Above-threshold ionization with highly charged ions in superstrong laser fields. I. Coulomb-corrected strong-field approximation

Abstract

Aiming at the investigation of above-threshold ionization in superstrong laser fields with highly charged ions, we develop a Coulomb-corrected strong-field approximation (SFA). The influence of the Coulomb potential of the atomic core on the ionized electron dynamics in the continuum is taken into account via the eikonal approximation, treating the Coulomb potential perturbatively in the phase of the quasiclassical wave function of the continuum electron. In this paper the formalism of the Coulomb-corrected SFA for the nonrelativistic regime is discussed, employing velocity and length gauge. Direct ionization of a hydrogenlike system in a strong linearly polarized laser field is considered. The relation of the results in the different gauges to the Perelomov-Popov-Terent'ev imaginary-time method is discussed.

Spin-asymmetric laser-driven relativistic tunneling frompstates

“…The time variable is changed to the phase variable η in Eq. (2) and the η-integral is calculated with the saddle point method; η s is the saddle point value for the phase η [44]. There exists no asymmetry between the ionization probabilities from the spin up and down states 2s + (m j = 1/2) and 2s − (m j = −1/2), i.e., the ionization probabilities are equal.…”

“…The matrix element M in the Coulomb corrected SFA reads [44]: where the final state ψ V C is the Eikonal-Coulomb-Volkov-state [44], i.e., the wave function in the eikonal approximation for the electron in continuum under the action of the laser and Coulomb field of the atomic core; E(η) = E 0 cos(ωη) is the laser field with the phase η = t − z/c, c is the speed of light, andψ i is the dressed initial bound state which is the solution of the following Schrödinger equation [44] i∂ tψi = H Bψi ,…”

Strong-field ionization via a high-order Coulomb-corrected strong-field approximation

“…Forseeing the subsequent calculation we can insert the typical value for the coordinate x ∼ √ κ/E s and time t ∼ κ/E s into the perturbation of the original differential equation: V ∼ Z/x ∼ Z √ E s /κ and ∂ xx S ∼ Vt/x 2 ∼ Z √ E s /κ and see that the quantum term is of the same order as the potential one and the simultaneous perturbative treatment of both of terms is justified when E 0 E a , see equation (22) in [31]. In the usual eikonal approximation, in particular in [14,17], the last quantum term ∂ xx S is neglected and the atomic potential is treated perturbatively in the eikonal equation (10).…”

Limits of Strong Field Rescattering in the Relativistic Regime

“…where p(η) = p+A(η)+T(η, p), q(η) = q+A(η)+T(η, q) are the relativistic kinetic momentum after the recollision and during excursion, respectively, the drift momentum T(η, p) =ẑ[p · A(η) + A 2 (η)/2]/c, and V (r) is the Coulomb-potential of the atomic core [58]. The findings presented here are not changed for CTMC calculations with more accurate potentials using numerical Dirac−Fock electron densities [59].…”

“…flux is calculated via RCCSFA based on the Dirac equation [47][48][49]. The wave function of the electron ionized from a hydrogen-like atomic bound state |φ 0 (η) in a strong laser field E(η) = −A (η), with the vector-potential A(η) = (E 0 /ω) sin(η)x, and the laser phase η = ω(t − z/c), is given by [49]:…”