Dipole moment matrix elements for the 1-0, 2-0, and 3-0 vibration-rotation bands of diatomic molecules

Abstract

Explicit expressions for the matrix elements of the dipole moment have been derived for the 1-0, 2-0, and 3-0 vibration-rotation bands of diatomic molecules. The derivation is based on a cubic dipole moment function and on radial wave functions obtained using a quintic power series expansion of the internuclear potential and third order perturbation theory. The results are given in the form of a rotationless matrix element multiplied by a rotational or Herman-Wallis factor. The expressions for the Herman-Wallis factors include the leading contributions from each dipole moment coefficient and have a reasonably simple form even in the case of the overtone bands. The rotationless matrix elements are similar to results obtained by Herman and Schuler except that their higher order terms are purposely omitted. The reason for this is discussed as are other approaches to the rotational problem which have incorporated a linear dipole moment function. It is pointed out that the results of the present theory for the case of CO are in very good agreement with the numerical treatment of CO by Young and Eachus. The actual comparison is given in a subsequent paper.