Time-dependent Close-coupling Method Research Articles

An analysis Differential Cross Section for Helium Atom Photo Double-Ionization

It is becoming increasingly clear how exactly the helium atom fragments completely after absorbing a single photon. In this review, the significant theoretical and experimental developments that have contributed to our comprehension of this basic photo-double-ionization process—particularly with regard to multiple differential cross-sections—are summarized. We discuss how the time-dependent close-coupling method, and the convergent close-coupling method were developed to explore atomic and molecular body dynamics.

Electron-impact ionization of the tantalum atom

Electron-impact ionization cross sections for the ground configuration of the tantalum (Ta) atom are calculated using a combination of non-perturbative time-dependent close-coupling and perturbative distorted-wave methods. Direct ionization of the 6s and 5d subshells leading to single ionization are presented. The inclusion of a polarization potential in the 6s direct ionization leads to a small reduction in the cross section. Angular factors are included that allow the configuration-average direct ionization cross sections to be split into LS term resolution. The magnitude of the ionization cross section suggests that the ionization mean free path for neutral Ta will be similar to that for tungsten (W) plasma facing components in fusion experiments, leading to similarly large fractions of prompt redeposition.

Electron-Impact Ionization of Heavy Atoms Using the Time-Dependent Close-Coupling Method

The time-dependent close-coupling method has been recently applied to calculate electron-impact direct ionization cross sections for the Kr, W, and Pb atoms. An overview is presented for these three heavy neutral atom systems. When the direct ionization cross sections are combined with excitation-autoionization cross sections, the total ionization cross sections were found to be in reasonable agreement with crossed-beams measurements for Kr and Pb.

Electron-impact double ionization of He (1s2s 3 S)

A time-dependent close-coupling method for three-electron atomic systems is used to calculate the electron-impact double ionization of the He (1s2s 3 S) excited state. Partial cross sections are calculated for total angular momenta from . An exponential fitting expression is used to extend the calculated partial cross sections to . The total cross sections at three different incident energies are compared with recent crossed-beams measurements and are found to lie within the experimental error bars. The magnitude of the double ionization cross section is found to be similar to that of the double ionization cross section from the ground state of He.

Multicenter continuum-distorted-wave eikonal-initial-state description of the electron-impact ionization of aligned H2 molecules

In this work, the multicenter continuum-distorted-wave (CDW) eikonal-initial-state (EIS) model is introduced. In contrast to previously reported CDW EIS analyses for electron-molecule collisions, in which the ionized electron interacted with the molecular ion via a one-center effective potential, the multicenter nature of the molecular ion is explicitly taken into account. Results obtained for electron-impact ionization of oriented ${\mathrm{H}}_{2}$ molecules at the fully differential level are presented and contrasted with recent experimental data and reported theoretical calculations obtained with the time-dependent close-coupling method. The present results suggest that this simple molecule still represents a challenging target from a theoretical point of view and that many aspects of the ionization process at the fully differential level remain to be understood.

Neutron ionization of helium near the neutron-alpha particle collision resonance

Neutron-impact single and double ionization cross sections of the He atom are calculated near the neutron-alpha particle collision resonance. Calculations using the time-dependent close-coupling method for total and differential cross sections are made at 8 incident neutron energies ranging from 250 to 2000 keV. At the resonance energy peak the double ionization cross sections unexpectedly become larger than the single ionization cross sections. This finding appears to be related to the high velocity of the recoiling alpha particle, which makes it unlikely that the atomic electrons can recombine with the alpha particle nucleus, enhancing the double ionization cross section.

Deep Minima in the Triply Differential Cross Section for Ionization of Atomic Hydrogen by Electron and Positron Impact

We investigate ionization of atomic hydrogen by electron- and positron-impact. We apply the Coulomb–Born (CB1) approximation, various modified CB1 approximations, the three body distorted wave (3DW) approximation, and the time-dependent close-coupling (TDCC) method to electron-impact ionization of hydrogen. For electron-impact ionization of hydrogen for an incident energy of approximately 76.45 eV, we obtain a deep minimum in the CB1 triply differential cross section (TDCS). However, the TDCC for 74.45 eV and the 3DW for 74.46 eV gave a dip in the TDCS. For positron-hydrogen ionization (breakup) we apply the CB1 approximation and a modified CB1 approximation. We obtain a deep minimum in the TDCS and a zero in the CB1 transition matrix element for an incident energy of 100 eV with a gun angle of 56.13 ° . Corresponding to a zero in the CB1 transition matrix element, there is a vortex in the velocity field associated with this element. For both electron- and positron-impact ionization of hydrogen the velocity field rotates in the same direction, which is anticlockwise. All calculations are performed for a doubly symmetric geometry; the electron-impact ionization is in-plane and the positron-impact ionization is out-of-plane.

Triple autoionization of atomic ions

A time-dependent close-coupling method for four-electron atomic systems is formulated to calculate the triple autoionization of atomic ions. Initial excited states are obtained by relaxation of the Schrodinger equation in imaginary time using a Schmidt orthogonalization method involving interior subshells. Autoionization rates are obtained by propagation in real time using projections onto products of bound and continuum single particle states. For the () excited configuration of the atomic ion, we obtain total, double, and triple autoionization rates. The total autoionization rates are in reasonable agreement with single autoionization rates obtained using configuration-average distorted-wave theory.

Electron-impact ionization of the Si atom

Electron-impact ionization cross sections are calculated for the ground configuration of the Si atom for application in erosion diagnostics of plasma facing components in magnetically confined fusion experiments. The single ionization cross sections include contributions from outer subshell direct ionization and excitation-autoionization. The dominant direct ionization cross sections are calculated using a non-perturbative time-dependent close-coupling method. A significant reduction in the direct ionization cross section is found when compared to perturbative distorted-wave results. The theoretical cross sections are compared with available crossed-beams measurements.

Proton impact excitation of the Na atom

A time-dependent close-coupling (TDCC) method is developed and used to calculate proton impact excitation cross sections for atoms. Cross sections for excitations of the Na atom are calculated for proton impact energies ranging from 1.0 to 100.0 keV. The TDCC cross sections are found to be in agreement for some energies with recommended cross sections from overall fits to theoretical and experimental atomic data.

Electron-impact double ionization of the H2 molecule

A time-dependent close-coupling method in spherical polar coordinates is developed to calculate the electron-impact double ionization of the H2 molecule. The full wavefunction is represented by an expansion in products of six-dimensional radial-angular numerical functions and three analytic rotational functions. For an incident energy of 100 eV, the total cross section is calculated for the electron-impact double ionization of H2 and compared with experiment.

Electron-impact single and double ionization of the Fe atom and atomic ions

Electron-impact single and double ionization cross sections for the Fe atom and atomic ions are calculated using a combination of perturbative distorted-wave (DW) and non-perturbative time-dependent close-coupling (TDCC) methods. The single ionization cross sections include contributions from outer subshell direct ionization and excitation-autoionization. The double ionization cross sections include contributions from direct double ionization, inner subshell direct ionization, and excitation-autoionization. The accuracy of the perturbative DW calculations for direct ionization of the outer subshells of Fe and Fe+ are checked by comparison with non-perturbative TDCC calculations. The cross sections for single and double ionization are then compared with crossed-beams measurements.

Multiphoton double ionization of helium using ultraviolet and infrared laser pulses

A time-dependent close-coupling method is used to calculate the multiphoton double ionization of He using a combination of ultraviolet and infrared laser pulses. Total probabilities for the two photon double ionization of He using a laser pulse at 42 eV and 1014 W cm−2 are compared with those in the presence of an additional laser pulse at 1.5 eV and a variety of intensities. Momentum space wavefunction densities calculated for the multiphoton double ionization of He at 42 eV and 1014 W cm−2 are compared with those in the presence of additional laser pulse at 1.5 eV and 1012 W cm−2. Single and triple differential probabilities for the two and three photon double ionization of He using a laser pulse at 42 eV and 1014 W cm−2 are compared with those in the presence of an additional laser pulse at 1.5 eV and 1012 W cm−2.

Multiphoton double ionization of H2 using circularly polarized laser pulses

A time-dependent close-coupling method is used to calculate the multiphoton double ionization of H2 using circularly polarized laser pulses. Total double ionization probabilities are calculated for 2, 3, and 4 photon absorption in the energy range from 10 to 50 eV. Single and triple differential probabilities are calculated at photon energies where the total ionization probability is near a maximum. For one electron emitted along the internuclear axis, the angular distribution for the other electron is similar for 2, 3, and 4 photon absorption. As one electron is emitted further away from the internuclear axis, the angular distribution for the other electron is similar for 2 and 4 photon absorption, but quite different for 3 photon absorption.

Multiphoton double ionization of helium using femtosecond laser pulses

A time-dependent close-coupling method is used to calculate the multiphoton double ionization of He using femtosecond laser pulses. Total double ionization probabilities are calculated for 2, 3, 4, and 5 photon absorption in the photon energy range from 10 to 60 eV. Single and triple differential probabilities are calculated for 2, 3, 4, and 5 photon absorption at energies where the total ionization probability is near a maximum. For circular polarization the total and differential probabilities are consistently smaller compared to linear polarization as the number of photons absorbed is increased while keeping the radiation field intensity constant. For linear polarization, the total and differential probabilities vary substantially as a function of photons absorbed due to the presence of more absorption pathways.

Five-photon double ionization of helium

A time-dependent close-coupling method is used to calculate the five-photon double ionization of He. It is found that the generalized cross section used in the past for two-photon double ionization of He cannot be extended to five-photon double ionization of He. Therefore only five-photon double ionization probabilities that depend on specific radiation field pulses can be calculated.

Antiproton stopping inH2andH2O

Stopping powers of antiprotons in ${\text{H}}_{2}$ and ${\text{H}}_{2}\text{O}$ targets are calculated using a semiclassical time-dependent convergent close-coupling method. In our approach the ${\text{H}}_{2}$ target is treated using a two-center molecular multiconfiguration approximation, which fully accounts for the electron-electron correlation. Double-ionization and dissociative ionization channels are taken into account using an independent-event model. The vibrational excitation and nuclear scattering contributions are also included. The ${\text{H}}_{2}\text{O}$ target is treated using a neonization method proposed by C. C. Montanari and J. E. Miraglia [J. Phys. B 47, 015201 (2014)], whereby the ten-electron water molecule is described as a dressed Ne-like atom in a pseudospherical potential. Despite being the most comprehensive approach to date, the results obtained for ${\text{H}}_{2}$ only qualitatively agree with the available experimental measurements.

Antiproton stopping in atomic targets

Stopping powers of antiprotons in H, He, Ne, Ar, Kr, and Xe targets are calculated using a semiclassical time-dependent convergent close-coupling method. The helium target is treated using both frozen-core and multiconfiguration approximations. The electron-electron correlation of the target is fully accounted for in both cases. Double ionization and ionization with excitation channels are taken into account using an independent-event model. The Ne, Ar, Kr, and Xe atom wave functions are described in a model of six $p$-shell electrons above a frozen Hartree-Fock core with only one-electron excitations from the outer $p$ shell allowed. Results obtained for helium in the multiconfiguration treatment are in better agreement with experimental measurements than other theories.

Two-photon triple ionization of Li

A time-dependent close-coupling method is used to calculate the two-photon triple ionization of Li. Our method combines approaches previously used for two-photon double ionization of two-electron atoms with approaches that have been used for single-photon triple ionization of three-electron atoms. At a photon energy of 115.0 eV the three outgoing electrons share an energy of 31.4 eV. We explore the energy and angle differential cross sections of the three outgoing electrons and compare and contrast these distributions with those arising from single-photon triple ionization of Li.

Energy differential cross sections for F9+-impact single and double ionization of He

Time-dependent close-coupling methods are used to calculate energy differential cross sections for the single and double ionization of He by impact with F9+ ions at 4.0 MeV amu−1. Single ionization energy differential cross sections using both a one active electron method and a two active electron method are compared with recent experimental results. Double ionization energy differential cross sections using a two active electron method are presented to guide future experiments.