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.     

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.     

Binary correlation and convergent collision integral for a plasma

The BBGKY hierarchy equations for a homogeneous plasma are used to derive an explicit expression for the time-asymptotic binary correlation function. Closure of the hierarchy equations is shown possible, mainly due to a difference in scaling behavior, as functions of impact parameter(s), between the driving terms in the second and third hierarchy equations. The final result is shown to be a uniform approximation for interparticle distances much smaller than the minimum of the mean free path and the density inhomogeneity length. The resulting expressions for the free energy and the collision integral are convergent.     

Construction of renormalized collision integral for a quantum gas

A quantum analog is obtained for the renormalized collision integral derived for a classical gas in [1]. As usual [2], considering lag effects in the renormalized collision integral corresponds to taking account of the nondissipative contribution of the interaction.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 107–109, August, 1978.It remains to thank L. Ya. Kobelev for his interest in the work, and for useful critical comments.     

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.     

The collision integral in nuclear matter at zero temperature

The collision rate in an infinite Fermi system having a deformed Fermi surface is computed in the limit of small deformation. For a given amount of internal energy, the damping rate is nearly independent of temperature. The calculation is applied to thermalization in heavy ion collisions. We find that the collisional damping time is comparable to the duration of the collision for medium-weight nuclei. Thus the predictions of mean field theory, such as the presence of a fusion window at small impact parameters, will only have validity for lighter ions.     

Theory of the generalized collision integral. IV

In the maximum time interval of kinetic evolution of the single-particle distribution function of a spatially homogeneous system summation of the step diagrams (without intersections of the lines of propagation and interaction) is carried out for an arbitrary nonequilibrium state in the Markov limit, as well as for a local equilibrium state with regard for memory effects. Procedures are indicated for the step renormalization of diagrams of arbitrary order with respect to the density in the Markov limit, with subsequent ladder renormalization. Ring diagrams with preliminary step and ladder renormalizations are summed. A more correct derivation is given for the generalized Boltzmann (Boltzmann-Landau) collision integrals for dense systems with a strong short-range (as well as strong long-range) potential. It is shown that the step, ring, and ladder renormalizations yield a nondivergent two-particle distribution function in a classical equilibrium plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 86–91, August, 1978.     

Theory of the generalized collision integral. I

A diagram method previously suggested [1] for the construction of the integral collision in the single-particle kinetic equations is developed in this paper. The so-called diagram ladder summation, both with a variable external field and without it, is performed for systems with a strong short-range potential to any order in the density. It is shown that in a strong field the lowest order diagram in the density with preliminary ladder renormalization leads to a generalized Boltzmann collision integral.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 117–121, August, 1973.     

Relations between nonlinear kernels of the collision integral

Previously, to solve the Boltzmann equation by the moments method with expansion of the distribution function by spherical Hermit polynomials, a new computational method was suggested which allowed to construct nonlinear matrix elements of the collision integral with very large indices. This made it possible to substantially advance in construction of the distribution function. Limitations to convergence of the distribution function that appear in moment method are eliminated if we come to expansion by spherical harmonics from expansion by spherical Hermit polynomials. In this case, a complex five-fold collision integral is replaced by a set of comparatively simple integral operators, and kernels G _l1,l2 ^l (c, c ₁, c ₂) of these operators become the analog of matrix elements. We found the relations between expansions of the distribution function in the reference frames with various velocities of motion along marked axis. Starting from the invariance condition of the collision integral with respect to selection of such reference frames, we derived recurrent relations between the kernels with various indices. These relations allow us to construct any nonlinear kernel G _{l1, l2} ^l (c, c ₁, c ₂), if the kernel G _0,0⁰(c, c ₁, c ₂) is known.     

Asymptotics of collision integral matrix elements in the isotropic case

The method of nonlinear moments, when used to solve the Boltzmann equation, necessitates the calculation of collision integral matrix elements. The matrix elements are hard to calculate numerically, especially at large indices. The asymptotics of the matrix elements are constructed. In terms of the model of pseudopower particle interaction, a formula free of summation is derived. This makes it possible to find the asymptotic behavior of linear and nonlinear elements when two indices are large. For an arbitrary interaction cross section, asymptotic expansions of linear and nonlinear matrix elements in one index are obtained. For Maxwellian molecules, asymptotic formulas are derived for three large indices.     

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)     

Triple correlation in a plasma and the collision integral for the dual correlation function

A solution is derived to the equation for the triple correlation function of a system of charged particles, allowing for the effects of dynamic polarization and yielding an equation for dual correlation analogous to the kinetic equation for the simple distribution function.     

High-spin two-quasiparticle bands in76Br

Excited states of the doubly-odd nucleus V6Br have been studied with in-beam γ-ray spectroscopy techniques. In addition to the positive parity band that has been extended up to I=(13) a I^π=4^? isomer (T_1/2=0.5±0.2 ns) and two bands of negative parity have been identified. The bands are discussed in terms of two-quasiparticle configurations. For the band built on the 4_? isomer the configuration πg9/2?νf5/2 or p3/2 is proposed.     

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.     

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.