Recoil-ion and electron momentum spectroscopy is a rapidly developing technique that allows one to measure the vector momenta of several ions and electrons resulting from atomic or molecular fragmentation. In a unique combination, large solid angles close to 4π and superior momentum resolutions around a few per cent of an atomic unit (a.u.) are typically reached in state-of-the art machines, so-called reaction-microscopes. Evolving from recoil-ion and cold target recoil-ion momentum spectroscopy (COLTRIMS), reaction-microscopes—the `bubble chambers of atomic physics'—mark the decisive step forward to investigate many-particle quantum-dynamics occurring when atomic and molecular systems or even surfaces and solids are exposed to time-dependent external electromagnetic fields. This paper concentrates on just these latest technical developments and on at least four new classes of fragmentation experiments that have emerged within about the last five years. First, multi-dimensional images in momentum space brought unprecedented information on the dynamics of single-photon induced fragmentation of fixed-in-space molecules and on their structure. Second, a break-through in the investigation of high-intensity short-pulse laser induced fragmentation of atoms and molecules has been achieved by using reaction-microscopes. Third, for electron and ion-impact, the investigation of two-electron reactions has matured to a state such that the first fully differential cross sections (FDCSs) are reported. Fourth, comprehensive sets of FDCSs for single ionization of atoms by ion-impact, the most basic atomic fragmentation reaction, brought new insight, a couple of surprises and unexpected challenges to theory at keV to GeV collision energies. In addition, a brief summary on the kinematics is provided at the beginning. Finally, the rich future potential of the method is briefly envisaged.

/pdf/recoil-ion-and-electron-momentum-spectroscopy-reaction-c7ai542e3l.pdf

Recoil-ion and electron momentum spectroscopy: reaction-microscopes

Time-dependent density functional theory (TDDFT) can be viewed as an exact reformulation of time-dependent quantum mechanics, where the fundamental variable is no longer the many-body wave function but the density. This time-dependent density is determined by solving an auxiliary set of noninteracting Schrodinger equations, the Kohn-Sham equations. The nontrivial part of the many-body interaction is contained in the so-called exchange-correlation potential, for which reasonably good approximations exist. Within TDDFT two regimes can be distinguished: (a) If the external time-dependent potential is "small," the complete numerical solution of the time-dependent Kohn-Sham equations can be avoided by the use of linear response theory. This is the case, e.g., for the calculation of photoabsorption spectra. (b) For a "strong" external potential, a full solution of the time-dependent Kohn-Sham equations is in order. This situation is encountered, for instance, when matter interacts with intense laser fields. In this review we give an overview of TDDFT from its theoretical foundations to several applications both in the linear and in the nonlinear regime.

/pdf/time-dependent-density-functional-theory-280q52hn1n.pdf

Time-Dependent Density Functional Theory

This review provides a perspective on the use of orbital-dependent functionals, which is currently considered one of the most promising avenues in modern density-functional theory. The focus here is on four major themes: the motivation for orbital-dependent functionals in terms of limitations of semilocal functionals; the optimized effective potential as a rigorous approach to incorporating orbital-dependent functionals within the Kohn-Sham framework; the rationale behind and advantages and limitations of four popular classes of orbital-dependent functionals; and the use of orbital-dependent functionals for predicting excited-state properties. For each of these issues, both formal and practical aspects are assessed.

Orbital-dependent density functionals: Theory and applications

Photoemission from atoms is assumed to occur instantly in response to incident radiation and provides the basis for setting the zero of time in clocking atomic-scale electron motion. We used attosecond metrology to reveal a delay of 21 +/- 5 attoseconds in the emission of electrons liberated from the 2p orbitals of neon atoms with respect to those released from the 2s orbital by the same 100-electron volt light pulse. Small differences in the timing of photoemission from different quantum states provide a probe for modeling many-electron dynamics. Theoretical models refined with the help of attosecond timing metrology may provide insight into electron correlations and allow the setting of the zero of time in atomic-scale chronoscopy with a precision of a few attoseconds.

http://science.sciencemag.org/content/sci/328/5986/1658.full.pdf

Delay in photoemission.

Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article discusses how TDDFT is much broader in scope, and yields predictions for many more properties. We discuss some of the challenges involved in making accurate predictions for these properties.

/pdf/time-dependent-density-functional-theory-past-present-and-4re9u3xgyh.pdf

Time-dependent density functional theory: Past, present, and future

For pt.I see ibid., vol.20, p.6363-78 (1987). A general description of the data requirements for opacity calculations has been given in paper I. The present paper gives a detailed description of the methods being used in a collaborative effort which is referred to as the Opacity Project. The close-coupling approximation of electron-atom collision theory is used to calculate energies and wavefunctions for bound states, oscillator strengths, photoionisation cross sections and parameters for line broadening by electron impact. The computations are made using the R-matrix method together with new codes for calculating outer-region solutions and dipole integrals. Use of these techniques provides an efficient means of calculating large amounts of accurate atomic data.

http://iopscience.iop.org/article/10.1088/0022-3700/20/23/027/pdf

Atomic data for opacity calculations. II. Computational methods

Electron energy distributions of singly and doubly ionized helium in an intense 390 nm laser field have been measured at two intensities ($0.8\text{ }\text{ }\mathrm{PW}/{\mathrm{cm}}^{2}$ and $1.1\text{ }\text{ }\mathrm{PW}/{\mathrm{cm}}^{2}$, where $\mathrm{PW}\ensuremath{\equiv}{10}^{15}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$). Numerical solutions of the full-dimensional time-dependent helium Schr\"odinger equation show excellent agreement with the experimental measurements. The high-energy portion of the two-electron energy distributions reveals an unexpected $5{U}_{p}$ cutoff for the double ionization (DI) process and leads to a proposed model for DI below the quasiclassical threshold.

/pdf/high-energy-cutoff-in-the-spectrum-of-strong-field-5ezhs17ep5.pdf

High-energy cutoff in the spectrum of strong-field nonsequential double ionization.

A general program to calculate atomic continuum processes using the R-matrix method

Numerical integration of the time-dependent Schrödinger equation for laser-driven helium

We present calculations of intense-field multiphoton ionization processes in helium at XUV wavelengths. The calculations are obtained from a full-dimensional integration of the two-electron time-dependent Schrodinger equation. A momentum-space analysis of the ionizing two-electron wavepacket reveals the existence of double-electron above threshold ionization (DATI). In momentum-space two distinct forms of DATI are resolved, namely non-sequential and sequential. In non-sequential DATI correlated electrons resonantly absorb and share energy in integer units of ωlaser.

Kenneth Taylor

Papers

Atomic data for opacity calculations. II. Computational methods

High-energy cutoff in the spectrum of strong-field nonsequential double ionization.

A general program to calculate atomic continuum processes using the R-matrix method

Numerical integration of the time-dependent Schrödinger equation for laser-driven helium

Double-electron above threshold ionization of helium