Turning point behaviour in tunnel ionization of atoms in super-strong, low-frequency laser fields

Ristić, V. M.; Radulović, M. M.; Premović, Tijana

doi:10.1002/lapl.200410187

Cited by 6 publications

(8 citation statements)

References 11 publications

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“…is small and could be neglected (for instance, in the case of potassium ionization in the laser field of 10 12 W/cm 2 , its value is 0.10876478, [1] [10]; also, it is extremely difficult to obtain so strong laser pulses as continuous -for higher intensities that is even impossible, for the moment), transition rate (1) shows behavior that was predicted many times theoretically [4]. Results of present calculation are shown on Figs.…”

Section: The Corrected Transition Ratementioning

confidence: 85%

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

Ristić¹,

Stevanović²,

Radulović³

2006

Laser Phys. Lett.

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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.

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Section: The Corrected Transition Ratementioning

confidence: 85%

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

Ristić¹,

Stevanović²,

Radulović³

2006

Laser Phys. Lett.

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“…This is, let us stress, all applicable only to multi-charged ions with the ion charge larger or equal to ten and with at least one electron left in a bound state. In our model the using of a laser whose intensity grows was assumed, thus giving atoms the opportunity to be multiply ionized via tunneling effect, while obtaining nucleus charge of Z ≥ 10, see, also [1,6]. Yet Fig.…”

Section: Final Remarksmentioning

confidence: 99%

“…In [3,5] it was noticed that, when constructing ADK-theory, the Coulomb interaction was not included into calculations for the turning point τ . This was not so important at the time as the laser fields in experiments were of the order of 10 12 W/cm 2 [6], and corresponding corrections were of the order of 0.10876478 [1,2,6].…”

Section: Introductionmentioning

confidence: 99%

Transition rate dependence on the atom charge states, Z

Ristić

Stevanović

2007

Laser Phys. Lett.

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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 1012 W/cm2 to 1017 W/cm2 and for Z = 1 to Z = 10, the two variants give behavior which were not predicted before, Fig. 1 and Fig. 2, showing in the cADK case pick which is not shown in the ADK case. But from results shown on Fig. 3 and Fig. 4, although they are giving only the illustration of the real behavior of the transition rates, the actual situation can be predicted. On Fig. 4 one has results of cADK, and obtains the strongest tunnel effect at 1013 W/cm2, differing from the ADK case (Fig. 3), which gives this effect at 1014 W/cm2, in accordance with our earlier result [1]. (© 2007 by Astro Ltd., Published exclusively by WILEY‐VCH Verlag GmbH & Co. KGaA)

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“…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.…”

Section: Introductionmentioning

confidence: 99%

“…Also, it was always assumed that the initial momentum of the electron leaving the atom is zero. Besides slight tries as in [6,7], until now there were no thorough estimations of what influence can have non-zero initial momentum on the processes thereof. Thus we are offering in this paper the calculation of transition rates for changeable initial momentum.…”

Section: Introductionmentioning

confidence: 99%

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

2007

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Tunneling regime, introduced by Keldysh, in the interaction of strong lasers with atoms has been now accepted as the reliable method for describing processes when low frequency lasers are involved. Yet it was always assumed that the ionized electrons are leaving the atom with zero initial momentum. Because we are interested in how non-zero momentum influences the transition probability of tunnel ionization, we obtained the exact expression for the momentum. Here the estimation of the transition probability with nonzero momentum included was conducted. Potassium atoms in the laser field whose intensity varied from 10 13 W/cm 2 to 10 14 W/cm 2 were studied. It seems that all energy of laser field is used for tunneling ionization process at the beginning of laser pulse -ionization probability is large. After that, with further action of laser pulse, ionization probability decreases, probably because part of laser pulse energy is used for increasing momentum of ejected electrons, leaving smaller amounts of light quanta available for ionization of remaining electrons. If laser pulse lasts long enough, then the amounts of light quanta available for ionization become larger, resulting in increase in ionization probability, now with greater starting energy of ejected electrons.

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Turning point behaviour in tunnel ionization of atoms in super-strong, low-frequency laser fields

Cited by 6 publications

References 11 publications

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

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

Transition rate dependence on the atom charge states, Z

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

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