.