By implementing a time-independent, nonperturbative many-electron, many-photon theory (MEMPT), cycle-averaged complex eigenvalues were obtained for the He atom, whose real part gives the field-induced energy shift, Δ(w1, F1; w2, F2, Mathematical bold italic small phi sign), and the imaginary part is the multiphoton ionization rate, Γ(w1, F1; w2, F2, Mathematical bold italic small phi sign), where w is the frequency, F is the field strength and Mathematical bold italic small phi sign is the phase difference. Through analysis and computation we show that, provided the intensities are weak, the dependence of Γ(w1, F1; w2, F2, Mathematical bold italic small phi sign) on Mathematical bold italic small phi sign is simple. Specifically, for odd harmonics, Γ varies linearly with cos(Mathematical bold italic small phi sign) whilst for even harmonics it varies linearly with cos(2Mathematical bold italic small phi sign). In addition, this dependence on Mathematical bold italic small phi sign holds for Δ(w1, F1; w2, F2, Mathematical bold italic small phi sign) as well. These relations may turn out to be applicable to other atomic systems as well, and to provide a definition of the weak field regime in the dichromatic case. When the combination of (w1, F1) and (w3, F2) is such that higher powers of cos(Mathematical bold italic small phi sign) and cos(2Mathematical bold italic small phi sign) become important, these rules break down and we reach the strong field regime. The herein reported results refer to Γ(w1, F1; w2, F2, Mathematical bold italic small phi sign) and Δ(w1, F1; w2, F2, Mathematical bold italic small phi sign) for He irradiated by a dichromatic ac-field consisting of the fundamental wavelength λ = 248 nm and its 2nd, 3rd and 4th higher harmonics. The intensities are in the range 1.0 × 1012-3.5 × 1014 W/cm2, with the intensity of the harmonics being 1-2 orders of magnitude smaller. The calculations incorporated systematically electronic structure and electron correlation effects in the discrete and in the continuous spectrum, for1S,1P,1D,1F,1G, and1H two-electron states of even and odd parity.
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