The time-dependent close-coupling method for atomic and molecular collision processes

An accurate knowledge of atomic collision processes is important for a better understanding of many astrophysical and laboratory plasmas. Collision databases which contain electron-impact excitation, ionization, and recombination cross sections and temperature dependent rate coefficients have been constructed using perturbative distorted-wave methods and non-perturbative R-matrix pseudo-states and time-dependent close-coupling methods. We present recent atomic collision results.

The key cycles of atomic and molecular collision processes contributing to the formation and quenching of the excited molecular states in exciplex (such as KrF*) and excimer (such as Xe/sub 2/*) laser systems are delineated and discussed.

In this lecture I shall review recent developments which have occurred in theoretical methods for calculating atomic collision cross sections. The lecture is an up-dated (but self-contained) version of the review I gave at the previous NATO Advanced Study Institute on “Atomic and Molecular Processes in Controlled Thermonuclear Fusion”1. It is meant to provide a general introduction to subsequent lectures by other speakers, who will deal in more detail with the theoretical analysis of specific atomic and molecular collision processes of interest in fusion research.

Many areas of science today, like atomic and molecular physics, nuclear physics, astrophysics, laboratory plasma research etc., depend on data for ionic, atomic, and molecular collision processes. The purpose of the Special Issue “Atomic and Ionic Collisions with Formation of Quasimolecules” in Atoms is to engage a broad community of researchers to consolidate knowledge, make new discoveries, and to continue the exchange of ideas.

Research in atomic and molecular collision processes and spectral line broadening has been very active since our last report (Schultz & Stancil 2007, Allard & Peach 2007). Given the large volume of the published literature and the limited space available, we have attempted to identify work most relevant to astrophysics. Since our report is not comprehensive, additional publications can be found in the databases at the web addresses listed in the final section. Elastic and inelastic collisions among electrons, atoms, ions, and molecules are included and reactive processes are also considered, but except for charge exchange, they receive only sparse coverage.

In 2-dimensional SCBF (Spherically Convergent Beam Fusion) device, the effect on neutron production rate of the grid cathode geometry was simulated. The motion of Particles was tracked using Monte Carlo Method including the atomic and molecular collision processes and potential distribution was calculated by Finite Element Method, Main processes of the discharge were the ionization of by fast . As the number of cathode rings was small and the size of grid cathode decreased, the ion current increased and neutron production rate will also increase. The star mode discharge which is a very important characteristic in SCBF device, was confirmed by the ionization position.

The electron-impact ionization cross sections of , and are calculated using both time-independent and time-dependent close-coupling methods. The time-independent methods are R-matrix and convergent close-coupling solutions based on a total wavefunction constructed using antisymmetrized products of Laguerre pseudo-orbitals and physical bound orbitals. The time-dependent method is based on the propagation of wavepackets constructed using excited-state orbitals calculated in a core pseudo-potential. The results of all three methods are in good agreement for ; there is also good agreement between the R-matrix and time-dependent methods for and , and all three methods yield ionization cross sections that lie substantially above the experimental crossed-beams measurements of Crandall et al. There is better accord with the crossed-beams measurements of Peart et al for , but the theoretical results still lie 10% higher at 50 eV. Some disagreement is noted, for both and , between the convergent close-coupling results and the R-matrix and time-dependent results.

Based on the time-dependent close-coupling method, energy and angular differential probabilities for various ionization processes of He atoms subjected to intense attosecond soft-x-ray pulses with a photon energy of 91.6 eV and a peak intensity of 10{sup 15} W/cm{sup 2} are calculated to explore their dependence on the duration and the chirp of the pulse. It is found that the single and the double electron energy distributions for two-photon double ionization are rather sensitive to chirps. That is, both the magnitudes and locations of the sequential peaks in the single electron energy distributions vary strongly with chirps and the two-electron energy distributions being broadened and stretched along the equal energy sharing direction as opposed to the usual total excess energy direction for the case of zero chirp. In addition, our calculation also reveals an unexpected structure formed between the two sequential peaks. In order to better understand the chirp effects on both independent-electron and correlated electron emissions and their relations to the origin of the structure, we analyzed the corresponding probability differential in energy and angle.

The XXVII International Conference on Photonic, Electronic and Atomic Collisions was held at Queen's University Belfast, Northern Ireland, 27 July – 2 August 2011. Members of the Local Organising Committee were drawn from the School of Mathematics and Physics of Queen's University Belfast, the School of Physical Sciences at Dublin City University, the School of Physics at University College Dublin and the Department of Experimental Physics at the National University of Ireland, Maynooth.The Conference was attended by 566 participants with contributions from 54 countries. The meeting attracted 786 contributed papers for presentation in the poster sessions. The conference included 20 Special Reports selected from the contributed papers, and these are included in part 1 of this volume. During the meeting a total of 65 Progress Reports were also presented, and the authors invited to submit written versions of their talks (see Part 1). Of the total number of contributed papers, 663 are included as refereed abstracts in parts 2 to 15 of this volume of Journal of Physics: Conference Series.Part 1 of this volume includes detailed write-ups of the majority of plenary lectures, progress reports and special reports, constituting a comprehensive tangible record of the meeting, and is additionally published in hard-copy as the Conference Proceedings.There were 5 plenary lectures given by Margaret Murnane on Ultrafast processes in atomic dynamics; Chris Greene on Few-body highly-correlated dynamics; Michael Allan on Electron-molecule collisions; Yasunori Yamazaki on Antiproton and positron collisions and Thomas Stöhlker on Relativistic ion collisions. Ian Spielman, winner of the IUPAP Young Scientist Prize for 2011, gave a special lecture entitled Modifying interatomic interactions using Raman coupling: a tale of slowly colliding Bose-Einstein condensates. In addition an evening public lecture by Mike Baillie on How precise tree-ring dating raises issues concerning the frequency of extraterrestrial impacts drew an attentive and appreciative audience.The editors are indebted to Tara Spencer for her exceptional organisation skills and support in compiling this volume. Thanks are also due to Ian Stewart for his assistance with gathering and indexing the documents.We would also like to express our sincere appreciation to the ICPEAC sponsors for their financial support. I D Williams Queen's University Belfast H W van der Hart Queen's University Belfast J F McCann Queen's University Belfast D S F Crothers Queen's University Belfast EDITORS

In anticipation of future experimental investigations of two-electron processes in endohedral atoms, the double photoionization and single photoionization with excitation of helium confined in the fullerenes C36, C60 and C82 have been studied using the time-dependent close-coupling method. It is found that both He@C60 and He@C82 display strong confinement resonances in the double photoionization cross section, whereas for He@C36, the confinement resonances are suppressed. For single photoionization leaving the He+ ion in its ground state, we found not only that the magnitudes of the cross sections for He@C36, He@C60 and He@C82 are similar to the case of helium but that confinement resonances are also apparent. For single photoionization with excitation to the n = 2 shell, the endofullerene cross sections showed a reduction as compared to bare He atoms, while for photoionization with excitation to the n = 3 shell, the cross sections for the endofullerenes are enhanced, with a particularly strong enhancement evident for He@C36.

To test the validity of classical trajectory and perturbative quantal methods for electron-impact ionization of H-like ions from excited states, we have performed advanced close-coupling calculations of ionization from excited states in H, Li2+ and B4+ using the R-matrix with pseudo states and the time-dependent close-coupling methods. Comparisons with our classical trajectory Monte Carlo (CTMC) and distorted-wave (DW) calculations show that the CTMC method is more accurate than the DW method for H, but does not improve with n and grows substantially worse with Z, while the DW method improves with Z and grows worse with n.

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.

The R-matrix with pseudostates method is applied to the case of two-electron excitation and ionization processes in He@C60. A finite spherical-well potential, which simulates the effect of the fullerene enclosing cage, is incorporated into the Hamiltonian using a modified R-matrix method, as recently applied to similar single photoionization studies of Xe@C60 and Ca@C60. Comparison is made with time-dependent close-coupling results for two-electron processes in He and He@C60, and excellent agreement is found in the respective descriptions of confinement resonances. Earlier findings are confirmed that the cage potential causes a redistribution between the n = 2 and n = 3 photoionization–excitation cross sections. The R-matrix with pseudostates method, in particular, is well-suited for treating atomic Feshbach resonances and studying multi-electron systems.

Double- and triple-differential cross sections are presented for the electron-impact ionization of ground-state hydrogen at incident electron energies of 15.6 and $17.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The time-dependent close-coupling method is used to calculate the differential ionization cross sections, and comparisons are made with previous theoretical calculations and with experimental measurements. Excellent agreement is obtained between our calculations and previous work.

Multi-electron processes in atomic collisions – theory