Radiative Recombination in ultracold plasmas

A symmetrized version of the Heisenberg correspondence principle is proposed and is used to derive ``classical" radial matrix elements for continuum-bound transitions. Classical cross sections for radiative recombination at low energies into a particular $n,\ell$ state are then derived and shown to be in excellent agreement with the quantal results. Classical cross sections also provide excellent agreement with the Kramers formula. Semi-classical transition probabilities for radiative cascade out of low $l$ Rydberg states have been derived. Results for radiative recombination into and radiative transitions out of various $n, \ell states$ are illustrated.