Ionization dynamics of simple metal clusters in intense fields by the Thomas-Fermi-Vlasov method

The time-dependent response of simple metal clusters to femtosecond laser pulses is investigated using the semiclassical theory based on the Vlasov equation. Starting from a Thomas-Fermi ground state the dynamics are calculated by use of the pseudoparticle method. Systems studied here are sodium clusters containing up to 147 atoms. Both, the energy transfer to the cluster, which is largely affected by the plasmon enhanced absorption, and the following release of energy to the ions are examined in detail. During the laser excitation the feedback of the absorption to the development of the plasmon energy is controlled by competing mechanisms: ionization and cluster expansion. Characteristics of the Coulomb explosion are studied as function of photon energy and cluster size, particularly with regard to the dynamical influence of collective excitations of the electrons. We also predict features in the angular distribution of the ions that could be measured to test the calculated dynamics.Received: 9 December 2003, Published online: 16 March 2004PACS: 52.50.Jm Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.) - 36.40.Vz Optical properties of clusters - 36.40.Gk Plasma and collective effects in clusters     

Dynamics simulation on interaction of intense laser pulses with atomic clusters

Under classical particle dynamics, the interaction process between intense femtosecond laser pulses and icosahedral noble-gas atomic clusters was studied. Our calculated results show that ionization proceeds mainly through tunnel ionization in the combined field from ions, electrons and laser, rather than the electron-impact ionization. With increasing cluster size, the average and maximum kinetic energy of the product ion increases. According to our calculation, the expansion process of the clusters after laser irradiation is dominated by Coulomb explosion and the expansion scale increases with increasing cluster size. The dependence of average kinetic energy and average charge state of the product ions on laser wavelength is also presented and discussed. The dependence of average kinetic energy on the number of atoms inside the cluster was studied and compared with the experimental data. Our results agree with the experimental results reasonably well.     

Configurational transitions in processes involving metal clusters

We define the configurational state of an atomic system, e.g. a cluster of metal atoms, in terms of the nuclear coordinates of a specific local minimum of the potential energy surface (PES). Three types of configurational transitions are reviewed: chemical reactions, phase transitions in clusters and catalytic chemical processes involving clusters as catalysts. The analysis of the first two cases shows that although vibrational degrees of freedom of nuclei and configurational degrees of freedom are separable in lowest order, thermal motion of nuclei nevertheless influences the rate of a configurational transition. Therefore the height of the barrier that separates configurational states of the transition for the PES differs from the effective activation energy for this transition. For example, ignoring the thermal motion of atoms in Lennard-Jones clusters leads to a predicted value of their melting points twice which accounts for the thermal motion of atoms. Hence, in determining parameters governing configurational transitions, evaluation of the PES parameters, say, within the framework of DFT (density functional theory) must be augmented by information from molecular dynamics or some other method that accounts for nuclear motion.     

Mechanisms for second harmonic generation in the interaction of a superintense ultrashort laser pulse with cluster plasma

The effects of the interaction of an intense femtosecond laser pulse with large atomic clusters are considered. The pulse intensity is of the order of 10¹⁸ W cm^?2. New effects appear when the magnetic component of the Lorentz force is taken into account. The second harmonic of laser radiation is generated. The second harmonic generation (SHG) efficiency is proportional to the square of the number of atoms in a cluster and the square of the laser radiation intensity. The resonance increase in the SHG efficiency at the Mie frequencies (both at the second harmonic frequency and fundamental frequency) proved to be insignificant because of the fast passage through the resonance during cluster expansion. The mechanisms of the expansion and accumulation of energy by electrons and ions in the cluster are discussed in detail. The energy accumulation by electrons mainly occurs due to stimulated inverse bremsstrahlung upon elastic reflection of the electrons from the cluster surface. The equations describing the cluster expansion take into account both the hydrodynamic pressure of heated electrons and the Coulomb explosion of the ionized cluster caused by outer shell ionization. It is assumed that both inner shell and outer shell ionization is described by the over barrier mechanism. It is shown that atomic clusters are more attractive for the generation of even harmonics than compared to solid and gas targets.     

Bremsstrahlung spectrum for α decay and quantum tunneling

Spectra of the electromagnetic radiation arising during α decay of atomic nuclei as a consequence of the motion of the α particle through a Coulomb potential barrier and in the Coulomb field of the daughter nucleus are calculated via a quantum-mechanical approach. The contributions of the E1 and E2 multipoles are calculated. Model problems of emission during motion of a charged particle through a spherically symmetric, rectangular potential barrier and a “cut-off” Coulomb barrier are treated. Numerical calculations are performed for ^210,214Po and ²²⁶Ra nuclei. Emission spectra are derived for an α particle propagating along classical trajectories in these potentials. Zh. éksp. Teor. Fiz. 116, 390–409 (August 1999)     

Theoretical description of ultrafast phenomena in clusters

A theoretical study of different ultrafast nonequilibrium processes taking place during and after ultrashort excitation of clusters is presented. We discuss similarities and differences for several processes involving nonequilibrium ultrafast motion of atoms and electrons. We study ultrashort relaxation of clusters in response to excitations produced by femtosecond laser pulses of different intensities. We show how different relaxation processes, such as bond breaking, melting, fragmentation, emission of atoms, or Coulomb explosion, can be induced, depending on the laser intensity and laser pulse duration. We also discuss processes involving nonequilibrium electron dynamics, such as intraband Auger decay in clusters and ultrafast electronic motion during collisions between clusters and surfaces. We show that this electron dynamics leads to Stückelberg-like oscillations of measurable quantities, such as the electron emission yield. Received: 4 April 2000 / Accepted: 6 November 2000 / Published online: 9 February 2001     

Atomic-core dynamics and the electronic structure of some endo-and exohedral complexes of fullerenes with light elements

The atomic and electronic structure of some endo-, exo-, and endo-exohedral complexes of the fullerene C₆₀ with various guest atoms and molecules (He_n, H₂, and Li₂) are investigated using semiempirical and nonempirical quantum-chemical methods. The atomic core dynamics is studied by the method of molecular dynamics. It is shown that guest atoms and molecules in fullerene polyhedra acquire an orbital angular momentum due to the correlated motion of nuclei above the low-energy barriers of the potential surface within the carbon polyhedron even at low temperatures (from 4 to 78 K). The emergence of orbital angular momenta of nuclei of guest atoms and molecules is attributed to a change in the contribution of the orbital angular momentum of electrons to the potential surface of the complexes. The motion of Li ions in a polyhedron leads to blurring of the top of the valence band and to the emergence of a charge polarization wave in the carbon polyhedron.     

The band structure of lithium with a screened non-local crystal potential

Wave functions and energy eigenvalues for Li have been calculated with the MAPW-method, using a one-particle potential constructed from the Coulomb potentials of the nuclei and the electrons and a non-local screened exchange potential. Using different interpolation schemes starting from the results along the principal axes, the Fermi energy, the Fermi surface, its extremal cross sections, different masses and the contribution of the conduction electrons to the Knight shift are determined.     

Metallization degree of hydrogen at a pressure of 1.4 Mbar and a temperature a 3000 K

The electrical resistivity of liquid metallic hydrogen at a temperature of 3000 K and a density of 0.35 mol/cm³ is calculated. Hydrogen is considered as a three-component system consisting of electrons, protons, and neutral hydrogen atoms. The second order of perturbation theory in electron-proton and electron-atom interactions is used to determine the inverse relaxation time for electric conductivity. The Coulomb electron-electron interaction is taken into account in the random phase approximation and the exchange interaction and correlation of conductivity electrons are included in the local-field approximation. The model of hard spheres is used for the proton and atomic subsystems. The concentration of the electrically neutral atomic component proved to be significantly lower than the value assumed by the discoverers of metallic hydrogen.     

Dynamics of resonant energy transfer in a cold Rydberg gas

We investigate excitation transfer and migration processes in a cold gas of rubidium Rydberg atoms. Density-dependent measurements of the resonant population exchange for atoms initially excited into the 32P_3/2(|m_J|=3/2) state are compared with a Monte Carlo model for coherent energy transfer. The model is based on simulations of small atom subensembles involving up to ten atoms interacting via coherent pair processes. The role of interatomic mechanical forces due to the resonant dipole-dipole interaction is investigated. Good agreement is found between the experimental data and the predictions of the model, from which we infer that atomic motion has negligible influence on the energy transfer up to Rydberg densities of 10⁸ cm^-3, that the system has to be described in terms of many-body dynamics, and that the energy transfer preserves coherence on microsecond timescales.     

Processes with heavy ion collisions

Some Coulomb effects in heavy ion collisions are considered. Among them the process of muon and lepton pair creation, Coulomb and unitary corrections, statistics of multiple pair production. Effects of multiple photon exchange in process of lepton pair production by linearly polarized photon on nuclei are considered. This process is used for measuring the polarization of initial photon. Relativistic muon energy loss due to the light lepton pair production in the Coulomb field are calculated. Also we consider the effects of multiple photon exchange in elastic lepton scattering on unscreened atomic field and discuss the possible experimental testing.     

Elastic-scattering cross-section for electrons and positrons from atomic hydrogen

The differential cross-sections of atomic hydrogen for elastic scattering of electrons and positrons have been rederived with the help of a method using a single parameter-dependent unitary shift operator for the calculation of the direct contribution. When the parameter approaches zerc the new method leads to the well-known conventional Glauber results. The numerical calculations include polarization effects and the exchange corrections obtained according to alternative approximation methods. Results calculated with Franco’s exchange show a definite improvement over the earlier results for medium energy electrons at large angles of scattering. Total elastic cross-sections have been calculated for 50 and 100eV electrons and positrons.     

Rescattering of electrons at laser-cluster interactions

The goal of this work is to derive the angular distributions of electrons irradiated at the outer ionization of large atomic clusters from Xe atoms by relativistic laser pulses taking into account rescattering processes. Both the magnetic field of the laser pulse and the Coulomb field of the ionized cluster significantly influence the rescattering of ejected electrons. The multiply inner ionization of atoms occurs at the leading edge of the laser pulse. The atomic ions with charge multiplicities up to Z = 26 are subsequently produced (each atomic ion with the next charge multiplicity appears in 3–5 fs) when the laser intensity increases. The measurements of the angular distributions of electrons allow us to reproduce the imaging dynamics of outer ionization of the cluster at the leading edge of the relativistic femtosecond laser pulse.     

Semi-classical limit theorems for Hartree-Fock theory

Consider a large number of electrons with Coulomb repulsion moving under the influence of static nuclei. It is assumed the potentials due to the nuclei are Coulombic away from their centers but are smooth at the centers, so no singularities exist. The author shows that the exchange energy for the Hartree-Fock ground state of this system converges in a suitable limit to the formula obtained by Dirac for exchange energy as an integral of the one body density.Research supported by NSF Grant No. MCS8100761     

Interference effects on the photoionization cross sections between two neighbouring atoms: nitrogen as an example

Interference effects on the photoionization cross sections between two neighbouring atoms are considered based on the coherent scattering of the ionized electrons by the two nuclei when their separation is less than or comparable to the de Broglie wave length of the ionized electrons. As an example, the single atomic nitrogen ionization cross section and the total cross sections of two nitrogen atoms with coherently added photoionization amplitudes are calculated from the threshold to about 60~\AA (1~\AA=0.1~nm) of the photon energy. The photoionization cross sections of atomic nitrogen are obtained by using the close-coupling R-matrix method. In the calculation 19 states are included. The ionization energy of the atomic nitrogen and the photoionization cross sections agree well with the experimental results. Based on the R-matrix results of atomic nitrogen, the interference effects between two neighbouring nitrogen atoms are obtained. It is shown that the interference effects are considerable when electrons are ionized just above the threshold, even for the separations between the two atoms are larger than two times of the bond length of N₂ molecules. Therefore, in hot and dense samples, effects caused by the coherent interference between the neighbours are expected to be observable for the total photoionization cross sections.     

Multiple recapture of electrons in multiple ionization of the argon dimer by a strong laser field

We observe multiply frustrated tunneling ionization-induced dissociation of the argon dimers by intense linearly polarized ultrashort laser pulses. By measuring the kinetic energy release and angular distribution of the Coulomb explosion of up to eightfold ionized argon dimers, we can trace the recapture of up to two electrons to Rydberg states of the highly charged compound at the end of the laser pulse. Upon dissociation of the dimer, the Rydberg electron prefers to localize at the atomic ion with the higher charge state. We probe the electron recapture dynamics by a time-delayed weak pulse.     

Heating of deuterium clusters by a superatomic ultra-short laser pulse

The mechanisms of heating of the electronic component of large deuterium clusters by a super-atomic ultra-short laser pulse field are considered. During pulse rise, the so-called “vacuum heating” plays the determining role. Electrons escaping from a cluster into the vacuum with a low energy return back in a time equal to the period of the laser under laser field action. The returning electrons have a higher energy (on the order of the vibrational energy in the laser radiation field), which causes cluster heating. As the laser field increases, the electronic temperature largely grows at the expense of decreasing the Coulomb potential energy of electron repulsion because of a decrease in the number of electrons. The dynamics of above-barrier cluster ionization at the leading edge of a superatomic laser pulse is calculated. The results are discussed in the light of recent experiments aimed at creating desktop sources of monoenergetic neutrons formed as a result of the fusion of deuterium nuclei in a cluster plasma.     

Nonlinear Waves in Carbon Nanotubes under Conditions of Electron-Phonon Bonding

Relative simplicity of the atomic structure of carbon nanotubes being hollow cylinders with walls formed by rings of six carbon atoms (generally, the walls can be multilayered) enables the researchers to use this class of substances as model one to reveal the basic mechanisms of the dynamics of quasi-one—dimensional systems. The present work studies the nonlinear properties of carbon nanotubes with strong electron interactions described by the Hubbard Hamiltonian. A microscopic Hamiltonian describing electrons in carbon nanotubes with allowance for the electron mobility, Coulomb repulsion of electrons in one site of carbon nanotubes, and changes in spacing of the neighboring sites caused by acoustic oscillations is suggested. An effective nonlinear system of equations describing the dynamics of electron wave functions within the framework of the suggested Hamiltonian is derived. The existence of nonlinear stable periodic oscillations of electron wave functions in the examined model, in particular, corresponding to acoustic oscillations with different polarization states is established. The influence of the problem parameters on the character of nonlinear wave stability is revealed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 76–81, June, 2005.     

Infinite nuclear matter model and a new mass formula for atomic nuclei

The ground-state energy of an atomic nucleus with asymmetryβ is considered to be equivalent to the energy of a perfect sphere made up of the infinite nuclear matter of the same asymmetry plus a residual energyη called the local energy,η represents the energy due to shell, deformation, diffuseness and exchange Coulomb effect etc. Using this picture and the generalized Hugenholtz- Van Hove theorem of many-body theory a new mass formula has been developed. Based on this, a mass table containing the mass excesses of 3481 nuclei in the range 18 ⩽A ⩽ 267 has been made. This mass formula is compared with other mass models.