Relativistic theory of tunnel and multiphoton ionization of atoms in a strong laser field

Попов, В. С.; Karnakov, B. M.; Mur, V. D.; Pozdnyakov, S. G.

doi:10.1134/s1063776106050086

Cited by 27 publications

(26 citation statements)

References 23 publications

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“…We use Coulomb gauge, interaction of the atom, and the external electromagnetic field is described by means of the vector potential A in Eq. (4). We employ here the definition of the vector potential commonly used in atomic physics so that electric field and vector potential are related as c a t ■ To solve Eq.…”

Section: H 'M I = Ca ■ Amentioning

confidence: 99%

“…A relativistic modification of this theory was proposed in [4]. It is clear that such relativistic modification is indispensable if our goal is the proper description of the ionization phenomena occurring for the field intensities of the order of several units of 1 x 1022 W /cm 2 which are currently available [5], or if we are interested in ionization driven by high-frequency electromagnetic fields.…”

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confidence: 98%

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Relativistic calculation of the electron-momentum shift in tunneling ionization

Ivanov

2015

Phys. Rev. A

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We describe a procedure for the solution of the time-dependent Dirac equation. The procedure is based on the relativistic generalization of the matrix iteration method. We use this procedure to study electron-momentum distribution along the laser-beam propagation direction for the process of the tunneling ionization of a hydrogen atom. We found, in agreement with the experimental observations [C. Phys. Rev. Lett. 106, 193002 (2011)], that relativistic effects lead to appreciable deviation of the distribution from the strict left-right symmetry present in the nonrelativistic case. The expectation value of the momentum along the laser-beam propagation direction grows linearly with intensity and follows closely the behavior of the expectation value of the kinetic energy divided by the speed of light. These features agree with the experimental results [C.Keldysh's pioneering work [1] and its subsequent develop ments [2,3] laid out a basis of our current understanding of the main features of the strong field ionization of atoms and molecules. According to this theory ionization phenomena can be separated into two broad classes: the multiphoton and tunneling ionization. Whether an ionization process can be characterized as a multiphoton or a tunneling one depends on the value of the Keldysh parameter y = Wy/2I/E (where w and E are the frequency and strength of the laser field, respectively, and I is the ionization potential of the target in atomic units). Values of y <£ 1 correspond to the tunneling regime, which interests us in the present work.Original Keldysh theory relied on a completely nonrela tivistic approach. A relativistic modification of this theory was proposed in [4]. It is clear that such relativistic modification is indispensable if our goal is the proper description of the ionization phenomena occurring for the field intensities of the order of several units of 1 x 1022 W /cm 2 which are currently available [5], or if we are interested in ionization driven by high-frequency electromagnetic fields. However, even for the infrared (IR) laser fields of much lower intensity, relativistic effects can manifest themselves. Even though the momentum of a photon is small, for the processes with participation of a large number of photons the total momentum delivered to the atom can be non-negligible. Smeenk et al. [6] report results of the study of the ionization process driven by the laser pulses with wavelengths of 800 and 1400 nm under experimental conditions where a large number of photons (30-50) is absorbed. The experiment demonstrated that the average electron-momentum component along the laser prop agation direction grows linearly with the laser field intensity and is nearly equal to the average photoelectron energy divided by the speed of light. Another example is provided by the recent study [7] of momentum sharing between the photoelectron and the parental ion in the processes of single-and multiphoton ionization. It was found [7] that momentum sharing is very different for the two processes, with intens...

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Section: H 'M I = Ca ■ Amentioning

confidence: 99%

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confidence: 98%

Relativistic calculation of the electron-momentum shift in tunneling ionization

Ivanov

2015

Phys. Rev. A

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“…В ионах с зарядом высокой кратности (релятивистский случай) радиальная волно-вая функция валентного электрона имеет вид биспинора (4) с асимптотикой (5). Безразмерные константы C ql и C qκ определяются зарядом ядра и структурой ионного остова.…”

Section: асимптотический вид волновой функции релятивистского электроunclassified

“…Их рассмотрению для водородоподобных ионов посвящены работы [4], [5]. Обобщение этих результатов на более сложные ионы требует релятивистского обобщения известного в атомной и молекулярной физике метода квантового дефекта (см.…”

Section: Introductionunclassified

Квазиклассическое Приближение Для Уравнения Дирака В Центральном Поле

Zon¹,

Kornev²

2012

ТМФ

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“…The ionization rates for the K-G and Dirac equations were calculated using the imaginary time method in [8,9]. Here, using the S-matrix approach, a novel ionization rate is derived for the K-G equation.…”

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confidence: 99%