An accurate quantum expression for radiative transition between nearby Rydbergstates

Abstract

The paper gives three main results as follows. (1) An accurate quantumexpression of the radial matrix element for radiative dipole transition betweennearby Rydberg states. Its remarkable numerical accuracy is demonstrated over avery wide range of principal and orbital angular momentum quantum numberscovering low-lying states to very high Rydberg states. (2) A simple but accurateapproximation to a class of terminating hypergeometric functions whosethree arguments are large. This result essentially solves the problem ofextracting analytic properties and performing numerical computations of suchhypergeometric functions over a large range of values of the arguments which wereearlier regarded to pose difficulties. (3) A derivation of the formula ofthe radial dipole matrix element of the correspondence principle methodstarting from the corresponding quantum expression, which, to the bestof our knowledge, was not previously available in the literature.