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Register a new userSolution of the time-dependent Dirac equation for describing multiphoton ionization of highly-charged hydrogenlike ions
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A theoretical study of the intense-field multiphoton ionization of hydrogenlike systems is performed by solving the time-dependent Dirac equation within the dipole approximation. It is shown that the velocity-gauge results agree to the ones in length gauge only if the negative-energy states are included in the time propagation. On the other hand, for the considered laser parameters, no significant difference is found in length gauge if the negative-energy states are included or not. Within the adopted dipole approximation the main relativistic effect is the shift of the ionization potential. A simple scaling procedure is proposed to account for this effect.
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We address the concept of direct multiphoton multiple ionization in atoms exposed to intense, short wavelength radiation and explore the conditions under which such processes dominate over the sequential. Their contribution is shown to be quite robust, even under intensity fluctuations and interaction volume integration, and reasonable agreement with experimental data is also found.
Two numerical methods are used to evaluate the relativistic spectrum of the two-centre Coulomb problem (for the $H_{2}^{+}$ and $Th_{2}^{179+}$ diatomic molecules) in the fixed nuclei approximation by solving the single particle time-independent Dirac equation. The first one is based on a min-max principle and uses a two-spinor formulation as a starting point. The second one is the Rayleigh-Ritz variational method combined with kinematically balanced basis functions. Both methods use a B-spline basis function expansion. We show that accurate results can be obtained with both methods and that no spurious states appear in the discretization process.
The validation and parallel implementation of a numerical method for the solution of the time-dependent Dirac equation is presented. This numerical method is based on a split operator scheme where the space-time dependence is computed in coordinate space using the method of characteristics. Thus, most of the steps in the splitting are calculated exactly, making for a very efficient and unconditionally stable method. We show that it is free from spurious solutions related to the fermion-doubling problem and that it can be parallelized very efficiently. We consider a few simple physical systems such as the time evolution of Gaussian wave packets and the Klein paradox. The numerical results obtained are compared to analytical formulas for the validation of the method.
We investigate scaling rules for the ionization cross sections of multicharged ions on molecules of biological interest. The cross sections are obtained using a methodology presented in [Mendez et al. J. Phys B (2020)], which considers distorted-wave calculations for atomic targets combined with a molecular stoichiometric model. We examine ions with nuclear charges Z from +1 to +8 impacting on five nucleobases -adenine, cytosine, guanine, thymine, uracil-, tetrahydrofuran, pyrimidine, and water. We investigate scaling rules of the ionization cross section with the ion charge and the number of active electrons per molecule. Combining these two features, we define a scaling law for any ion and molecular target, which is valid in the intermediate to high energy range, i.e., 0.2-5 MeV/amu for oxygen impact. Thus, the forty ion-molecule systems analyzed here can be merged into a single band. We confirm the generality of our independent scaling law with several collisional systems.
We present a non-perturbative solution of the Schrodinger equation $ipsi_t(t,x)=-psi_{xx}(t,x)-2(1 +alpha sinomega t) delta(x)psi(t,x)$, written in units in which $hbar=2m=1$, describing the ionization of a model atom by a parametric oscillating potential. This model has been studied extensively by many authors, including us. It has surprisingly many features in common with those observed in the ionization of real atoms and emission by solids, subjected to microwave or laser radiation. Here we use new mathematical methods to go beyond previous investigations and to provide a complete and rigorous analysis of this system. We obtain the Borel-resummed transseries (multi-instanton expansion) valid for all values of $alpha,omega,t$ for the wave function, ionization probability, and energy distribution of the emitted electrons, the latter not studied previously for this model. We show that for large $t$ and small $alpha$ the energy distribution has sharp peaks at energies which are multiples of $omega$, corresponding to photon capture. We obtain small $alpha$ expansions that converge for all $t$, unlike those of standard perturbation theory. We expect that our analysis will serve as a basis for treating more realistic systems revealing a form of universality in different emission processes.
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