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Physical Review A

Spin-exchange cross sections for hydrogen-atom–alkali-metal-atom collisions

H. R. Cole, R. E. Olson

Published Apr 1, 1985• 25 citations

Abstract

The pseudopotential molecular-structure method has been used to calculate the ${X}^{1}$\ensuremath{\Sigma} and ${a}^{3}$\ensuremath{\Sigma} interaction potentials for the alkali-metal-atom--hydrogen-atom systems. These potentials were then used in a quantum-mechanical calculation to determine the spin-exchange cross sections in the energy range from 2.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ eV to 2.5 eV. The cross sections follow the general form ${Q}^{1/2}$=a-b lnv. However, abundant structure on the cross sections is present due to orbiting resonances induced by the deeply bound well of the ${X}^{1}$\ensuremath{\Sigma} molecular state. The spin-exchange cross sections range from 17\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}16}$ to 25\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}16}$ ${\mathrm{cm}}^{2}$ at room temperature for H(F=1) transferring to H(F=0) in collision with unpolarized lithium and cesium, respectively.

DOI: 10.1103/physreva.31.2137

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The pseudopotential molecular-structure method has been used to calculate the

{X}^{1}

\ensuremath{\Sigma} and

{a}^{3}

\ensuremath{\Sigma} interaction potentials for the alkali-metal-atom--hydrogen-atom systems. These potentials were then used in a quantum-mechanical calculation to determine the spin-exchange cross sections in the energy range from 2.5\ifmmode\times\else\texttimes\fi{}

{10}^{\mathrm{\ensuremath{-}}4}

eV to 2.5 eV. The cross sections follow the general form

{Q}^{1/2}

=a-b lnv. However, abundant structure on the cross sections is present due to orbiting resonances induced by the deeply bound well of the

{X}^{1}

\ensuremath{\Sigma} molecular state. The spin-exchange cross sections range from 17\ifmmode\times\else\texttimes\fi{}

{10}^{\mathrm{\ensuremath{-}}16}

to 25\ifmmode\times\else\texttimes\fi{}

{10}^{\mathrm{\ensuremath{-}}16}

{\mathrm{cm}}^{2}

at room temperature for H(F=1) transferring to H(F=0) in collision with unpolarized lithium and cesium, respectively.

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.

Potential scattering and spin-exchange scattering cross sections in the energy range from 10 -3 cm -1 to 100 cm -1 have been calculated numerically for hydrogen atoms in collision based on the most accurate Kołos-Woniewicz adiabatic potentials available at present. The scattering lengths for the singlet and triplet states are calculated to be a 0 s =0.595 a.u. and a 0 t =1.34 a.u., respectively. The quasi-bound state with ν=14 and l =4 is found to be at E =1.675 cm -1 above the dissociation limit. The thermally averaged spin-exchange cross section has the low temperature limit \barσ ex (0 K)=0.982 A 2 with a minimum \barσ ex (2.5 K)=0.329 A 2 .

Complex spin-exchange cross sections are calculated on the basis of the data on the singlet (X 1Σ+) and triplet (a 3Σ+) potentials describing the interaction of isotopes of Rb alkali-metal atoms in the ground state. The cross sections calculated in this study are compared with the cross-section data obtained earlier with the model interaction potentials. The cross-section values allow one to calculate the processes of polarization transfer and the relaxation times, as well as the magnetic resonance frequency shifts caused by the Rb‒Rb spin-exchange collisions.