On the accuracy of the BGK model for ion drift in own gas

The model of collisions of ions with gas atoms, considering resonant charge exchange of ions, polarization and elastic (gas-kinetic) interactions is constructed. Ion drift characteristics in the dc electric field are calculated. The results are compared to calculations based on the Bhatnagar-Gross-Krook model collision integral (BGK integral). It is shown that the use of the BGK collision integral leads to significant errors due to the specificity of ion-atom collisions.     

Matrix elements and kernels of the collision integral in the Boltzmann equation

This article elaborates upon our previous work in which some general properties of the matrix elements and kernels of the gain and loss terms of the collision integral were found. The object of study is the loss term of the collision integral, since related analytical expressions are simple. Formulas to calculate the matrix elements are derived. The kernels of power-law interaction potentials are completely investigated and constructed using analytical and numerical approaches.     

Some general properties of the nonlinear collision integral in the Boltzmann equation

A new method for computing matrix elements of the collision integral in the Boltzmann equation makes it possible to consider many problems of the kinetic theory of gases in a new way. Nonlinear kernels of the collision integral are studied and similarity relations, which simplify significantly the problem of constructing of such kernels, are proved.     

Theory of generalized collision integral. III

The general formalism of diagram technique in the theory of collision integrals of classical systems [1] is applied for summing ring diagrams that first undergo ladder renormalization or renormalization because of a strong applied variable field at the “first” stage of the time history. Non-Markov retardation effects, which are particularly substantial in dense systems experiencing a rapidly variable field, are rigorously taken into account. Procedures are indicated for reducing the generalized collision integral to a non-Markov Balescu collision integral, and to a Silin collision integral in a rapidly variable applied field.     

Electron-ion collision integral in a strong magnetic field

Boltzmann’s collision integral is extended to the case of helical (Larmor) particle trajectories in a magnetic field of arbitrary strength. The main characteristics of collisions of electrons with positively charged ions in strong magnetic fields, where the Larmor radius of electrons becomes less than the characteristic impact parameter of close collisions in the absence of a magnetic field (Landau’s parameter), are investigated. The differential scattering cross section and the corresponding electron-ion collision integral in strong fields are found. The transport collision frequencies are calculated, and the results are compared with the similar quantities for weaker magnetic fields.     

Measurement of the electron-atom collision integral in low-temperature helium plasma

An expression is obtained for the electron-atom collision integral for axisymmetric low-temperature plasmas. The Legendre components of the collision integral are determined experimentally by the probe method. Comparison of the measured Legendre components with their theoretical values shows that, depending on the plasma conditions, the collisional regime or a regime of dominant collective interactions is established in the system. Zh. Tekh. Fiz. 67, 19–24 (April 1997)     

General Properties of Collision Integral Kernels of the Nonlinear Boltzmann Equation

Technical Physics - We consider general properties of kernels of the inverse collision integral, as well as kernels of integral operators appearing in the expansion of the collision integral in...     

To the theory of the generalized collision integral. II

The method of nonstationary diagram summation, previously developed [1], is applied to constructing the collision integral for a classical plasma, in which ring diagrams with prior ladder renormalization are included, which is equivalent to including screening of a long-range potential and finite momentum transfer in binary collisions. For a spatially homogeneous plasma it is shown that in the collision integral obtained the collision cross section does not contain the characteristic Coulomb divergences.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 119–122, September, 1973.     

Thermalization of nonequilibrium electrons in quantum wires

We study the problem of energy relaxation in a one-dimensional electron system. The leading thermalization mechanism is due to three-particle collisions. We show that for the case of spinless electrons in a single channel quantum wire the corresponding collision integral can be transformed into an exactly solvable problem. The latter is known as the Schr?dinger equation for a quantum particle moving in a P?schl-Teller potential. The spectrum for the resulting eigenvalue problem allows for bound-state solutions, which can be identified with the zero modes of the collision integral, and a continuum of propagating modes, which are separated by a gap from the bound states. The inverse gap gives the time scale at which counterpropagating electrons thermalize.     

20 Ne(34 Ne)原子与18 Na2(23 Na2,37 Na2)分子低温下冷碰撞的同位素效应研究

本文用多体刚性椭球模型计算了相对入射能量为190 meV时,氖的同位素原子²⁰Ne,³⁴Ne与钠的同位素分子¹⁸Na₂,²³Na₂,³⁷Na₂ 替代碰撞体系的态态转动激发积分散射截面和总转动激发积分散射截面,在此基础上计算并分析了相互作用势的不同区域对²⁰Ne-¹⁸Na_{2关键词： 多体刚性椭球模型 转动激发积分散射截面 钠同位素分子 椭球等势面}     

Generalized quantum kinetic equation for conducting disordered media

A quantum kinetic equation for disordered structures is derived using the Kadanoff-Baym technique. The nonlocal nature of the collision integral and the influence of the external field are taken into account by the generalized Kadanoff-Baym ansatz (GKB ansatz). The collision integral is explicitly constructed for the substitional A_xB_1–x binary alloy system.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 14–20, May, 1989.     

Precritical increase of particle collision rates

In quantum kinetics the collision integral follows from the imaginary part of the mass operator. Using this connection we demonstrate that the coupling of single particle motion to precritical density fluctuations causes a strong increase of the collision integral near the point of instability.     

Generalization of the Hecke theorem for the nonlinear Boltzmann collision integral in the axisymmetric case

The properties of the nonlinear collision integral in the Boltzmann equation are studied. Expansions in spherical Hermitean polynomials are used. It was shown [1] that the nonlinear matrix elements of the collision operator are related to each other by simple expressions, which are valid for arbitrary cross sections of particle interaction. The structure of the collision operator and the properties of the matrix elements are studied for the case when the interaction potential is spherically symmetric. In this case, the linear Boltzmann operator satisfies the Hecke theorem. The generalized Hecke theorem, from which it follows that many nonlinear matrix elements vanish, is proved with recurrence relations derived. It is shown that the generalized Hecke theorem is a consequence of the ordinary Hecke theorem.     

Inclusion of interparticle correlations in the collision integral by means of continuous integration. II

Representation of the causal two-body Green's function in the form of a double (with respect to the external fields and the trajectories) continuous integral with a subsequent density expansion and termwise integration with respect to the external fields is used to consider correlation corrections to the collision integral for charged quantum particles in the field of the compensating background. The first-order coupling approximation leads to a nonlinear dependence of the collision integral on the two-particle Green's function, and in developing different approximations for the latter, collision integrals associated with the ring and ladder diagrams of Silin and Balescu that allow for a slow time delay, as in [1, 2], are obtained, as is a collision integral with an exponential cutoff for small distances.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 118–121, April, 1976.The author is grateful to L. Ya. Kobelev for suggesting the topic and his interest in the work, and to B. N. Shalaev for useful discussions.     

Bootstrap und Feuerballverteilungen

It is assumed that in an inelastic collision of two particles at high energy fireballs are created, the decay of which produces the observed particles. The fireball distribution results from the decay of the primary hadron system into a leading fireball and a rest system, which can decay further. The decay is assumed to behave according to a bootstrap condition, making the fireball distribution, that results from the rest system in its rest frame, equal to the fireball distribution in the total collision in the c.m. frame. This bootstrap condition leads to an integral equation. Approximate solutions of this integral equation in the scaling limit are discussed.     

Isotropic matrix elements of the collision integral for the Boltzmann equation

We have proposed an algorithm for constructing matrix elements of the collision integral for the nonlinear Boltzmann equation isotropic in velocities. These matrix elements have been used to start the recurrent procedure for calculating matrix elements of the velocity-nonisotropic collision integral described in our previous publication. In addition, isotropic matrix elements are of independent interest for calculating isotropic relaxation in a number of physical kinetics problems. It has been shown that the coefficients of expansion of isotropic matrix elements in Ω integrals are connected by the recurrent relations that make it possible to construct the procedure of their sequential determination.     

Calculation of the collision integral linear kernel for Maxwellian molecules in the isotropic case

Application of the method of nonlinear moments to solve the Boltzmann equation generates the need to sum a series that is the expansion of the distribution function in basis functions. This series converged only if the Grad test is fulfilled. Such a limitation can be removed if the expansion of the distribution function is summed over the index related to only the expansion in velocity magnitude. In this case, the distribution function and the collision integral become expanded in only spherical harmonics and the expansion coefficients satisfy integro-differential equations. The kernels of these equations are the sums of the Sonine polynomials in the velocities of colliding and outgoing particles multiplied by matrix elements of the collision integral. For a number of arguments, the direct calculation of the kernels requires that a very large number of terms in the sum be taken into consideration. In this respect, an approach seems to be promising in which the asymptotics of the matrix elements and Sonine polynomials at large indices are used and summation over index is replaced by integration. In this paper, we apply this approach to calculate the linear kernel in the isotropic case, assuming that interaction between particles is described by a pseudopower law. With this approach, the collision integral kernel can be calculated with a high accuracy using as little as a few tens of series terms and the asymptotic estimate of the residue.     

O+DC1→OD+Cl反应在~3 A″势能面上的动力学研究(英文)

在~3A″势能面上,在散射能为14～20 kcal/mol的范围内,运用准经典轨线方法对O+DCl→OD+Cl进行了动力学研究.我们发现积分散射截面随着散射能的增加而增大,产物OD的振动分布发生了很强的粒子数的反转现象,且振动激发较弱、转动激发较强.后向散射居于主导地位,碰撞能的变化对产物转动取向的影响不大.     

钠分子同位素替代对低温下的He-Na2冷碰撞体系转动激发积分散射截面的影响

用多体刚性椭球模型计算了不同能量下氦的同位素原子⁴He,¹⁰He与钠的同位素分子¹⁸Na₂,²³Na₂,³⁷Na₂ 替代碰撞体系的转动激发积分散射截面.通过分析⁴He,¹⁰He-¹⁸Na₂,²³Na₂,³⁷Na₂各转动激发积分散射截面的差异,总结出在钠分子的对称同位素替代情形下⁴He,¹⁰He -¹⁸Na₂,²³Na₂,³⁷Na₂碰撞体系转动激发积分散射截面随钠分子转动量子数和体系约化质量变化的规律.结果表明,体系的约化质量及入射原子相对碰撞能量的变化均给体系的碰撞截面带来不同程度的影响.另外,计算了相对入射能量为100 meV时,相互作用势的不同区域对¹⁰He-¹⁸Na₂,²³Na₂,³⁷Na₂各碰撞体系转动激发积分散射截面的贡献情况. 关键词： 多体刚性椭球模型 转动激发积分散射截面 钠同位素分子 椭球等势面