Einstein A Coefficient for the Λ Doublet Transitions of the Ground State of OH

Abstract

FOR some time now there has been some uncertainty in the literature of the correct value for the Einstein A coefficients for the ground state Λ doublet transitions of OH. Barrett¹ calculated A = 2.66 × 10⁻¹¹ sec⁻¹ for the 1,667 Mc/s line using a matrix element |μ_ij|² taken from Dousmanis, Sanders and Townes². This element is incorrect both because the form of its dependence on the rotational quantum number J was incorrectly given as [(J + 1)(2J + 1)]⁻¹, and also because the element was incorrectly defined as (1). The appropriate definition is given below. The correct J-dependence, which is [J(J + 1)]⁻¹, was given by Meyer³, in connexion with the Stark-effect determination of the OH dipole moment, μ because Meyer used an electric field directed so that only transitions of type ΔM_J = 0 occurred between the magnetic sub-levels characterized by quantum number M_J, the problem of combining these elements with those for which ΔM_J = ±1 to form an overall matrix element μ_ij was not encountered. To derive the overall matrix element between the Λ doublet levels of the ground state of OH, Goss and Weaver⁴ combined the correct J-factor of Meyer with standard relative intensity formulae for hyperfine transitions as given by Townes and Schawlow⁵ to derive A = 0.9640 × 10⁻¹¹ sec⁻¹ for the 1,667 Mc/s line. They also used the most recent values for the OH dipole moment and the fine structure interaction constant, the calculation making use of the theory for intermediate coupling between Hunds's cases (a) and (b), as given by Dousmanis, Sanders and Townes².