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- W2077978259 abstract "We consider the lowest-order nonlinear contributions to the electric dipole moment induced in closed-shell atomic systems by intense electromagnetic fields. These contributions are comprised of two terms: (i) an intensity-dependent refractive-index coefficient ${ensuremath{chi}}_{mathrm{zzzz}}(ensuremath{-}ensuremath{omega};ensuremath{omega},ensuremath{omega},ensuremath{-}ensuremath{omega})$, and (ii) a third-harmonic coefficient ${ensuremath{chi}}_{mathrm{zzzz}}(ensuremath{-}3ensuremath{omega};ensuremath{omega},ensuremath{omega},ensuremath{omega})$. The problem is formulated within the framework of time-dependent Hartree-Fock perturbation theory. The expressions for ${ensuremath{chi}}_{mathrm{zzzz}}(ensuremath{-}ensuremath{omega};ensuremath{omega},ensuremath{omega},ensuremath{-}ensuremath{omega})$ and ${ensuremath{chi}}_{mathrm{zzzz}}(ensuremath{-}3ensuremath{omega};ensuremath{omega},ensuremath{omega},ensuremath{omega})$ contain third- and lower-order frequency-dependent wave functions. It is found possible to eliminate the third-order terms from the expressions for the $ensuremath{chi}'mathrm{s}$. A variational method for solving the required second-order integrodifferential equations is proposed. Numerical results for helium are obtained. A zero-frequency Hartree-Fock hyperpolarizability for helium of 35.8 a. u. is obtained which agrees reasonably well with the previous Hartree-Fock calculations of Sitter and Hurst. The Hartree-Fock wave functions give static hyperpolarizability results which are about 17% smaller than more accurate calculations. A static second-order function approximation for calculating the $ensuremath{chi}'mathrm{s}$ is developed and is shown to be useful for obtaining the $ensuremath{chi}'mathrm{s}$ at low frequencies with a substantial saving in computing effort." @default.
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- W2077978259 date "1971-11-01" @default.
- W2077978259 modified "2023-10-17" @default.
- W2077978259 title "Hartree-Fock Theory of Third-Harmonic and Intensity-Dependent Refractive-Index Coefficients" @default.
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- W2077978259 doi "https://doi.org/10.1103/physreva.4.1760" @default.
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