On the validity of the JWKB approximation to radial integrals of electric multipole transitions between atomic Rydberg states

Semiclassical approximations to radial integrals for transitions between hydrogenic states are derived considering the conditions of their applicability as the quantum numbers vary. It is shown that the well known approximations derived using the correspondence principle fail in the case of low radial quantum numbers, even in the limit n to infinity . A modification of the eccentricity is then derived which corrects the approximation without changing the basic formulae. Results obtained with the improved expressions are also given.