FREQUENCY DEPENDENCE OF HIGHER SUSCEPTIBILITIES

Expressions for the susceptibilities appropriate to third harmonic generation, second harmonic generation, and the induced Kerr effect are derived using time-ordered time-dependent pertubation theory. These expressions are used to calculate the susceptibilities for atomic hydrogen and helium. Using a six-pole trial function we obtain for He λ = 6943 Å, χzzzz(-3ω; ω, ω, ω) =47.7 a.u.; λ = 6943 Å, χzzzz(- 2ω; ω, ω) = 45.2 a.u. ; λ = 6328 Å, χ,(-ω 0, 0, ω) = 43.6 a.u.; χzzzz(0; 0, 0, 0) =42.6 a.u. The experimental value of χzzzz(-w; 0, 0, ω) obtained from Kerr-effect measurements is 51.6±8:6. a.u. The calculations are checked by the use of a number of sum rules with the largest disagreement being 0.05%.