Comparison of quasiclassical and exact dipole moments for bound-free transitions in hydrogen

A quasiclassical expression for the bound-free dipole moment in hydrogen is found to be in good agreement with the exact Gordon formula values. The approximation has the advantage of clearly indicating the dependence of the dipole moment on the initial- and final-state parameters. The quasiclassical expression is derived for small angular momentum states. The lowest-order angular momentum correction is required for good agreement in the visible frequency range. This correction term scales as ω(l+1)3 rather than ω(l+1/2)3 as might be expected for the Langer modification