Solution of two-center time-dependent Dirac equation in spherical coordinates: Application of the multipole expansion of the electron-nuclei interaction

Abstract

A non-perturbative approach to the solution of the time-dependent, two-center Dirac equation is presented with a special emphasis on the proper treatment of the potential of the nuclei. In order to account for the full multipole expansion of this potential, we express eigenfunctions of the two-center Hamiltonian in terms of well-known solutions of the "monopole" problem that employs solely the spherically-symmetric part of the interaction. When combined with the coupled-channel method, such a wavefunction-expansion technique allows for an accurate description of the electron dynamics in the field of moving ions for a wide range of internuclear distances. To illustrate the applicability of the proposed approach, the probabilities of the K- as well as L- shell ionization of hydrogen-like ions in the course of nuclear alpha-decay and slow ion-ion collisions have been calculated.

References in corpus (5)

• Dual kinetic balance approach to basis set expansions for the Dirac equation
• Relativistic calculations of the charge-transfer probabilities and cross sections for low-energy collisions of H-like ions with bare nuclei
• Calculation of electron-positron production in supercritical uranium-uranium collisions near the Coulomb barrier
• Numerical solution of the time-independent Dirac equation for diatomic molecules: B-splines without spurious states
• Relativistic calculations of the K-K charge transfer and K-vacancy production probabilities in low-energy ion-atom collisions

Cited by in corpus (13)

• Algorithm for the solution of the Dirac equation on digital quantum computers
• Electron-positron pair creation in low-energy collisions of heavy bare nuclei
• A Split-Step Numerical Method for the Time-Dependent Dirac Equation in 3-D Axisymmetric Geometry
• Dual Kinetic Balance Approach to the Dirac Equation for Axially Symmetric Systems: Application to Static and Time-Dependent Fields
• Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis
• One-center calculations of the electron-positron pair creation in low-energy collisions of heavy bare nuclei
• Estimating the radiative part of QED effects in superheavy nuclear quasimolecules
• Resonant Generation of an Electron-Positron Pair by Two Photons to Excited Landau Levels
• K-shell ionization of heavy hydrogen-like ions
• Relativistic calculations of the U91+(1s)-U92+ collision using the finite basis set of cubic Hermite splines on a lattice in coordinate space
• Ionization in a laser assisted ion-ion collision
• The possibility to experimentally determine the structure of a fermionic vacuum in quantum electrodynamics
• Relativistic effects in ionization of heavy hydrogen-like ions by short X-ray pulses