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

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.