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Journal of Physics B Atomic and Molecular Physics

The interpretation of experimental scattering cross sections with pseudopotential calculations for the alkali-mercury interaction

Rudolf Düren

Published Dec 1, 1977• 23 citations
Publisher

Abstract

For the example of collisions of alkali metals with mercury the potentials for the ground state and the lowest excited states are determined by a comparison of a pseudopotential calculation with experiments. The potentials for Na, K, Rb and Cs are described by one common pair of parameters in the pseudopotential. From this example a new method for the evaluation of scattering data is derived, which should allow a uniform description of the potentials of a class of collision systems.

DOI
10.1088/0022-3700/10/17/021

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Journal of Physics Conference Series•Dec 1, 2018•0 citations
For the example of collisions of alkali metals with mercury the potentials for the ground state and the lowest excited states are determined by a comparison of a pseudopotential calculation with experiments. The potentials for Na, K, Rb and Cs are described by one common pair of parameters in the pseudopotential. From this example a new method for the evaluation of scattering data is derived, which should allow a uniform description of the potentials of a class of collision systems.
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.
The differential cross section has been measured for the interaction of Na 2 P 3/2 with Hg. The excitation of Na has been achieved with linearly polarised light of a CW dye laser. The measurements have been evaluated by fitting the parameters of a pseudopotential from which the interatomic potentials have been obtained. The scattering calculation for these interatomic potentials is performed by integrating the coupled Schrodinger equations for the six coupled channels resulting from the P states with J= 3 / 2 and 1 / 2 and their respective values of m j . This experiment and the experiment for the ground-state interaction are now both described by a common calculation using the pseudopotential method.
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{}${10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2.
The pseudopotential molecular-structure method has been used to calculate the X1{X}^{1}X1\ensuremath{\Sigma} and a3{a}^{3}a3\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 Q1/2{Q}^{1/2}Q1/2=a-b lnv. However, abundant structure on the cross sections is present due to orbiting resonances induced by the deeply bound well of the X1{X}^{1}X1\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{}${10}^{\mathrm{\ensuremath{-}}16}$ cm2{\mathrm{cm}}^{2}cm2 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.