Many-electron, many-photon theory of nonlinear polarizabilities

Abstract

We present a many-electron, many-photon (MEMP) nonperturbative theory of nonlinear static and dynamic polarizabilities of polyelectronic atoms and molecules. The time-dependent, dynamic polarization is treated as a frequency-dependent problem with the Floquet assumption that the computed quantities are averaged over a cycle. The MEMP theory defines a non-Hermitian problem whose efficient solution yields a complex eigenvalue to all orders in the interelectronic and the electron ac or dc field interactions. When the real part is subtracted from the unperturbed energy of the free state, we are left with the frequency-dependent total energy shift Δ(ω). This is then fitted to a polynomial expansion whose coefficients are the required polarizabilities representing the induced polarization averaged over a cycle. Results are given for the α, α(ω), and γ, γ(ω) of H and of Li−. For Li−, only α had been computed earlier by many-electron approaches. The dynamic α (ω) was computed before in a quasi-classical approximation with a simple wave function. Comparison shows a qualitative agreement but not a quantitative one.