One-photon double ionization of helium: a heuristic formula for the cross section

Without a formal derivation, we propose a formula for the total and single-differential cross in the problem of one-photon double ionization of an atom. The formula is benchmarked against accurate experimental data for the total cross section of helium. Furthermore, a direct comparison with ab initio calculations for the double ionization of Li+ suggests that the framework is valid for the entire helium isoelectronic sequence. To this end, we introduce a formula for the double ionization of lithium, as well as for the triple ionization of lithium and beryllium

Nonsequential Two-Photon Double Ionization of Atoms: Identifying the Mechanism

We develop an approximate model for the process of direct (nonsequential) two-photon double ionization of atoms. Employing the model, we calculate (generalized) total cross sections as well as energy-resolved differential cross sections of helium for photon energies ranging from 39 to 54 eV. A comparison with results of \textit{ab initio} calculations reveals that the agreement is at a quantitative level. We thus demonstrate that this complex ionization process is fully described by the simple model, providing insight into the underlying physical mechanism. Finally, we use the model to calculate generalized cross sections for the two-photon double ionization of neon in the nonsequential regime.Comment: 4 pages, 4 figure

Breakdown of the nonrelativistic approximation in superintense laser-matter interactions

We study the breakdown of the nonrelativistic approximation in the multiphoton ionization of atomic hydrogen by some intense x-ray laser pulse, in a regime where the dipole approximation is no longer valid. To this end, both the time-dependent Dirac equation as well as its nonrelativistic counterpart, the time-dependent Schrödinger equation, are solved within an ab initio numerical framework. It is demonstrated that a recently developed semirelativistic Schrödinger equation for superintense laser fields [Lindblom et al., Phys. Rev. Lett. 121, 253202 (2018)] yields results in excellent agreement with the fully relativistic treatment. The semirelativistic equation is then used in an investigation of the role of higher-order beyond-dipole corrections to the laser-matter interaction. The result of the present study can be summarized into two main findings: (1) relativistic effects predict a blueshift of the multiphoton ionization spectrum, and (2) higher-order beyond dipole corrections (beyond the leading-order term) indicate a corresponding redshift of the photoelectron spectrum. However, the two shifts turn out to be of the same order of magnitude, effectively leading to a net cancellation of their respective contributions. This apparent cancellation effect raises an important question: Is the distinction between relativistic blueshifts and higher-order beyond dipole redshifts meaningful from an experimental point of view? The result of the present study indicates that the answer is negative because the two effects nonetheless cannot be measured separately. Therefore, instead, we suggest that the present findings should merely be taken as a demonstration that caution should be exercised when higher-order beyond-dipole and relativistic corrections are to be taken into account in approximation schemes in the modeling of superintense laser-matter interactions.publishedVersio

Multiphoton ionization and stabilization of helium in superintense xuv fields

Multiphoton ionization of helium is investigated in the superintense field regime, with particular emphasis on the role of the electron-electron interaction in the ionization and stabilization dynamics. To accomplish this, we solve ab initio the time-dependent Schr\"odinger equation with the full electron-electron interaction included. By comparing the ionization yields obtained from the full calculations with corresponding results of an independent-electron model, we come to the somewhat counterintuitive conclusion that the single-particle picture breaks down at superstrong field strengths. We explain this finding from the perspective of the so-called Kramers-Henneberger frame, the reference frame of a free (classical) electron moving in the field. The breakdown is tied to the fact that shake-up and shake-off processes cannot be properly accounted for in commonly used independent-electron models. In addition, we see evidence of a change from the multiphoton to the shake-off ionization regime in the energy distributions of the electrons. From the angular distribution it is apparent that correlation is an important factor even in this regime

A Schr\"{o}dinger equation for relativistic laser-matter interactions

A semi-relativistic formulation of light-matter interaction is derived using the so called propagation gauge and the relativistic mass shift. We show that relativistic effects induced by a super-intense laser field can, to a surprisingly large extent, be accounted for by the Schr{\"o}dinger equation, provided that we replace the rest mass in the propagation gauge Hamiltonian by the corresponding time-dependent field-dressed mass. The validity of the semi-relativistic approach is tested numerically on a hydrogen atom exposed to an intense XUV laser pulse strong enough to accelerate the electron towards relativistic velocities. It is found that while the results obtained from the ordinary (non-relativistic) Schr{\"o}dinger equation generally differ from those of the Dirac equation, merely demonstrating that relativistic effects are significant, the semi-relativistic formulation provides results in quantitative agreement with a fully relativistic treatment

Quantitative modeling of spin relaxation in quantum dots

We use numerically exact diagonalization to calculate the spin-orbit and phonon-induced triplet-singlet relaxation rate in a two-electron quantum dot exposed to a tilted magnetic field. Our scheme includes a three-dimensional description of the quantum dot, the Rashba and the linear and cubic Dresselhaus spin-orbit coupling, the ellipticity of the quantum dot, and the full angular description of the magnetic field. We are able to find reasonable agreement with the experimental results of Meunier et al. [Phys. Rev. Lett. 98, 126601 (2007)] in terms of the singlet-triplet energy splitting and the spin relaxation rate, respectively. We analyze in detail the effects of the spin-orbit factors, magnetic-field angles, and the dimensionality, and discuss the origins of the remaining deviations from the experimental data

Alternative gauge for the description of the light-matter interaction in a relativistic framework

We present a generalized velocity gauge form of the relativistic laser-matter interaction. In comparison with the (equivalent) regular minimal coupling description, this new form of the light-matter interaction results in superior convergence properties for the numerical solution of the time-dependent Dirac equation. This applies both to the numerical treatment and, more importantly, to the multipole expansion of the laser field. The advantages of the alternative gauge is demonstrated in hydrogen by studies of the dynamics following the impact of superintense laser pulses of extreme ultraviolet wavelengths and sub-femtosecond duration