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Physical Review A

Cold collisions of spin-polarized metastable hydrogen atoms

Robert C. Forrey, S. Jonsell, Alejandro Sáenz, Piotr Froelich, A. Dalgarno

Published Apr 10, 2003• 15 citations
Publisher

Abstract

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 $n=2$ atoms leads to an attractive van der Waals potential for two ${2s}_{1/2}$ 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.

DOI
10.1103/physreva.67.040701

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Cold collisions of metastable neon atoms

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

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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.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 3, 2007•12 citations
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.
We have calculated cross sections and rate coefficients for elastic scattering, ionization, and double excitation transfer in collision of two hydrogen atoms in the 2s state. We find that for collision energies between 5 × 10-10 a.u. and 10-6 a.u. elastic scattering has the largest cross section. For temperatures below 0.02 K ionization is the dominant loss process, while for higher temperatures double excitation transfer dominates. Our results for the total loss rate are found to be within a factor 2 or 3 of the error bars of recent measurements.
The interaction of two excited hydrogen atoms in metastable states constitutes a theoretically interesting problem because of the quasidegenerate 2P1/22{P}_{1/2}2P1/2​ levels that are removed from the 2S2S2S states only by the Lamb shift. The total Hamiltonian of the system is composed of the van der Waals Hamiltonian, the Lamb shift, and the hyperfine effects. The van der Waals shift becomes commensurate with the $2S\ensuremath{-}2{P}_{3/2}$ fine-structure splitting only for close approach (R<100a0R<100{a}_{0}R<100a0​, where a0{a}_{0}a0​ is the Bohr radius) and one may thus restrict the discussion to the levels with n=2n=2n=2 and J=1/2J=1/2J=1/2 to a good approximation. Because each SSS or PPP state splits into an F=1F=1F=1 triplet and an F=0F=0F=0 hyperfine singlet (eight states for each atom), the Hamiltonian matrix a priori is of dimension 64. A careful analysis of the symmetries of the the problem allows one to reduce the dimensionality of the most involved irreducible submatrix to 12. We determine the Hamiltonian matrices and the leading-order van der Waals shifts for states that are degenerate under the action of the unperturbed Hamiltonian (Lamb shift plus hyperfine structure). The leading first- and second-order van der Waals shifts lead to interaction energies proportional to 1/R31/{R}^{3}1/R3 and 1/R61/{R}^{6}1/R6 and are evaluated within the hyperfine manifolds. When both atoms are metastable 2S2S2S states, we find an interaction energy of order ${E}_{h}\ensuremath{\chi}{({a}_{0}/R)}^{6}$, where Eh{E}_{h}Eh​ and L\mathcal{L}L are the Hartree and Lamb shift energies, respectively, and $\ensuremath{\chi}={E}_{h}/\mathcal{L}\ensuremath{\approx}6.22\ifmmode\times\else\texttimes\fi{}{10}^{6}$ is their ratio.
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.
In this thesis we investigate theoretically the cold collision properties of metastable neon (Ne*). The collisions of metastable rare gases (Rg*) exhibit a plethora of interesting phenomena: Due to the high internal excitation energies of the metastable atoms ionization processes are very likely. The produced ions can be detected with single-ion efficiency in the experiment. In experiments with atomic Rg* gases at cold temperatures T~1 mK, this allows for in-situ monitoring of the real-time dynamics of the atomic gas and for example for the study of two-particle correlations. Furthermore, in cold Rg* gases one can examine the prospects of creating a Bose-Einstein condensate or a degenerate Fermi gas of Rg*. Ne* is a promising candidate for Bose-Einstein condensation and in the group of G. Birkl the properties of cold gases of Ne* are investigated experimentally. Two-body loss rate coefficients due to the ionization processes and elastic cross sections have been measured. It is useful to complement the experimental measurements with a theoretical study in order to obtain a better understanding of the cold Ne* gases and the collision physics of Ne*. At the low temperatures of the atomic gases, these gases are dilute with particle number densities of n~10^9 cm^{-3}. For these low densities, the behavior of the gas is determined mainly by two-body collision physics which is solved by quantum scattering theory in terms of the S matrix. The collision physics is given by short-range interactions and long-range interactions of the atoms. The short-range and long-range interaction potentials of Ne* have been calculated in the molecular basis of Ne2. In this thesis we first calculate short-range and long-range interactions of atoms and molecular basis states of diatomic molecules with a simpler electronic structure than Ne* and Ne2 in order to introduce the notation and to discuss the characteristics of the calculated molecular interaction potentials and in order to employ them in the scattering calculations for Ne*. Instead of solving the full scattering equations by taking into account all the molecular interaction potentials, we demonstrate that the collision physics of Ne* can be described in terms of a coupled two-channel model with a single interaction potential only which describes the elastic scattering of Ne*. In this model, ionization in Ne* collisions is described by the transition of the upper elastic interaction channel to the lower channel, representing the loss or ionization channel. We introduce two versions of the two-channel model in this work. In the first version, the two channels are given by square-well potentials. We can solve the scattering equations analytically and for complex wave numbers k and study the solutions in the complex k plane. With an expansion of the S matrix in terms of its poles in the complex k plane we find a parametrization of the two-body loss rate coefficients. We show that these coefficients describe ionizing collisions of Ne* by comparing them to the experimental measurements and to the numerical results obtained by the two-channel model in the second version. In this second version of the two-channel model, the elastic scattering channel is given by a realistic interaction potential of Ne*, consisting of a calculated short-range and long-range molecular potential, and the loss channel by a model ionization potential. For this model we calculate the two-body loss rate coefficients and the elastic cross sections for the isotope mixtures of Ne* which have been measured experimentally and demonstrate that the free potential parameters can be optimized to the experimental data to achieve very good agreement of the numerical results with the experimental measurements. We discuss the validity of the two-channel model by comparing the results to existing models for cold Rg* collisions and find that the two-channel model of this work is a useful extension to these models.