Transition rate dependence on the improved turning point in ADK-theory

Abstract

Estimation of transition rate of ionization of atoms for short range potential, based on assumptions of Keldysh approximation, shows that short-range potential does not affect the energy of the final state of ejected electron, when it leaves the atom. Coulomb potential is then treated as perturbation of final state energy leading to the ADK-theory. But Coulomb interaction was not originally included in calculating the turning point. This we corrected in [1], though only for fields with intensities below those of the atomic field. But as the ADK-theory was recently extended to the case of superstrong fields, our calculations now include extension of potential range up to 1017 W/cm2; this leads to the shift of position of the turning point τ, which then influences transition rates for atoms in the low-frequency electromagnetic field of superstrong lasers. On Figs. 1 and 2 obtained from our calculations the value of Z was switched from 1 to 10 at field intensity of 5 × 1013 W/cm2 (atomic unit system), which is done for the first time ever. The second figure also indicates an enormous activity at fields 1013 W/cm2, which is due to strong tunneling effect for this energies of laser field. After that, there is saturation at a very low level of transition rate for fields from 1015 W/cm2 to 1017 W/cm2.

Transition rate dependence on the atom charge states, Z

“…4 one has results of cADK, and obtains the strongest tunnel effect at 10 13 W/cm 2 , differing from the ADK case (Fig. 3), which gives this effect at 10 14 W/cm 2 , in accordance with our earlier result [1]. W ADK plotted vs. laser field intensities and atom charge states, Z…”

“…Abstract: Here are shown two different transition rates, one obtained in the ADK-theory [1,2] and the other one for ADK result with turning point corrected with the Coulomb interaction -let us denote it cADK [1,3], in both cases the changing of charge states Z of atoms was performed. If plotted for the fields from 10 12 W/cm 2 to 10 17 W/cm 2 and for Z = 1 to Z = 10, the two variants give behavior which were not predicted before, Fig.…”

Transition Rate Dependence on the Non-Zero Initial Momentum in the ADK-Theory

“…From this equation, in the paper [9] there was obtained the following expression for turning point (in the zero-order approximation)…”

“…Theoretical framework was given by Keldysh [1]; it was further developed, resulting in emerging of the ADK--theory (Ammosov, Delone, Krainov) [2]. Some recent papers [3][4][5] improved it further, but in them the authors always assumed that the ionized electrons are leaving the atom with zero initial momentum (except say in [6,7]). Except for aforementioned papers, in [8] it was given thorough calculation of dependence of the initial momentum on the parabolic coordinate η.…”

“…The external (Coulomb) potential was then treated as perturbation of final state energy, resulting in ADK-theory [2]. In [9] in constructing the ADK--theory the Coulomb interaction was included into calculations for the turning point τ , which was not done before. Also, it was always assumed that the initial momentum of the electron leaving the atom is zero.…”