The multiphoton ionization rate and the energy shift of atoms interacting with weak dichromatic fields with commensurate frequencies are simple functions of the phase difference

By implementing a time-independent, nonperturbative many-electron, many-pho ton theory (MEMPT), cycle-averaged complex eigenvalues were obtained for th e He atom, whose real part gives the field-induced energy shift, Delta(omeg a (1), F-1; omega (2), F-2, phi), and the imaginary part is the multiphoton ionization rate, Gamma(omega (1),F-1; w(2), F-2, phi), where omega is the frequency, F is the field strength and cp is the phase difference. Through analysis and computation ive show that, provided the intensities are weak, the dependence of Gamma(omega (1), F-1; omega (2), F-2, phi) on phi is simp le. Specifically, for odd harmonics, Gamma varies linearly with cos(phi) wh ilst for even harmonics it varies linearly with cos(2 phi). In addition, th is dependence on phi holds for Delta(omega (1), F-1 omega (2), F-2, phi) as well. These relations may turn out to be applicable to other atomic system s as well, and to provide a definition of the weak field regime in the dich romatic case. When the combination of (omega (1), F-1) and (omega (2), F-2) is such that higher powers of cos(phi) and cos(2 phi) become important, th ese rules break down and we reach the strong field regime. The herein repor ted results refer to Gamma(omega (1), F-1; omega (2), F-2, phi) and Delta(o mega (1), F-1; omega (2), F-2, phi) for He irradiated by a dichromatic ac-f ield consisting of the fundamental wavelength lambda = 248 nm and its 2nd, 3rd and 4th higher harmonics. The intensities are in the range 1.0 x 10(12) -3.5 x 10(14) W/cm(2), with the intensity of the harmonics being 1-2 order s of magnitude smaller. The calculations incorporated systematically electr onic structure and electron correlation effects in the discrete and in the continuous spectrum, for S-1; P-1; D-1; F-1, (1)G, and H-1 two-electron sta tes of even and odd parity.