Vibration-rotational and rotational intensities for CO isotopes

Abstract

Dipole moment matrix elements have been computed for the five most abundant isotopes of CO. The wave functions utilized were obtained from a direct solution of the Schrödinger equation with an accurate RKR potential. The dipole moment function, in the form of a Padé approximant, was chosen to reproduce the experimental measurements near equilibrium, to have the proper united and separated atom limits, and to have the correct long-range asymptotic functional dependence on internuclear separation. Because of the large number of transitions involved, and to facilitate applications, the squares of the dipole moment matrix elements were fitted by a least-squares procedure to polynomials in v and J. Predictions for the 5-0 and 6-0 rotationless matrix elements and Herman-Wallis coefficients are given, and their dependence on the isotopic reduced mass is discussed. For the pure rotational band, v = v′ = 0, explicit Einstein A values and transition frequencies were calculated for the three most abundant isotopes for J up to 55. The corresponding dipole moment matrix elements were also fitted to simple polynomials in m and the dependence of the coefficients on the reduced mass given. The present results incorporate the most accurate and extensive intensity measurements and theoretical dipole moment function data for any heteronuclear diatomic molecule. In view of this, because of the importance of the CO laser, the accuracy of the spectral frequencies, and the ubiquity of the CO molecule, it is reasonable to expect that some of these lines, in particular, in the fundamental band of 12C 16O, can serve as laboratory standards for intensity measurements.