The Asymmetric Rotor. VI. Calculation of Higher Energy Levels by Means of the Correspondence Principle

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Abstract
The rotational levels of the rigid asymmetric rotor can be calculated by means of the correspondence principle. It is shown that the quantum-number ratio K/J(J+1) is the complete elliptic integral of the third kind tabulated by Heuman in the case of the energy levels of a hypothetical rotor with reciprocal moments of inertia −1, κ, and +1. The parameter of the integral is the reduced-energy ratio E(κ)/J(J+1), and its modulus is a function of both the reduced-energy ratio and asymmetry parameter. A double inverse interpolation has been made by Heuman's table to give the energy ratio directly in terms of quantum-number ratio and asymmetry. Power series expansions have been developed around limiting cases and around each point in the table, so that formulas for interpolation and estimating errors are available.

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