Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

The authors review progress in understanding the nature of atomic collisions occurring at temperatures ranging from the millidegrees Kelvin to the nanodegrees Kelvin regime. The review includes advances in experiments with atom beams, light traps, and purely magnetic traps. Semiclassical and fully quantal theories are described and their appropriate applicability assessed. The review divides the subject into two principal categories: collisions in the presence of one or more light fields and ground-state collisions in the dark.

Experiments and theory in cold and ultracold collisions

Photoassociation is the process in which two colliding atoms absorb a photon to form an excited molecule. The development of laser-cooling techniques for producing gases at ultracold !!1 mK" temperatures allows photoassociation spectroscopy to be performed with very high spectral resolution. Of particular interest is the investigation of molecular states whose properties can be related, with high precision, to the properties of their constituent atoms with the “complications” of chemical binding accounted for by a few parameters. These include bound long-range or purely long-range vibrational states in which two atoms spend most or all of their time at large internuclear separations. Low-energy atomic scattering states also share this characteristic. Photoassociation techniques have made important contributions to the study of all of these. This review describes what is special about photoassociation spectroscopy at ultracold temperatures, how it is performed, and a sampling of results including the determination of scattering lengths, their control via optical Feshbach resonances, precision determinations of atomic lifetimes from molecular spectra, limits on photoassociation rates in a Bose-Einstein condensate, and briefly, production of cold molecules. Discussions are illustrated with examples on alkali-metal atoms as well as other species. Progress in the field is already past the point where this review can be exhaustive, but an introduction is provided on the capabilities of photoassociation spectroscopy and the techniques presently in use.

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Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering

This paper describes program LEVEL, which can solve the radial or one-dimensional Schrodinger equation and automatically locate either all of, or a selected number of, the bound and/or quasibound levels of any smooth single- or double-minimum potential, and calculate inertial rotation and centrifugal distortion constants and various expectation values for those levels. It can also calculate Franck–Condon factors and other off-diagonal matrix elements, either between levels of a single potential or between levels of two different potentials. The potential energy function may be defined by any one of a number of analytic functions, or by a set of input potential function values which the code will interpolate over and extrapolate beyond to span the desired range.

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LEVEL: A computer program for solving the radial Schrödinger equation for bound and quasibound levels

Dissociation energy and long range interatomic potential of diatomic molecules from vibrational spacings of higher levels

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Dissociation Energy and Long‐Range Potential of Diatomic Molecules from Vibrational Spacings of Higher Levels

A reanalysis of the spectroscopic data for ground-state iodine yields improved rotational constants and vibrational energies which are used to compute a new RKR potential. Polynomial representations of the vibrational energies and rotational constants are presented which fit all the data to within the respective experimental precision of Verma and of Rank and Baldwin. New approaches are introduced for separately obtaining the rotational Bυ and Dυ constants and for estimating error bounds for computed RKR turning points.

Molecular Constants and Internuclear Potential of Ground-State Molecular Iodine

Dissociation energies of diatomic moleculles from vibrational spacings of higher levels: application to the halogens*

The need for better potential-energy models for atom–molecule and molecule–molecule interactions is discussed and the utility of the exchange–coulomb (XC) model is critically examined, by fitting a potential based on it to new high-resolution discrete infrared data for the He–CO Van der Waals molecule. In addition to explaining the observed spectrum as well as does an optimized empirical potential previously determined from the same data, the resulting XC surface is expected to be more realistic in regions not directly sampled by the fitted data.

Improved modelling of atom–molecule potential-energy surfaces: illustrative application to He–CO

In an attempt to elucidate the discrepancy between the theoretical and experimental dissociation energies of H2, accurate binding energies and term differences have been computed for the 15 vibrational levels using the Kolos and Wolniewicz clamped‐nuclei potential with its various corrections. The results suggest possible interpretations of the discrepancy. In one of these an extrapolation method is introduced which combines experimental term differences with computed binding energies for the uppermost levels to yield the dissociation energy; this result is in accord with the experimental value of Herzberg and Monfils. The effect of uncertainties in the values of the natural constants is considered. Apparent inconsistencies between previously computed vibrational energies are explained.

Robert J. LeRoy

Papers

Dissociation Energy and Long‐Range Potential of Diatomic Molecules from Vibrational Spacings of Higher Levels

Molecular Constants and Internuclear Potential of Ground-State Molecular Iodine

Dissociation energies of diatomic moleculles from vibrational spacings of higher levels: application to the halogens*

Improved modelling of atom–molecule potential-energy surfaces: illustrative application to He–CO

Dissociation Energy and Vibrational Terms of Ground‐State (X 1Σg+) Hydrogen