A DISPERSION FORMULA FOR THE 2ND DYNAMIC HYPERPOLARIZABILITY AS EXEMPLIFIED BY HELIUM

A simple one-parameter formula: gamma(alpha-beta-gamma-delta)(-omega(sigma);omega-1,omega-2,omega-3) = gamma(alpha-beta-gamma-delta)(0;0,0,0)(1 - A(alpha-beta-gamma-delta)omega(L)2)-1 is introduced for the description of the dispersion in the second dynamic hyperpolarizability (gamma), where omega(delta) = omega-1 + omega-2 + omega-3 and omega(L)2 = omega(delta)2 + omega-1(2) + omega-2(2) + omega-3(2). This formula is appropriate for both atoms and the macroscopic hyperpolarizabilities of molecules (as defined with respect to laboratory axes). Its suitability is tested for helium for five different nonlinear optical processes (including, for the first time, the ac Kerr effect). A comparison is made between the values of A found by fitting ab initio gamma-values and those derived from a formula proposed by Hellwarth et al.