Frequency Dependence of the 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; 0, ω, ω) = 45.2 a.u.;λ = 6328 Å,χzzzz(− ω, 0, 0, ω) = 43.6 a.u.; χzzzz(0; 0, 0, 0) = 42.6 a.u. The experimental value of χzzzz(− ω; 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%.