Low-frequency theory of multiphoton ionization. II. General formulation and further results for ionization of H(1s)

Abstract

The ac quasienergy for an atom irradiated by a strong field of low frequency ω can be expressed as an asymptotic expansion in powers of ${\mathrm{\omega }}^2$, with coefficients that depend on the field strength F. In this paper we give a prescription for calculating these coefficients for arbitrary polarization, and we show explicitly that the leading term of the expansion is the cycle-averaged dc quasienergy. We have calculated the first four coefficients in the case of ground-state atomic hydrogen in a linearly polarized field, and we present a table of these coefficients for various values of F. As an application, we compare the estimate of the ac width obtained from the first four terms of the expansion with the exact value when the (linearly polarized) light has the wavelength 616 nm and an intensity in the range 3×${10}^{13}$ to 3×${10}^{14}$ W/${\mathrm{cm}}^2$; the sum of the first four terms give an excellent interpolation through the exact results (though does not reproduce the resonance structure). When the F-dependent coefficients are expanded in powers of ${\mathit{F}}^2$ to yield a double series ${\mathit{tsum}}_{\mathit{m}}$ ${\mathit{tsum}}_{\mathit{n}}$ ${\mathrm{\beta }}_{2\mathit{n}}^{2\mathit{m}}$F 2n${\mathrm{\omega }}^{2\mathit{m}}$, the constant coefficients ${\mathrm{\beta }}_{2\mathit{n}}^{2\mathit{m}}$ are real and (in the case of atomic hydrogen) are rational numbers that can be evaluated exactly. We verify, for m=1 and for linearly or circularly polarized light, that in the large-n limit the ${\mathrm{\beta }}_{2\mathit{n}}^{\left(2\mathrm{}\mathit{m}\right)}$ satisfy an asymptotic formula of the Bender-Wu type. We show that just 19 coefficients ${\mathrm{\beta }}_2^{\left(2\mathrm{}\mathit{m}\right)}$ are needed to accurately reproduce the second-order (order ${\mathit{F}}^2$) ac shift and width over a remarkably large range of frequencies.