Non-partial-wave Coulomb-Born theory for the excitation of many-electron atomic ions II: Numerical description and application

A non-partial-wave Coulomb-Born theory is recently formulated to treat the excitation of many-electron atomic ions for impact by an arbitrary charged particle [Y.B. Duan et al., Phys. Rev. A 56, 2431 (1997)]. The multiple expansion of the transition matrix element is decomposed into the target form factor and the projectile form factor. These are the matrix elements of the tensor operators between quantum states so that any complicated wave function for the target ion can be employed. In this formal theory, an infinitesimally small positive quantity is introduced artificially to guarantee the convergence of integrals. As a supplementary part of the theory, we discuss how to choose the value of . It is found that the should be taken as functions of the momentum transfer and multipolarity . Illustrations are carried out by calculating the cross-sections for some typical transitions n _a l _a -n _b l _b of hydrogen-like ions for impact by electron, positron, and proton, respectively. The resulting cross-sections are in good agreement with ones produced by using a method available for ion targets with Slater-type orbitals [N.C. Deb, N.C. Sil, Phys. Rev. A 28, 2806 (1993)]. Comparisons demonstrate that the Coulomb-Born theory with non-partial wave analysis provides a powerful method to treat the excitation of many-electron atomic ions impact by an arbitrary charged particle. Received 6 April 1999     

Nondipole parameters of TDCS for electron impact ionization and drag current

A comprehensive study is undertaken of angular distributions of electron knock-out from atomic targets by fast electrons with a small transfer of momentum. The general expressions for the parameters of the triple differential cross-section of impact ionization in the optical limit are derived. The calculated parameters are compared with those of the angular distribution of electrons ejected from an atom in the process of photoionization. In these processes, when the multipole transitions are involved, the one-to-one correspondence between the photoionization and impact ionization parameters disappears. The nondipole transitions lead to the backward/forward asymmetry of the angular distribution of ejected electrons that is absent in the dipole approximation for ionization by both fast electrons and photons. Using the He atom as an example, the character of the asymmetry for these two processes is qualitatively different and the backward/forward asymmetry results in macroscopic directed motion of secondary electrons accompanying the passing of a fast electron beam through gas or plasma. The general formulas for this drag current are derived and applied to gaseous He.     

Electron-molecule scattering processes

Summary The collisions of slow electrons (k ²<2 Ryd) with gaseous molecules provide a very powerful experimental tool for the study of molecular properties and for correlating their structural characteristics with the specific ways in which energy is exchanged and stored during each encounter between the impinging light charge and the various molecular degrees of freedom. In the present study a generalab initio approach is described for treating the various parts of the interaction occurring between the bound molecular electrons and those in the continuum of the probing beam. It is shown that the results found with this method are closely correlated with our knowledge of the molecular structure which thus bears great significance when interpreting collisional events involving simple molecular targets.

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Riassunto Le collisioni di elettroni lenti con molecole gassose forniscono un potente mezzo sperimentale per correlare specifiche proprietà molecolari con il comportamento dinamico del sistema e con i processi competitivi di deposizione selettiva di energia nei vari gradi di libertà molecolare. In questo studio si descrive un metodo completamente generale edab initio per trattare le varie componenti dell'interazione fra gli elettroni legati e quelli nel continuo del fascio incidente. Si mostra, per molecole polari come esempio iniziale, che tale metodo permette di correlare in modo chiaro le nostre conoscenze di struttura molecolare con il dettagliato comportamento dinamico del processo collisionale in questione.

     

Dynamics of ionization mechanisms in relativistic collisions involving heavy and highly-charged ions

The dynamics of mechanisms associated with the ionization of inner-shell electrons in relativistic collisions involving heavy and highly-charged ions is investigated within a nonperturbative approach formulated explicitly in the time domain. The theoretical treatment is based on the exact numerical solution of the time dependent Dirac equation for two Coulomb centers on a lattice in momentum space. We present results for ionization in encounters between 100 MeV/u Au⁷⁹⁺ projectile ions impinging on a hydrogen-like uranium target. By directly visualizing the collision dynamics we identify a new ionization mechanism in which electrons are emitted from the internuclear region preferentially in the transverse direction with respect to the projectile trajectory. A striking characteristic of this ionization mechanism is that the velocity of the electron is higher than the projectile velocity. Received 26 June 2001 and Received in final form 27 November 2001     

Electron scattering from an assembly of point scatterers in the presence of a quantizing magnetic field

Summary We have studied the scattering of electrons by a structured target in the presence of a quantizing static magnetic field, under the assumption that the presence of the field does not affect the behaviour of the massive target nuclei, but it influences only the motion of the incident electrons. In this case, the electron motion in the plane perpendicular to the magnetic field is confined within a typical distance given by the cyclotron radius ρ₀=(cℏ/|e|B)^1/2, that for particular values of the intensity of the magnetic field can be comparable with the distance between two scattering centres. The known field-free interference conditions are modified, depending both on the energy of the incident particle and on the intensity and the direction of the magnetic field. The general case of a three-dimensional scattering array has been derived in detail. Numerical results are given for the case of two scattering centres in perpendicular geometry. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Identification of structural vacancies in carbides,oxides, and sulfides by Doppler broadening of the gamma-ray line

A method has been developed to identify the sublattices of a crystal structure in which there are atomic vacancies. This method is based on determining the chemical environment of vacancies and is implemented using the method of the positron annihilation by measuring the momentum distribution of core electrons. To determine the characteristic momentum distribution of electrons, a special two-detector spectroscopy is used, which ensures measurements of Doppler broadening of the annihilation gamma-ray line with a high (up to 10⁶) signal-to-noise ratio. To test the method, vacancies in irradiated silicon carbide (6H-SiC), sintered nonstoichiometric titanium carbides (TiC _y ) and titanium monoxides (TiO _y ), and chemically deposited lead and cadmium sulfides (PbS and CdS) have been identified. Vacancies in the carbon and silicon sublattices have been identified in silicon carbide after irradiation by low- and high-energy electrons, respectively. Vacancies in the nonmetal sublattice have been identified in TiC _y . Vacancies in the metal sublattice have been identified in TiC _y , as well as in PbS and CdS.     

Laser radiation-induced acceleration of forbidden captures of orbital electrons by nuclei

The effect of linearly polarized laser radiation on the rate of the capture of atomic electrons by nuclei has been investigated. The allowed capture of s-state bound electrons from (inner) K,L, and M shells can only be weakened by the external electric field due to the shift of the maximum of the wavefunction of the bound electron with respect to the nucleus; at the same time, the wavefunctions of electrons in states with a nonzero orbital angular momentum on the nucleus can increase. The probability of various forbidden unique electron captures involving these states increases correspondingly. The problem has been examined in the simple Slater approximation. The calculations indicate that laser fields with the amplitude larger than the atomic value can significantly accelerate the first forbidden capture of p electrons, whereas laser fields with the amplitude smaller than the atomic value can significantly accelerate the second forbidden capture of d electrons.     

Coplanar (<Emphasis Type="Italic">e</Emphasis>, 3<Emphasis Type="Italic">e</Emphasis>) differential cross-section of He atom

We present in this paper the results of our calculation of five-fold differential cross-section (FDCS) for (e,3e) process on He atom in low momentum transfer and high electron impact energy in shake-off mechanism. The formalism has been developed in Born approximation using plane waves, Byron and Joachain as well as Le Sech and correlated BBK-type wave functions respectively for incident and scattered, bound and ejected electrons. The angular distribution of FDCS of our calculation is presented in various modes of coplanar geometry and comparison is made with the available experimental data. We observe that the present calculation is able to reproduce the trend of the experimental data. However, it differs in magnitude from the experiment. The present theory does not predict four-peak structure insummed mutual angle mode for lower excess ejected electron energies. We also discuss the importance of momentum transfer, post-collision interaction (PCI) and ion participation in the (e,3e) process in constant θ₁₂ mode     

Small bipolarons in the 2-dimensional Holstein-Hubbard model. I. The adiabatic limit

The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction , which tends to break them, generates many different ground-states. There are four domains in the phase diagram delimited by first order transition lines. Except for the domain at weak electron-phonon coupling (small g) where the electrons remain free, the electrons form bipolarons which can 1) be mostly located on a single site (small , large g); 2) be an anisotropic pair of polarons lying on two neighboring sites in the magnetic singlet state (large , large g); or 3) be a “quadrisinglet state” which is the superposition of 4 electronic singlets with a common central site. This quadrisinglet bipolaron is the most stable in a small central domain in between the three other phases. The pinning modes and the Peierls-Nabarro barrier of each of these bipolarons are calculated and the barrier is found to be strongly depressed in the region of stability of the quadrisinglet bipolaron. Received 10 December 1998     

A simple non-perturbative approach of atom ionisation by intense and ultra-short laser pulses

A simple theoretical approach based on Coulomb-Volkov states is introduced to predict ionisation of atoms by intense laser pulses in cases where the effective interaction time does not exceed one or two optical cycles [M. Nisoli et al., Opt. Lett. 22, 522 (1997)]. Under these conditions, the energy distributions of ejected electrons predicted by this non-perturbative approach are in very good agreement with “exact" results obtained by a full numerical treatment. The agreement is all the better that the principal quantum number of the initial state is high. For very strong fields, most electrons are ejected at an energy which is close to the classical kinetic energy that would be transferred to free electrons by the electromagnetic field during the pulse. The power of the present approach appears when keV. In this region, full numerical treatments become very lengthy and finally do not converge. However, the present Coulomb-Volkov theory still makes reliable predictions in very short computer times. Received 19 November 1999 and Received in final form 19 January 2000     

Scaling of cross-sections for asymmetric (e, 3e) process on helium-like ions by fast electrons

An approximate simple scaling law is obtained for asymmetric (e, 3e) process on helium-like ions for double ionization by fast electrons. It is based on the equation (Z ^′3π) exp[-Z(r₁ + r₂)],Z′ = Z – (5/16) for ground state wave function of helium-like ions and Z^′2 scaling of energies. The scaling law is found to work very well if the lower energy electron is ejected along the momentum transfer direction and the other one is ejected in the opposite direction. It also works quite well if this electron is ejected within about 90° of the momentum transfer direction with the other electron going in the opposite direction. The scaling law becomes increasingly accurate as the target nuclear charge and the energy increase.     

Auger electron emission from metals induced by low energy ion bombardment: Effect of the band structure and Fermi edge singularity

Calculations of the kinetic energy distributions of electrons ejected from plane metal surfaces by Auger neutralization of slow monoatomic ions are reported. A many body theory is used that includes both the band structure of the target material and the Fermi singular response of metal electrons (to the sudden neutralization of the projectile). Application is made to experiments of electron emission from polycrystalline Al by Ar⁺-ions, at varying incident energies and angles. Adjustment of the broadening parameters of the distribution of shake-up electrons leads to excellent agreement between the theory and the measurements.     

Small polaron formation in many-particle states of the Hubbard-Holstein model: The one-dimensional case

We investigate polaron formation in a many-electron system in the presence of a local repulsion sufficiently strong to prevent local-bipolaron formation. Specifically, we consider a Hubbard-Holstein model of interacting electrons coupled to dispersionless phonons of frequency . Numerically solving the model in a small one-dimensional cluster, we find that in the nearly adiabatic case , the necessary and sufficient condition for the polaronic regime to occur is that the energy gain in the atomic (i.e., extremely localized) regime overcomes the energy of the purely electronic system . In the antiadiabatic case, , polaron formation is instead driven by the condition of a large ionic displacement (g being the electron-phonon coupling). Dynamical properties of the model in the weak and moderately strong coupling regimes are also analyzed. Received 15 February 1999     

Limitations of the strong field approximation in ionization of the hydrogen atom by ultrashort pulses

We present a theoretical study of the ionization of hydrogen atoms as a result of the interaction with an ultrashort external electric field. Doubly-differential momentum distributions and angular momentum distributions of ejected electrons calculated in the framework of the Coulomb-Volkov and strong field approximations, as well as classical calculations are compared with the exact solution of the time dependent Schr ödinger equation. We show that in the impulsive limit, the Coulomb-Volkov distorted wave theory reproduces the exact solution. The validity of the strong field approximation is probed both classically and quantum mechanically. We found that classical mechanics describes the proper quantum momentum distributions of the ejected electrons right after a sudden momentum transfer, however pronounced the differences at latter stages that arise during the subsequent electron-nucleus interaction. Although the classical calculations reproduce the quantum momentum distributions, it fails to describe properly the angular momentum distributions, even in the limit of strong fields. The origin of this failure can be attributed to the difference between quantum and classical initial spatial distributions.     

Negative muon capture in very light atoms

The transition rates for unbound muons to be captured into atomic bound states are calculated as functions of (1) incident muon center-of-mass energy, (2) muon principal quantum number n, and (3) muon (final) angular momentum l, for the hydrogen, helium, and lithium atoms. These rates reflect differences in electron binding energies. At muon energies of several hundred electron volts, lithium K-shell electrons are more likely to be ejected than the L-shell electron, while this behavior is reversed for energies ? 10 eV. However, in each case when the capture rate is folded with a muon stopping power function, the result is that more than half of the unbound muons are absorbed above 75 eV. Implications for experiments which look at muon transfer processes are noted.     

Quantum decoherence from adiabatic entanglement with external one or a few degrees of freedom

Based on the Born-Oppenhemer approximation, the concept of adiabatic quantum entanglement is introduced to account for quantum decoherence of a quantum system due to its interaction with a large system of one or a few degrees of freedom. In the adiabatic limit, it is shown that the wave function of the total system formed by the quantum system plus the large system can be factorized as an entangled state with correlation between adiabatic quantum states and quasi-classical motion configurations of the large system. In association with a novel viewpoint about quantum measurement, which has been directly verified by most recent experiments [e.g., S. Durr et al., Nature 33, 359 (1998)], it is shown that the adiabatic entanglement is indeed responsible for the quantum decoherence and thus can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. By taking the large system respectively to be a macroscopically distinguishable spatial variable, a high spin system and a harmonic oscillator with a coherent initial state, three illustrations are presented with their explicit solutions in this paper. Received 26 February 2000 and Received in final form 14 July 2000     

Analyzing the transition rates of the ionization of atoms by strong fields of a CO<Subscript>2</Subscript> laser including nonzero initial momenta

Here, the method of including nonzero initial momenta for ejected electrons in strong infrared laser fields is further developed [8]. It has been shown that, apart from being natural, including the nonzero initial momenta enables one to go into a deeper analysis of the process of tunnel ionization of atoms in strong laser fields (intensity up to 10¹⁶ W/cm²). This is due to looking closely at Fig. 2, which indicates that all electrons that could be ejected, under the circumstances, are ejected at a field intensity ～10¹³ W/cm², and that the effect of ionization after that is strongly diminished, which can be seen from the slope of the plates on Figs. 2 and 4. This also explains the saturation effect for fields up to 10¹⁶ W/cm² [1, 4, 5, 7], and probably this saturation goes on until the fields raising relativistic effects ～10¹⁸ W/cm² [7]. Opposite to what was believed earlier [7], the atomic field intensities could be increased to values over 10¹⁷ W/cm² only when more than 10 electrons are ejected from the atom, it is shown that the properly calculated ionization of 9 electrons increases the atomic field intensity to ～10¹⁸ W/cm².     

Theoretical studies of inelastic atomic collisions in a two-state model problem

A two-state scattering problem in which two non-crossing Morse curves are coupled by an exponential potential is discussed theoretically in both the diabatic and adiabatic approximations. Inelastic cross sections are estimated by various approximate analytical formulas, which are expressed in terms of the distorted wave matrix elements. The Landau (steepest descent) method is applied to estimate the distorted wave matrix element. The previously proposed separable potential approximation in the adiabatic method is found to be best among others by comparing with the exact numerical results. Transition probability as a function of l (angular momentum of relative motion) is well reproduced by this approximation. A glory effect in the velocity dependence of the cross section is found in the low energy region, and the adiabatic approximation reproduces this undulation phenomenon well.