The static approximation in the interpretation of collision broadening

The validity of the static approximation for analyses of spectral line profiles is considered. The Fourier transform of the profile of an isolated line is compared for representative cases with the unified theory, and it is shown that the simple static approximation can be used effectively to interpret low spectral resolution experiments. This result applies to the entire profile in the limit of high density, but it also applies at low density if the instrumental line width is sufficiently large. Furthermore, in the absence of turning points in the interatomic potential, the unified and static theories produce almost identical line-wing profiles. Easily evaluated criteria are provided to guide application of the straightforward static theory to the interpretation of interatomic potentials.     

Theory of tamm surface states in approximation higher than tight-binding approximation

The influence of the non-zero value of exchange integrals between Wannier functions, localized in non-neighbouring elementary cells (higher approximation than tight-binding), on the conditions of existence of Tamm surface states and the position of the energy level corresponding to the surface state is shown.

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This paper is part of M. Tomáek's candidate's thesis.     

Random phase approximation and continuum states

For scattering of nucleons the possibilities of including ground state correlations are investigated in a formalism similar to the usual shell model formalism. It is shown that the effect of the ground state correlations may be considerable.     

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.     

Construction of Pomeron states in the zero-width approximation

We present a kinematical construction for the Pomeron in models of relativistic composite particles in the zero-width approximation.     

Surface densities of states in the tight-binding approximation

We present a summary of the main results obtained by a new method of calculating the electronic structure of solids and their surfaces in the tight-binding approximation. In addition to being able to reproduce the results of Kalkstein and Soven, we obtain the local density of states at atoms in the low index surfaces of fcc, hcp and bcc d-bands. We also include examples of the effect of surface dilation, the density of states at atoms in subsurface layers, and a very simple example of the adatom density of states.     

Effective collision strengths among the fifteen lowest states of FeXVII

Collision strengths have been calculated for electron impact excitation of neon-like Fe XVII for all transitions within its 15 lowest states. Configuration interaction wavefunctions have been used to represent the target states. The standardR-matrix code has been used to calculate the contribution from the lower scattering partial waves (L⩽9), while the no exchange version of the same code has been used to compute efficiently the contribution of higher partial waves (L⩾10). Effective collision strengths for all the 105 transitions are tabulated for elected temperatures in the range logT _e=5.40 to logT _e=7.00 withT _e expressed in °K.     

Binary collision approximation for solitary waves in a Y-shaped granular chain

We implement a binary collision approximation to study solitary wave propagation in a two-dimensional double Y-shaped granular chain. The solitary wave was transmitted and reflected when it met the interface of the bifurcated branches of the Y-shaped granular chains. We obtain the analytic results of the ratios of the transmitted and reflected speeds to the incident speed of the solitary wave, the maximum force between the two neighbor beads in a solitary wave, and the total time taken by the pulse to pass through each branch. All of the analytic results are in good agreement with the experimental observations from Daraio et al. [Phys. Rev. E 82 036603 (2010)]. Moreover, we also discuss the delay effects on the arrival of split pulses, and predict the recombination of the split waves traveling in branches in the final stem of asymmetric systems. The prediction of pulse recombination is verified by our numerical results.     

Threshold singularities of theS-matrix and convergence of Haag-Ruelle approximations

We establish a one-to-one correspondence between the continuity properties of theS-matrix at the 2-particle threshold and the rate of convergence of the Haag-Ruelle approximations ψ(t) for asymptotic 2-particle states ψ with smooth wavefunctions. It turns out that the norm distance ∥ψ?ψ(t)∥ approaches 0 liktt ^?5/4 if theS-matrix has the normal threshold singularities and liket ^?3/4 in the exceptional case where the threshold has “absorbed” a bound state. These connections are valid both in relativistic quantum field theory and in non-relativistic models with short range interaction.     

周期型二元颗粒链中孤波传播的二体碰撞近似分析

本文运用二体碰撞近似理论研究了孤波在周期型二元颗粒链中的传播. 周期型二元颗粒链由N个大球和一个小球交替排列而成, 球的材质都相同. 将小球和与之相邻的大球等效成一个球, 形成一条等效链. 采用二体碰撞近似理论, 推导了孤波在颗粒链中传播的速度、通过颗粒链时间以及小球的振荡频率. 理论分析得到小球振荡频率随着半径的增大而减小, 该结果与计算机模拟结果符合得相当好. 二体碰撞近似理论给出的波通过整条颗粒链时间, 在N ≤ 2时与计算机模拟结果符合得很好. 理论计算的误差随链长的变化不大. 但随着N的增大, 理论得到的结果相对误差变大.     

Comparisons between statistics of low energy collision cascades generated by full molecular dynamics and by its binary collision approximation

Abstract

Collision cascades in Cu, Au and Cu₃Au are generated by full molecular dynamics (MD) and by its binary collision approximation (BCA) with the Marlowe program. Cu and Au primaries have 1 keV initial energy.

The same Molière repulsive potential is used in both models for close encounters. In the MD model, this potential is carefully splined to the pair component of the N-body potential developed by Ackland and Vitek. In the BCA, this N-body interaction is roughly modeled by a constant isotropic 4 eV binding energy of the target atoms to their rest positions.

Time distributions of the number of atoms moving with a total energy higher than a threshold value E _d are compared and discussed. Recoil range distributions during the cascade development are discussed as well. The agreement between MD and BCA is fairly good in all cases for E _d larger than about 3 eV. In the case of smaller E _d-values, the BCA may result in an overestimate of the number of moving atoms in the late development of the cascades. This discrepancy is suggested to originate in the lack of attractive forces between the moving particles and the surrounding atoms in the BCA.     

Interacting boson approximation for two-quasiparticle and collective states

The boson-fermion mapping problem is investigated for the case when pure collective quadrupole and two-quasiparticle modes are considered. Approximate expressions of the boson images of the fermion operators are derived.Dedicated to the memory of M. Gmitro.     

Temperature dependence of collective states in the random-phase approximation

We investigate the temperature dependence of collective states in the framework of the random-phase approximation at finite temperature. We show that sum rules can be extended to collective energies at finite temperature. Numerical methods are developed to solve the RPA equations at finite temperature. Results are presented and discussed in the case of ⁴⁰Ca for isovector dipole and isoscalar octupole vibrations, using oscillator wave functions and a zero-range force. We show that the broadening of giant dipole resonances observed experimentally, appears as a natural consequence of the structure of the RPA equations. Comparison is made with the schematic model for which the temperature dependence of collective states can be worked out analytically.     

Ion core approximation in calculations of excited atomic states

A one-configuration approximation is used to analyze the possibility of employing the frozen ion core model to calculate excited states with low-lying configurations of the same symmetry when the wave functions of the excited states are orthogonal to the function of the ground state. The nonorthogonality of the wave functions of different excited configurations is then weak. A calculation is made for certain Isns¹S and 1s²2sns¹S terms of two-and four-electron ions, respectively, and the relaxation effects in the core are investigated for these excited states. This approximation is employed to obtain a variational equation for virtual orbitals allowing for the core relaxation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 71–77, June, 1980.     

The inelastic contributions to transport collision integrals in the infinite-order sudden approximation

The transport collision integrals of the Wang Chang and Uhlenbeck kinetic theory of polyatomic gases have been evaluated for an anisotropic intermolecular pair potential model for the He-CO₂ interaction. The calculations have made use of the infinite-order sudden approximation to evaluate the state-to-state differential cross-sections, but otherwise involve no approximations.

The results indicate that some earlier approximate methods for the evaluation of the collision integrals are quantiatively correct, although they are given a new interpretation. In particular, the simplifications introduced by Mason and Monchick are shown to yield essentially the same collision integral for viscosity as the more exact treatment. On the other hand, several long established procedures for treating the transport properties of polyatomic gases and gas mixtures are shown to be significantly in error. Specifically the diffusion coefficient for internal energy is some 10 per cent higher than the diffusion coefficient for mass, and the latter itself quite different from that obtained on the basis of the treatment of Monchick and Mason.     

The Haag-Ruelle formulation of scattering in hyperfunction quantum field theory

The Källén-Lehmann representation for two-point Wightman Fourier hyperfunctions and the cluster property for truncated vacuum expectation values are established in the framework of hyperfunction quantum field theory. With some additional assumptions these properties allow one to verify the Haag-Ruelle asymptotic conditions.     

Excited states for Coulomb systems in the Hartree-Fock approximation

In this paper, we define excited states for Coulomb systems in the Hartree-Fock approximation as minima of the Hartree-Fock energy on a set of constraints depending on excited states of the lower energy. There are several ways to define such a procedure: we study four of them and prove an existence result for these excited states.