EXPLICIT NONDIVERGENT FORMULAS FOR ATOMIC AND MOLECULAR DYNAMIC HYPERPOLARIZABILITIES

Two methods are used to develop nondivergent, compact, sum-over-states formulas for dynamic hyperpolarizabilities up to fifth order. Express ions for both atoms and molecules are given; those at fourth and fifth order for the first time. The fifth-order formula is related to such nonlinear optical phenomena as stimulated hyper-Raman scattering and t he self-induced intensity-dependent refractive index. Questions of tim e-reversal invariance are also discussed. Importantly, the derivations explicitly take into account secular divergences in a simple and clea r way.