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Journal of Physics B Atomic Molecular and Optical Physics

S-wave scattering lengths and effective ranges for collisions of ground state Be atoms

Michael J. Jamieson, A. S.‐C. Cheung, Henni Ouerdane, G. H. Jeung, Neri Geum

Published Aug 28, 2007• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/40/17/016

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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.
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.
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.
We calculate the s-wave scattering length and effective range and the p-wave scattering volume for 7 Li atoms interacting with 133 Cs atoms via the X 1 Σ + molecular potential. The length and volume are found by fitting the log-derivative of the zero energy wave function evaluated at short range to a long range expression that accounts for the leading van der Waals dispersion potential and then incorporating the remaining long range dispersion contributions to first order. The effective range is evaluated from a quadrature formula. The calculated parameters are checked from the zero energy limits of the scattering phase shifts. We comment on ill-conditioning in the calculated s-wave scattering length.
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.
We present ab initio potentials for ground state lithium, sodium, potassium and rubidium atoms interacting with ground state chromium atoms via the 6 Σ + and 8 Σ + states of the corresponding dimers. Each potential is matched to the leading van der Waals dispersion energy − C 6 / R 6 − C 8 / R 8 and an exchange energy; we list the values of C 6 , C 8 and the exchange fitting parameters. We present calculated values from quantal and semi-classical approximations for the s-wave scattering length and effective range and the p-wave scattering volume for collisions of each of the alkali-metal atoms lithium, sodium, potassium and rubidium with 52 chromium atoms and comment on s-wave scattering by 53 chromium atoms.
For elastic scattering of 133 Cs atoms by 85 Rb and 87 Rb atoms, interacting via the X 1 Σ + and a 3 Σ + molecular states of RbCs, calculations are presented of the scattering length and the effective range and also of two volume parameters, one for low energy p-wave scattering and one for the energy of an ensemble of fermions. The calculations are performed by various methods, with several representations of the interatomic potentials, including new ab initio potentials presented here. It is shown how the calculated data may be corrected to include the influence of the long range interactions, thus removing the need for numerical solutions of the radial Schrödinger equation at very large interatomic separations. The sensitivity of the results to the choice of potentials, to the van der Waals dispersion coefficient C 6 and to the reduced mass of the colliding atoms is explored, and is found to be great.