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A generating function for associated Laguerre polynomials and Louck's recursion relations have been employed independently to formulate radial matrix elements of rn for g-fold (g = 2, 3) isotropic simple harmonic oscillators in terms of quantum numbers v and l. This paper gives all relevant matrix elements (vl|rn|v′l′) of rn for n = 1,2, …, 7 and the diagonal element of r8. Introduction of the quantities, V = 1 2 (v + v′ + g) and L = 1 2 (l + l′ + g − 2) , simplifies the expressions and reveals symmetries and patterns occurring as n increases. Results are compared with those for the one-fold oscillator and sample computer routines have been prepared for numerical evaluation of the matrix elements for g = 1, 2, 3.

Line intensities of the (21 1 0-000) I and (21 1 0-000) III bands of CO 2 have been measured at high resolution and fitted to F -factors of the form F ( m ) = (1 + ξm ) 2 to yield coriolis interaction coefficients, ξ, of 0.14 and 0.33, respectively. Explicit expressions are derived for these coefficients in terms of the molecular parameters and observed and calculated values are compared both for these bands and the previously measured (21 1 0-000) II , (11 1 0-000) I , and (11 1 0-000) II bands. A consistent choice of relative signs of the rotationless dipole moment matrix elements yields agreement within experimental error.

A computer listing of the diagonal F/sup 4/ and F/sup 6/ coefficients of Moret--Bailly (Cah. Phys., 15: 237 (1961)) was prepared for 2