Adiabatic approximation on the impact-parameter model

In this paper we study the impact-parameter model for the scattering of a light particle by two heavy ones in the case when the coupling constants of the potentials acting on the light particle due to the presence of the two heavy ones are the same. We study the asymptotic behavior of the transition probability when the relative velocity of the heavy particles goes to zero. We show that the probability of a transition can be arbitrarily close to the one of no transition.     

Proton and α-particle impactM-shell ionization of atoms in binary encounter approximation

M-shell ionization cross sections for atoms due to the impact of proton and α-particles have been calculated in the binary encounter approximation. The effects of Coulomb deflection of the incident projectile and increase in binding of the target electron have been investigated. Roothan-Hartree-Fock velocity distribution for the target electrons has been used in the present work. The calculated cross-sections have been compared with experimental results and other theoretical calculations wherever available. The present calculations give a good account of experimental observations.     

The effect of the relativistic Hartree-Fock-Roothaan momentum distribution in the binary encounter approximation for inner shell ionization

K- and L-shell ionization cross sections of gold due to impact of proton and alpha particles have been calculated in the binary encounter approximation incorporating the effects of Coulomb deflection of the projectile, of increase in binding of the target electron, and of polarization and relativity. Relativistic Hartree-Fock-Roothaan (RHFR) momentum distributions for the target electron along with an approximate relativistic correction to the collision dynamics have been used in the present calculations. A comparison with the corresponding calculations using non-relativistic Hartree-Fock-Roothaan wave functions, experimental results and other available calculations is presented.     

The binary encounter peak in radiative ionization

It is shown that the radiative electron capture to continuum in energetic collisions with fast heavy projectiles also leads to a binary-encounter type peak in the high-energy electron spectrum. In contrast to the nonradiative target ionization this peak results from a higher-order process, involving near-elastic scattering, and its shape is different from the target Compton profile. Numerical results within the impulse approximation are presented for 30 MeV/amu Kr³⁶⁺ + H collisions, and the dependence of the peak on collision velocity, target binding and electron emission angle is discussed.     

A time dependent Born-Oppenheimer approximation

We consider the dynamics of a quantum mechanical system which consists of some particles with large masses and some particles with small masses. As we increase the large masses to infinity we obtain the following results: The particles of smaller mass move adiabatically and determine an effective potential in which the heavier particles move semiclassically. Our methods can be applied to diatomic molecules with Coulomb forces.Supported in part by the National Science Foundation under Grant PHY 78-08066     

Remarks concerning the nuclear surface and curvature energy

The $\text{A}\text{1}\text{3}$ term in the nuclear mass formula is studied. The curvature correction is investigated within the framework of the energy density formalism; the compression term is evaluated from a phenomenological point of view. The results are in fair agreement with the droplet model values obtained by Myers and Swiatecki.     

Reversible charge transfer in solids; binary approximation

A common theory of reversible charge transfer (RCT) kinetics for low and high excitation power with the use of the conditional concentration of acceptors is presented. A comparison with recently published RCT theory is given. The results are similar or identical only in restricted or fractal spaces of low dimension, and in the case of low concentration of acceptors, i.e. in all the cases when the conditions of the binary approximation are fulfilled. The deviation from the binary approximation results in a physically incorrect picture, the cause being due to the different space averaging procedure. The probability of the donor's cation state is an increasing function of the concentration of the acceptor and of the characteristic parameters of the rate constants. Received 26 May 1999     

Remarks concerning the derivation and the expansion of the master equation

The present work consist of two parts: In the first part we apply the method of quasilinearization to the differential equation describing the time development of the quantum-mechanical probability density. In this way we derive the master equation without resorting to perturbation theory. In the second part of the paper, for a general form of the master equation which is an integro-differential equation, we test the accuracy of the Fokker-Planck approximation with the help of a solvable model. Then we study an alternative way of reducing the integro-differential equation to a partial differential equation. By expanding the transition probability W(q, q′), and the distribution function in terms of a complete set of functions, we show that for certain forms of W(q, q′), the master equation can be transformed exactly to partial differential equations of finite order.     

Remarks concerning the notion of free fall in axiomatic space-time theory

The notion of free fall plays a central role in EPS axiomatics. A constructive procedure for the detection of freely falling gravitational monopoles has been elaborated by Coleman and Korté. This was done in order to eliminate the vagueness of the primitive notion of free fall from spacetime theory. In this paper it is shown that neither the gravitational monopoles nor their free fall can be detected by the proposed procedure alone, without using physical laws beyond the mentioned spacetime theories. For this purpose, two examples of geodesic directing fields in a Schwarzschild space time are presented, one for particles obeying a special Lorentz-force equation and one for objects obeying Papapetrou's spinning particle equation. Two possibilities are discussed to overcome the difficulties of the constructive procedure.     

Coherent potential approximation to order-disorder transition in binary alloys

A band theory of order-disorder transition in an AB alloy is studied using the locator formalism in the coherent potential approximation. The influence of the difference in the band widths of A and B metals on the transition temperature is discussed.     

Microkinetics of the Ising-Glauber model in the binary approximation

Phase transitions in ferromagnets described by the Ising model are investigated in terms of the solution of a hierarchy of microscopic equations for unary and binary distribution functions. A dynamical procedure for making the equations self-consistent is developed. For cubic crystals, an equation of state relating the long-range order parameter to temperature and magnetic field is obtained in analytic form. The temperature dependence of the magnetic susceptibility and of the specific heat are calculated. A stability criterion is obtained for the stationary states of the system is obtained. The dynamics of magnetization reversal by constant and ac external fields are investigated. Fiz. Tverd. Tela (St. Petersburg) 40, 519–523 (March 1998)     

Binary encounter approximation for the electron-impact double ionization cross section of atoms and ions

An binary encounter approximation is formulated for the direct (without any excitation of autoionization levels) double ionization of atoms and ions by electron impacts. Analytical expressions are derived for the cross section, which qualitatively represent the main dependences on the incident electron energy and atomic parameters.     

Computer simulation of low-energy sputtering in the binary collision approximation

The sputtering of amorphous Cu targets by low-energy atoms has been investigated in the binary collision approximation using the computer program MARLOWE. Particular attention was given to the influence of the surface binding model on the results. Calculations were made of the dependence of the sputtering yield on the incident particle direction, energy, and mass. Angular-, energy-, and yield-distributions of the ejected atoms were evaluated. Comparisons with experimental results on polycrystalline targets show that the planar surface binding model is to be preferred over the isotropic surface binding model, especially with regard to the angular- and energy-distributions. Calculated yields are in reasonable agreement with experiment at energies below about 1 keV, but deviate at higher energies, apparently because of crystal correlation effects that are neglected in the amorphous model. Operated by Union Corporation under contract W-7405-eng-26 with the U.S. Department of Energy.     

Doubly differential cross section for binary encounter with massive projectile and isotropic target velocities

The nonrelativistic doubly differential cross section for electrons ejected from atoms by a massive beam of bare ions is derived in the binary encounter approximation. For cases already published the results sometimes differ by as much as a factor of 80 from those of Bonsen and Vriens, although the agreement should be exact. The case when the struck electron was initially very slow or stationary is also considered. Methods are presented for visualizing the kinematics including questions of minimum and maximum initial electron velocity for a given energy transfer. Also presented is a graphical means of visualizing the origin of the binary peak and of other effects for various atomic numbersZ of the target and various projectile velocities.     

Electron-electron correlation in disordered binary alloys: The T-matrix approximation

Dynamical electron-electron correlation in paramagnetic disordered binary alloys described by the Hubbard-type Hamiltonian is studied using the T-matrix approximation (TMA) valid for low concentration of particles ( $\text{\$}\text{?}$0.6/atom). We introduce the terminal-point approximation for the many-body quantities, which allows us to solve the random part of the problem within the single-site approximation (CPA). The one-centre version of the TMA is used in numerical calculations. Results are compared with those of the Hartree-Fock approximation, and with the model of a pair of interacting electrons in a random alloy (CPA II).     

Remarks concerning the applicability of an Arrhenius-type relation to infrared multiphoton dissociation processes

It is shown that, in the case of some halomethanes for which an Arrhenius-type relation can be fitted to the IRMPD probabilities as a function of CO₂-laser pulse energy, the pre-exponential factor is about equal to the ratio of the reaction volume to the total gas volume.     

Remarks concerning the solution of the equations of quantum geometrodynamics by successive approximations

The improved version of the Einstein-Schrödinger equation of quantum gravity found by one of us is solved in the linear approximation. The solution differs from that obtained by K. Kucha for the original version of the equation by an additional quantum effect: The energy, as deduced from measurements of the gravitational potential at infinity, has an error function probability distribution about its eigenvalue. The higher approximations are also considered and the appearance of a third quantum number, possibly related to the transition matrix, is deduced.