E. Suraud

NONLINEAR ELECTRON DYNAMICS IN METAL CLUSTERS

Abstract Recent experimental developments give more and more access to cluster excitations beyond the regime of linear response. Most theoretical descriptions of the induced nonlinear electron dynamics are based on the time-dependent local density approximation (TDLDA) and related schemes. We review the present status of TDLDA calculations for metal clusters, considering formal aspects of the theory, recipes for its numerical implementation as well as a variety of applications. These applications are presented by first summarizing basic linear spectral properties of the systems under study and then introducing two mechanisms for strong excitations: collision with highly charged and fast ions, and irradiation with strong femtosecond laser pulses. We present results for observables that are relevant for experiments, including ionization, energy balance, second-harmonic generation, electron emission spectra and, last but not least, we discuss the effects of ionic motion during the electronic dynamics. On the theoretical side, we also discuss semiclassical approaches and extensions beyond TDLDA, such as self-interaction corrections and the influence of electron–electron collisions.

On stochastic approaches of nuclear dynamics

Abstract We present recent developments of stochastic descriptions of nuclear dynamics. We focus on the newly introduced microscopic descriptions, such as stochastic extensions of currently used kinetic equations, as well as on more phenomenological, macroscopic approaches. We show to what extent these stochastic descriptions may offer a proper picture of nuclear dynamics both in strongly out of equilibrium situations, such as the ones encountered in energetic heavy-ion collisions or in closer to equilibrium situations such as the deexcitation of hot nuclei by thermal fission. In Section 1 we present a pedestrian introduction to the stochastic description of dynamical systems. We start from the elementary Brownian motion and introduce the Langevin and Fokker-Planck descriptions of the motion on that occasion. A few words are then spent to discuss the numerical methods developed for simulating stochastic equations. Section 2 of the paper is devoted to a formal introduction and discussion of both macroscopic and microscopic stochastic descriptions of nuclear dynamics. After a brief introduction reminding general concepts of equilibrium statistical physics we focus on microscopic descriptions of the many-body problem. We introduce here the Boltzmann Langevin equation which will provide a basis for many subsequent discussions. After having discussed the obtention of this equation from various points of view (from density matrix and Greens function techniques in particular), we consider reduced versions of this equation as well as a Fokker-Planck alternative. Section 3 is devoted to an analysis of fission by means of Langevin or Fokker-Planck-like approaches. We mainly discuss phenomenological approaches and spend some time in a detailed presentation of the ingredients entering these models. We present results obtained in these dynamical calculations when a proper account of particle evaporation is included for describing the fission of hot nuclei. Critical comparisons with experimental data are also provided. In Section 4 we focus on the application of the Boltzmann Langevin Equation to various situations encountered in energetic nuclear collisions. We first remind some typical examples for which this stochastic approach is both necessary and well suited. Typical applications are nuclear multifragmentation and subthreshold particle production, such as in particular kaon production. We discuss possible simulations of this equation and present some results in realistic calculations of collisions. We particularly focus on the dynamics of collective variables such as the quadrupole moment of the momentum distribution. We finally discuss other numerical simulations developed in the field. The last section before conclusion is devoted to extensions presently developed in the field of microscopic stochastic descriptions of nuclear dynamics. We present as a first step a relativistic version of the theory, then focus on fluid dynamics reductions. We finally discuss in some detail the recently introduced Stochastic time-dependent Hartree-Fock theory, which could provide new interesting developments.

Comparison of self-interaction-corrections for metal clusters

We present a simple density-averaged approach to the self-interaction-correction (SIC) methods of density functional theory. We discuss both formal properties and applications, considering particularly metal clusters as test cases. We show that the density averaged ansatz exhibits crucial, original (as compared to other SIC schemes) properties such as unitary robustness and applicability to semi-classical approaches. It is ideally suited to systems with well defined length and energy scales such as simple metal clusters.

Simple DFT model of clusters embedded in rare gas matrix: Trapping sites and spectroscopic properties of Na embedded in Ar

We present a theoretical model to study the dynamics of metallic clusters embedded in a rare gas matrix. We describe the active electrons of the embedded cluster using time dependent density functional theory, while the surrounding matrix is described in terms of classical molecular dynamics of polarizable atoms. The coupling between the cluster and the rare gas atoms is deduced from the work of Gross and Spiegelmann [J. Chem. Phys. 108, 4148 (1998)] and reformulated explicitly in a simple and efficient density functional form. The electron rare gas interaction takes the form of an averaged dipole fluctuation term, which retains the van der Waals long range interaction, and a short range repulsive pseudopotential, which accounts for the Pauli repulsion of the electron by the rare gas atom. We applied our model to Na clusters embedded in Ar matrix. For the latter we developed an efficient local pseudopotential, which allows studying systems containing more than 10(3) Ar atoms. We show that large systems are indeed necessary to account properly for long range polarization of the matrix, that competes with the matrix confinement effect. We focus our study on Na(2), Na(4), and Na(8). For each system, we have determined the geometry of the most favorable trapping site by means of damped molecular dynamics. We present the effect of matrix embedding on the optical absorption spectrum. For Na(2), the trapping site can be unambiguously identified by comparison of the absorption spectrum with experiment. For Na(4) the spectrum of the embedded cluster is significantly different from the free cluster spectrum, while for Na(8) differences are less pronounced.

Metallic clusters in strong femtosecond laser pulses

We study the electron response of a cluster excited by strong femtosecond laser pulses by means of a time-dependent density-functional method. We investigate the full electronic dipolar response and multiphoton ionization processes. A strong correlation between induced electronic dipole oscillations and electron emission is observed, leading to a pronounced resonant enhancement of ionization when using lasers operating at the frequency of the Mie plasmon. We also examine the probabilities for producing differently charged ionic states of the system.

Coulomb explosion of an cluster in a diabatic electron-ion dynamical picture

We present non-adiabatic simulations of the excitation and de-excitation of an sodium cluster irradiated by intense femtosecond lasers. Both electronic and ionic degrees of freedom are explicitly accounted for, whatever nonlinear regime is accessed. We find that the Coulomb fragmentation of the thus excited cluster depends sensitively on the laser frequency. We furthermore show that in the first 100 fs following the laser excitation, ionic degrees of freedom can safely be considered to be frozen. They then couple quickly to the electronic ones, within about another 100 fs, well before electronic excitation has fully levelled off.

Electron dynamics in strongly excited sodium clusters: a density-functional study with self-interaction correction

We study the linear and nonlinear electron dynamics of a cluster using time-dependent density functional theory. Exchange-correlation (xc) effects are treated in the adiabatic local density approximation with and without self-interaction correction (SIC). The latter is implemented within the time-dependent optimized effective potential method, leading to a self-interaction-free xc potential which is orbital independent. The method is applied to compare the electronic response of the cluster, calculated with and without SIC, in different dynamical regimes. We focus on the dipole response in the weakly excited regime, and on multiphoton ionization induced by strong femtosecond laser pulses. It is found that including SIC produces minor differences in the dipole power spectra and leaves the ionization mechanism essentially unchanged.

Nuclear fission with a Langevin equation

Abstract A microscopically derived Langevin equation is applied to thermally induced nuclear fission. An important memory effect is pointed out and discussed. A strong friction coefficient, estimated from microscopic quantities, tends to decrease the stationary limit of the fission rate and to increase the transient time. The calculations are performed with a collective mass depending on the collective variable and with a constant mass. Fission rates calculated at different temperatures are shown and compared with previous available results.

The Boltzmann-Langevin equation derived from the real-time path formalism

Abstract We derive the Boltzmann-Langevin equation using Greens function techniques in the real-time path formalism. We start from the Martin-Schwinger hierarchy and close it approximately at the two-body level. A careful discussion of the initial conditions for the free two-body Greens function provides the flexibility to recover the discarded correlations as fluctuations leading to the Langevin force. The derivation is generalized to the T-matrix approach which allows to prove that one can use the same effective interaction in the mean-field as well as in the collision term and Langevin force.

Ionic structure and plasmon response in sodium clusters

The linear and nonlinear optical response of sodium clusters is studied using fully three-dimensional electronic dynamics with frozen ionic positions. The detailed ionic structure produces more spectral fragmentation than a comparable jellium model, and the fragmentation patterns come close to measured spectra, even at low temperatures. The nonlinear response shows the same trends as found in former, symmetry restricted, investigations, namely that the plasmon resonance is a very harmonic mode showing no trace of nonlinear effects as secondary harmonics or spectral diffusion.