Effect of an intense electromagnetic field on a weakly bound system

TLDR: In this article, a general basis for the formalism is developed, and it is then applied to find transition probabilities for any order of interaction for both linearly and circularly polarized plane-wave fields.

Abstract: The approximation method introduced by Keldysh is revised and extended. The technique is applicable to the photodetachment by a plane-wave field of an electron bound by a short-range potential. The approximation is to neglect the effect of the binding potential as compared to the field effects on the final state of the detached electron. By choice of a different gauge than that used by Keldysh, the formalism becomes very simple and tractable. A general basis for the formalism is developed, and it is then applied to find transition probabilities for any order of interaction for both linearly and circularly polarized plane-wave fields. The low-intensity, first-order limit and the high-intensity, high-order limit yield the correct results. Two intensity parameters are identified. The fundamental one is $z=\frac{{e}^{2}{a}^{2}}{4m\ensuremath{\omega}}$, where $a$ is the magnitude of the vector potential (in radiation gauge) of the field of circular frequency $\ensuremath{\omega}$. The second parameter is ${z}_{1}=\frac{2z\ensuremath{\omega}}{{E}_{B}}$, where ${E}_{B}$ is binding energy, and it becomes important only in the asymptotic case. With the assumption that the field leaves the neutral atomic core relatively unaffected, the formalism is applied to the example of the negative hydrogen ion irradiated by circularly or linearly polarized 10.6-\ensuremath{\mu}m radiation. Photodetachment angular distributions and total transition probabilities are examined for explicit intensity effects. It is found that total transition probability $W$ is not sensitive to intensity since $\frac{d(logW)}{d}$ ($logz$) retains low-intensity straight-line behavior up to quite high values of $z$. An important intensity effect is the major significance of higher-than-lowest-order terms when $z$ is large, especially for circular polarization. A sensitive indicator of intensity is the ratio of photodetachment probabilities in circularly and linearly polarized fields, which increases sharply with intensity. An investigation of the convergence of perturbation expansions gives the upper limit $zl[\frac{{E}_{B}}{\ensuremath{\omega}}]\ensuremath{-}\frac{{E}_{B}}{\ensuremath{\omega}}$, where the square bracket means "smallest integer containing" the quantity in brackets. This limit is $zl0.59$ for ${\mathrm{H}}^{\ensuremath{-}}$ in 10.6-\ensuremath{\mu}m radiation. The failure of perturbation theory is not necessarily manifest in qualitative ways. For example, it is not apparent in total photoelectron yield as a function of intensity.