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Journal of Physics B Atomic Molecular and Optical Physics

Quantum reflection model for ionization rate coefficients in cold metastable helium collisions

A S Dickinson

Published Aug 3, 2007• 12 citations
Publisher

Abstract

A simple, quantum-reflection based, model is presented for describing ionization in collisions of cold metastable helium atoms (He*). This model employs only the van der Waals coefficient and the reduced mass. For atoms reaching short distances an ionization probability of 100% is assumed. The ionization rate coefficient can be written in closed form. Good agreement with more elaborate calculations for collisions of 3 He* and 4 He* is obtained for temperatures up to a few mK.

DOI
10.1088/0953-4075/40/16/f02

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A simple, quantum-reflection based, model is presented for describing ionization in collisions of cold metastable helium atoms (He*). This model employs only the van der Waals coefficient and the reduced mass. For atoms reaching short distances an ionization probability of 100% is assumed. The ionization rate coefficient can be written in closed form. Good agreement with more elaborate calculations for collisions of 3 He* and 4 He* is obtained for temperatures up to a few mK.
A quantum-reflection model is employed to calculate the rate coefficient for the Penning ionization of rubidium by cold metastable helium atoms in unpolarized collisions. Various results for the p-wave transmission coefficient on a 1/R-6 long-range potential are discussed. The dispersion coefficient for the interaction of these atoms is estimated as 3540 au. The calculated value of the rate coefficient is about four times lower than the recently measured value (Byron et al 2010a Phys. Rev. A 81 013405) for this process when both atoms are held in magneto-optical traps.
A quantum-mechanical close-coupled calculation of field-free collisions of cold metastable helium atoms has been performed. Theoretical predictions of the rate coefficients for elastic processes and losses due to the Penning and associative ionization processes are reported for temperatures ranging from 1 $\ensuremath{\mu}\mathrm{K}$ to 1 K. The sensitivity of the rate constants to uncertainties in the molecular potentials and autoionization widths has been investigated. The total ionization loss rates were found to be sensitive to the short-range form of the ${}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ molecular potential and the autoionization widths, while the total elastic rate constants exhibit greater sensitivity to the short-range ${}^{5}{\ensuremath{\Sigma}}_{g}^{+}$ molecular potential.
We have studied the optical collisions of cold, metastable helium atoms in a magneto-optical trap. We have detected the rate of Penning and associative ionization of two metastable helium atoms at a temperature of 1 mK with and without nearly resonant light. We find that the associative ionization rate is increased with more than a factor 20 due to the presence of the light field. We present a simple, semiclassical model, which accounts for all the observed features, and which agrees, also on an absolute scale, with our experimental results.
We have investigated cold ionizing heteronuclear collisions in dilute mixtures of metastable (23S1)(2\phantom{\rule{0.2em}{0ex}}^{3}S_{1})(23S1​) 3He^{3}\mathrm{He}3He and 4He^{4}\mathrm{He}4He atoms, extending our previous work on the analogous homonuclear collisions [R. J. W. Stas et al., Phys. Rev. A 73, 032713 (2006)]. A simple theoretical model of such collisions enables us to calculate the heteronuclear ionization rate coefficient, for our quasiunpolarized gas, in the absence of resonant light (T=1.2mK)(T=1.2\phantom{\rule{0.2em}{0ex}}\mathrm{mK})(T=1.2mK): ${K}_{34}^{(\mathrm{th})}=2.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$. This calculation is supported by a measurement of K34{K}_{34}K34​ using magneto-optically trapped mixtures containing about $1\ifmmode\times\else\texttimes\fi{}{10}^{8}$ atoms of each species, ${K}_{34}^{(\mathrm{exp})}=2.5(8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$. Theory and experiment show good agreement.
A quantum-mechanical close-coupled calculation for collisions of spin-polarized triplet helium atoms in a magnetostatic trap is presented in which the Penning and associative ionization processes are represented by a complex optical potential. The rate coefficients for the spin relaxation and relaxation-induced Penning ionization processes for a range of magnetic fields and temperatures, spanning the cold and ultracold temperature regimes, have been calculated and the sensitivity of these results to uncertainties in the molecular potentials and autoionization width investigated. The rate constants for both elastic and inelastic processes were found to be particularly sensitive to the short-range ${}^{5}{\ensuremath{\Sigma}}_{g}^{+}$ molecular potential and, to a lesser extent, the rate constants for relaxation-induced Penning ionization displayed sensitivity to the short-range form of the ${}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ molecular potential and the autoionization width.
Cross sections and rate coefficients for collisions of two spin-polarized metastable hydrogen atoms are calculated at low energies and temperatures using complex scaling and Feshbach projection methods for the determination of the molecular potential-energy curves. The inclusion of the Lamb shift and fine-structure splitting of the excited n=2n=2n=2 atoms leads to an attractive van der Waals potential for two 2s1/2{2s}_{1/2}2s1/2​ atoms with an exceptionally large coefficient. The quenching of the metastable atoms is dominated at temperatures below 20 mK by ionization. The calculated values for the total loss rate coefficient at 87 \ensuremath{\mu}K and 230 \ensuremath{\mu}K are within a factor of 2 or 3 of the error bars of recent measurements of metastable loss rate coefficients.