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Journal of Physics B Atomic Molecular and Optical Physics

Scattering lengths for collisions of hydrogen and deuterium atoms

X Chu, Michael J. Jamieson, A. Dalgarno

Published Oct 23, 2003• 2 citations
Publisher

Abstract

The scattering lengths for hydrogen and deuterium atoms interacting via the potentials of the X 1 Σ g + , b 3 Σ u + and e 3 Σ u + molecular states are calculated. An estimate of the uncertainty in the X 1 Σ g + scattering length arising from the coupling to the 1 Σ u + states is made. The recommended scattering lengths are −0.67 and 148 bohr for the b 3 Σ u + and e 3 Σ u + interaction potentials, respectively, and 11.1 bohr for the X 1 Σ g + interaction potential. It is suggested that deuterium atoms would be cooled efficiently by collisions with metastable hydrogen atoms.

DOI
10.1088/0953-4075/36/22/l01

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The scattering lengths for hydrogen and deuterium atoms interacting via the potentials of the X 1 Σ g + , b 3 Σ u + and e 3 Σ u + molecular states are calculated. An estimate of the uncertainty in the X 1 Σ g + scattering length arising from the coupling to the 1 Σ u + states is made. The recommended scattering lengths are −0.67 and 148 bohr for the b 3 Σ u + and e 3 Σ u + interaction potentials, respectively, and 11.1 bohr for the X 1 Σ g + interaction potential. It is suggested that deuterium atoms would be cooled efficiently by collisions with metastable hydrogen atoms.
Scattering lengths for the collisions of ground and metastable state hydrogen atoms interacting via the B′1∑u +, EF 1∑g +, e3∑u + and h3∑g + molecular potentials are evaluated from published ab initio Born-Oppenheimer potentials with adiabatic corrections, matched to multipole expansions at large interatomic separations. It is demonstrated that the scattering lengths are very sensitive to the connections between the ab initio potentials and their asymptotic forms and the need is shown for accurate interatomic potential calculations at greater separations than are currently available. The density-dependent shift and broadening of the 1S–2S transition frequency in atomic hydrogen caused by two-body elastic collisions are presented.
The scattering lengths and effective ranges for collisions of ground state Be atoms interacting via the X 1Σ + g molecular state of the Be 2 dimer are calculated for two published X 1Σ + g potentials. A new ab initio X 1Σ + g potential is presented with its vibrational energies and rotational constants. The scattering parameters calculated with it and with the existing potentials are compared. Simple formulae showing how the scattering parameters are influenced by adiabatic coupling to electronic motion are derived within the semi-classical formulation and evaluated for the potentials considered. The formulae imply that a semi-classical account of adiabatic coupling can be made by increasing each atomic mass by one electron mass. © 2007 IOP Publishing Ltd.
We report scattering lengths for the ${}^{1}{\ensuremath{\Sigma}}_{g}^{+},$ ${}^{3}{\ensuremath{\Sigma}}_{u}^{+},$ and ${}^{5}{\ensuremath{\Sigma}}_{g}^{+}$ adiabatic molecular potentials relevant to collisions of two metastable 23S2{}^{3}S23S helium atoms as a function of the uncertainty in these potentials. These scattering lengths are used to calculate experimentally observable scattering lengths, elastic cross sections, and inelastic rates for any combination of states of the colliding atoms, at temperatures where the Wigner threshold approximation is valid.
The scattering lengths that characterize the low-energy elastic scattering of 23 Na atoms by 39 K, 40 K and 41 K atoms, when they interact via the X 1 Σ + and a 3 Σ + states of the NaK dimer, are calculated. The systematic variation of the short- and long-range parts of the interaction potentials reveals that the calculated scattering lengths are sensitive to uncertainties in the potentials. It is concluded that precise spectroscopic measurements of the least-bound ro-vibrational levels supported by the ground electronic state, which would reduce the uncertainties in both the molecular potentials, are needed for an accurate determination of the scattering lengths.
The possibility that the non-adiabatic correction to the scattering length of a pair of hydrogen atoms interacting via the ground state molecular potential, X1Σ+g , of H2 could be made by replacing the mass of each nucleus by a different effective mass is explored. The Born-Oppenheimer potential with adiabatic, relativistic and radiative corrections is used in calculations of the scattering lengths and the mass-dependent shifts of the rotationless vibrational levels with fixed and varying effective masses. The shifts are compared with established values and it is demonstrated that the semi-classical formula for the scattering length accounts well for the effect of changing the mass. A perturbing potential that is equivalent to a change in mass is derived and it is compared to a published local non-adiabatic potential.