Infrared catastrophe in a two-quasiparticle collision integral

Relaxation of a nonequilibrium state in a disordered metal with a spin-dependent electron energy distribution is considered. The collision integral due to the electron-electron interaction is computed within the approximation of a two-quasiparticle scattering. It is shown that the spin-flip scattering processes with a small energy transfer may lead to the divergence of the collision integral for a quasi one-dimensional wire. This divergence is present only for a spin-dependent electron energy distribution that corresponds to the total electron spin magnetization M = 0 and only for nonzero interaction in the triplet channel. In this case, a nonperturbative treatment of the electron-electron interaction is needed to provide an effective infrared cutoff. The text was submitted by the authors in English. An erratum to this article is available at .     

Electron energy relaxation in the presence of magnetic impurities

We study inelastic electron-electron scattering mediated by the exchange interaction of electrons with magnetic impurities and find the kernel of the corresponding two-particle collision integral. In a wide region of parameters, the kernel K is proportional to the inverse square of the transferred energy, K proportional to J4/E2. The exchange constant J is renormalized due to the Kondo effect. At small energy transfers, the 1/E2 divergence is cut off; the cutoff energy is determined by the dynamics of the impurity spins. The obtained results may provide a quantitative explanation of the experiments of Pothier et al. [Phys. Rev. Lett. 79, 3490 (1997)] on anomalously strong energy relaxation in short metallic wires.     

Femtosecond laser-induced heating of electron gas in aluminium

The distribution function of free electrons in metal is calculated for irradiation of aluminium with an ultrashort laser pulse of moderate intensity. We consider inverse Bremsstrahlung absorption, electron-electron and electron-phonon interaction. Our theoretical model is based on Boltzmann equations and describes each considered process by a corresponding collision integral. The results show the excitation and relaxation of the free electron gas. Energy transfer to the phonon gas is calculated. Our model predicts linear absorption for intensities up to damage threshold. The calculated absorbed energy compares very well with known absorption characteristics.     

On the dynamics of electrons in an impure metal

The inelastic scattering of the electrons of an impure metal by a screened Coulomb interaction is investigated. It is found that the rate of such an inelastic scattering is increased which can be explained by a loss of momentum conservation which in turn results from loss of translational symmetry introduced by the defects of an impure metal. Eventually, a linearised Boltzmann equation is derived for time and space dependent perturbances of the electronic distribution function. The collision integral takes into account impurity scattering as well as electron-electron and electron-phonon scattering. In an impure metal the terms corresponding to the last two processes are modified as discussed above and in a previous paper on the electron-phonon interaction.     

The effect of multiple electron-electron scattering on the energy distribution of electrons in a correlated pair

A unit event of electron-electron scattering in LiF layers is studied by correlation spectroscopy of scattered electrons. The energy distribution of electrons in a correlated pair when a 15-to 55-eV free electron is scattered by a valence electron of LiF is studied. It is shown that single electron-electron scattering prevails and the distribution is uniform when the energy of the primary electron is below 25 eV. As the energy of the primary electron increases, the formation of correlated pairs of electrons with equal energies becomes the most probable. With the energy of the primary electron above 40 eV, the pairs with substantially different electron energies dominate. Such evolution of the energy distribution of the electrons in the pair stems from the fact that first one and then the other electron of the pair successively takes part in electron-electron scattering. A phenomenological model for the single scattering and double scattering of primary electrons in LiF films is considered. Results obtained indicate that the strengths of single scattering and double scattering channels become comparable at electron energies above 25 eV.     

Energy relaxation in the spin-polarized disordered electron liquid

Energy relaxation is studied in the spin-polarized disordered electron systems in the diffusive regime. We derive a quantum kinetic equation in which the kernel of the electron-electron collision integral explicitly depends on the electron magnetization. As a consequence, the inelastic scattering rate has a nonmonotonic dependence on the spin polarization of the system.     

Thermalization time of noble metal nanoparticles: effects of the electron density profile

The lack of d-electron screening in the s-electron spill-out region at the surface of Ag nanoparticles increases the electron-electron interaction in this region compared to the bulk. Therefore when comparing the electron-electron interaction contribution to the thermalization time of nanoparticles of varying radius, smaller particles thermalize faster due to the increased surface to bulk ratio. One aspect which has not been addressed is the effect of the spatial distribution of charge at the surface of the nanoparticle. In this work it is shown that the size dependence of the thermalization time is very sensitive to the surface density profile. The electron thermalization time of conduction electrons in noble metal nanoparticles as a function of the radius is calculated. The sensitivity of the scattering rate to the spatial distribution of charge at the surface of the nanostructure is analyzed using several model surface profiles. The change in surface charge distribution via charging or coating of the nanospheres is shown to be a tool for control and probing of the ultra-fast electron-electron dynamics in metallic nanoparticles.     

Double ionization and excitation ionization in the Compton scattering of high-energy photons for metastable states of heliumlike ions

Double ionization and excitation ionization in Compton scattering for heliumlike ions in metastable states are investigated. The electron energy distribution for double ionization and the total cross sections for both processes are calculated. The calculations are carried out in the zeroth order of perturbation theory with respect to electron-electron interaction, using Coulomb wave functions as the first approximation. The resulting equations are valid only in the high-energy nonrelativistic range. It is assumed that Z≫1, but αZ≪1 (Z is the charge of the nucleus, and α is the fine-structure constant). Zh. éksp. Teor. Fiz. 116, 1889–1902 (December 1999)     

Nonmonotonic bias voltage dependence of the magnetocurrent in GaAs-based magnetic tunnel transistors

Magnetic tunnel transistors are used to study spin-dependent hot electron transport in thin CoFe films and across CoFe/GaAs interfaces. The magnetocurrent observed when the orientation of a CoFe base layer moment is reversed relative to that of a CoFe emitter, is found to exhibit a pronounced nonmonotonic variation with electron energy. A model based on spin-dependent inelastic scattering in the CoFe base layer and strong electron scattering at the CoFe/GaAs interface, resulting in a broad electron angular distribution, can well account for the variation of the magnetocurrent in magnetic tunnel transistors with GaAs(001) and GaAs(111) collectors.     

Spin-dependent low-energy 4He+ ion scattering from nonmagnetic surfaces

We investigated electron-spin-polarized (4)He(+) ion scattering on various nonmagnetic surfaces at kinetic energies below 2 keV. It was observed that the scattered He(+) ion yield depends on the He(+) ion spin. We interpret this spin-dependent scattering in terms of the spin-orbit coupling that acts transiently on the He(+)1s electron spin in the He(+)-target binary collision. This interpretation qualitatively explains the relationship between the spin-dependent scattering and the scattering geometry, incident velocity, and magnetic field arrangement. This is the first study to report spin-orbit coupling caused by projectile electron spin in ion scattering.     

Multiplication of high-energy electrons in irradiated materials studied using the Boltzmann kinetic equation

Processes involved in the formation of electron collision cascades created by nonrelativistic high-energy electrons, which can develop in materials exposed to electron and gamma radiation fluxes, have been considered. The problem is solved using the Boltzmann kinetic equation for high-energy electrons moving in a medium. A model scattering indicatrix is constructed for this equation with an arbitrary potential of interaction between colliding particles. Using this scattering indicatrix, the distribution of the particle energies is obtained. Based on this energy distribution (with an arbitrary interparticle interaction potential), a cascade function is found that describes the multiplication of knock-out electrons (electron cascade) generated when a high-energy electron with a certain energy is scattered on the electron subsystem of the irradiated material. The cascade function has been calculated for the Coulomb potential of the interaction between a high-energy electron and atomic-shell electrons.     

Separation of angular and energy relaxations of nonequilibrium electrons in a solid

We demonstrate that the collision integral of the kinetic equation for the interaction of hot electrons with phonons can be split into substantially different parts that correspond to elastic and inelastic collisions. In particular, this applies to electrons with energies of about 1 eV that propagate in semiconductors. The difference in the characteristic energy and momentum relaxation times makes it possible to separate the angular and energy relaxation processes. If the differential cross section of elastic scattering depends, not on the scattering angle, but on the directions of incident and scattered electrons (which is observed, e.g., for the interaction of an electron with piezoelectric lattice vibrations in A^IIIB^V compounds), the Laplacian in the equation that describes the spatial and energy distributions of electrons can be replaced by an elliptical operator; i.e., the electron diffusion turns out to be anisotropic.     

Barrier penetration effects for electrons in quantum wells: screening,mobility, and shallow impurity states

A two-dimensional electron gas in a quantum well confined by finite barriers is considered. We present analytical expressions for the finite confinement effects of a square-well potential and calculate the electron-electron interaction potential, the electron-impurity interaction potential, the interface-roughness scattering potential and the alloy-disorder scattering potential. The dielectric function of the interacting electron gas, the mobility (for charged-impurity scattering, for interface-roughness scattering, and for alloy-disorder scattering), and the binding energy of hydrogenic impurities (screened and unscreened) are discussed.     

Study of elastic electron collisions by plasma electron spectroscopy

In this work we study elastic electron collisions by using the plasma electron spectroscopy method, which is based on the study of the electron energy distribution function in a plasma afterglow. We give the results of this method for the electron-electron collision frequency, and the frequency and cross section of the elastic collision of electrons with helium atoms.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 7–11, February, 1987.In conclusion, the authors express their gratitude to Professor N. P. Penkin for useful discussions concerning this work.     

Oscillatory screening and quantum interference effects on electron collisions in quantum plasmas

The oscillatory screening and collision-induced quantum interference effects on electron-electron collisions are investigated in dense quantum plasmas. The modified Debye-Hückel potential with the total spin states of the system is considered to obtain the differential electron-electron scattering cross section in quantum plasmas. It is shown that the electron-electron scattering cross section decreases with an increase of the quantum wave number. In addition, the minimum position of the cross section has been appeared with increasing the collision energy at the scattering angle θL=π/4. It is also found that the oscillatory screening effects strongly suppress the cross section near θL=π/4. In addition, it is found that the quantum interference effects suppress the cross section, especially, for the forward and backward scattering cases.     

Application of R-matrix method to electron-H<Subscript>2</Subscript>S collisions in the low energy range

Electron-H₂S collision process is studied using the R-matrix method. Nine low-lying states of H₂S molecule are considered in the R-matrix formalism to obtain elastic integral, differential, momentum transfer and excitation cross sections for this scattering system. We have represented our target states using configuration interaction (CI) wavefunctions. We obtained adequate representation of vertical spectrum of the target states included in the scattering calculations. The cross sections are compared with the experiment and other theoretical results. We have obtained good agreement for elastic and momentum transfer cross sections with experiment for entire energy range considered. The differential cross sections are in excellent agreement with experiment in the range 3–15 eV. A prominent feature of this calculation is the detection of a shape resonance in ²B₂ symmetry which decays via dissociative electron attachment (DEA). Born correction is applied for the elastic and dipole allowed transition to account for higher partial waves excluded in the R-matrix calculation. The electron energy range is 0.025–15 eV.     

Electron-spin-dependent 4He+ ion scattering on Bi surfaces

We studied low-energy (～ 1.55 keV) electron-spin-polarized ⁴He⁺ ion scattering on a Bi(111) ultrathin film epitaxially grown on a Si(111) substrate. We observed that the scattered ion intensity differed between the incident He⁺ ions with up and down spins even though Bi is a non-magnetic element. To analyze the origin of this spin-dependent ion scattering (the spin asymmetry), we investigated the detailed relationship between the spin asymmetry and the incident angle, the azimuthal angle, the scattering angle, and the incident energy. All the data indicate that the spin asymmetry originates from the scattering cross section owing to the non-central force in the He⁺–Bi atom binary collision. The non-central force is most likely attributed to the spin–orbit coupling that acts transiently on the He⁺ 1s electron spin in the binary collision.     

Die Methode der Normallösungen für die Vlasov-BGK-Gleichung

The linearized Vlasov equation with collision damping is solved by the method of normal modes of Van Kampen and Case. The system considered is an infinitely extended nonrelativistic nondegenerate electron gas with neutralizing ion background and neutral particles. There is no magnetic field. Collision damping is taken into account by complete Bhatnagar-Gross-Krook collision integrals for electron-electron collisions and electronion collisions; in the case of a partially ionized gas elastic collisions between electrons and neutrals can be included likewise. The Vlasov-BGK operator is transformed into an integral operator yielding complex singular normal modes even if the equilibrium distribution is a Maxwellian. The adjoint integral equation belongs to a more complicated type than that of a collision-free system. Its solutions must be orthogonalized. The set of all normal modes is complete rendering the exact solution of the initial value problem possible. The completeness is shown by transformations and regularization of the singular integral equation of the initial value problem, the techniques of Case not being applicable because of the complicated type of this equation.     

Collision operator for relativistic electrons in a cold gas of atomic particles

The collision operator of relativistic electrons with a cold gas of atomic particles is derived consistently taking into account elastic interactions, excitation of electron shells, and ionization. The creation of secondary electrons is described accurately. In the range of energies exceeding the binding energy of atomic electrons, the operator implicates only the angular scattering by nuclei and the ionization integral that automatically allows for scattering by atomic electrons. The collision operator used earlier for studying the kinetics of avalanches of relativistic runaway electrons is analyzed. A more exact operator derived in the present study is simpler in form and saves time in computer calculations.