Einstein A Coefficients for the 18 cm Transitions of OH

Abstract

A NUMBER of recent papers^1–6 have dealt with the values of the Einstein A coefficients describing spontaneous emission for the hyperfine split ²π_3/2, J=3/2, Λ-doublet transition in OH. These values are important in connexion with determinations of the interstellar abundance of OH and the non-Boltzmann population of the hyperfine levels. At least four different sets of calculated values have been presented. All previous authors, however, have attacked the problem by the methods outlined in the books of Condon and Shortley⁷ and Townes and Schawlow⁸. Because these methods involve complicated algebraic manipulation and, moreover, a pertinent matrix element listed by Townes and Schawlow has been shown to be incorrect, we decided to approach the problem differently, using Racah algebra and the transformation theory of the group of all rotations in free space^9–11. This method gives a check on previous calculations; it also provides a general formula for the squared matrix elements in the A coefficient which is applicable for any multipole transition within or between J levels in a Hund's case (a) molecule containing a single magnetic nucleus of spin I. Our calculation shows that Turner's set of values² is correct, contrary to Lide's recent note¹, although we agree with Lide's criticisms of certain expressions in Turner's paper. The more general approach presented here is also, in some ways, easier than the previous calculations in that the sum rules and orthogonality relations of the general theory allow one to apply checks to the calculation at various stages.