Test for the cumulant approximation in the critical region

A cumulant approximation in wide use is tested, in the critical region, against a straightforward product-average decomposition approximation previously used in conjunction with a new integral representation for the Ising model. It is found that for the calculation of the transition temperature, the cumulant approximation is significantly inferior to the product-average approximation.     

Neutrino oscillations: Deriving the plane-wave approximation in the wave-packet approach

The plane-wave approximation is widely used in the practical calculations conserning neutrino oscillations. A simple derivation of this approximation starting from the neutrino wave-packet framework is presented.     

Improving the Born approximation for the scattering of ultrasound in elastic solids

It has recently been demonstrated that the Born approximation for predicting the scattering response of flaws can be improved through the use of simple modifications called the "doubly distorted Born approximation". In this paper the doubly distorted Born approximation itself is modified with phase and amplitude corrections that further improve the Born scattering results for isotropic elastic media. The reliability of this new modification of the Born approximation has been evaluated by comparison with the exact solution for spherical inclusions obtained with the method of separation of variables. Unlike the ordinary Born approximation which works well only for very weak scattering inclusions, our modification of the doubly distorted Born approximation gives improved scattering results for both weak and strong scattering inclusions.     

Magnetic field effects in the presence of electrostatic interactions

Magnetic field effects on ion radical pair (IRP) recombination reactions are considered. In the diffusion approximation simple analytical expressions for the magnitudes of these effects are obtained. They are reduced to those obtained within the simple cage approximation in the case, when the intramolecular spin interactions are strong enough and to those obtained within the free radical approximation in the opposite case. The applicability of both simple approximations are shown to be closely connected with peculiarities of the IRP decay kinetics. Namely, the cage approximation is applicable for the strong spin interactions because the IRP decays exponentially at small times. The free radical approximation is valid in the opposite limit of weak interactions since at large times the IRP decays as a free radical pair.     

On the relaxation-time approximation for the two-body dissipation in HI collisions

In several previous publications the author has treated two-body collisions between the nucléons (the two-body dissipation) encountered in heavy-ion collisions by a relaxation-time approximation. This approximation is here tested against the calculations of Danielewicz in which he studied the dynamics of two slabs of nuclear matter (two Fermi spheres in momentum space) colliding with the NN interactions parameterized to fit NN cross sections. The relaxation-time approximation is found to be in good agreement especially with quantum-dynamical calculations.     

Inclusion of the exchange-correlation effects in Ab initio methods for calculating the plasmon dispersion and line width in metals

A self-consistent analog of the Hubbard local-field factor accounting for a real band structure of the metal under investigation is proposed for the calculation of the exchange-correlation corrections to the randomphase approximation. The plasmon energy and the plasmon line width for potassium are calculated as a function of the wave vector. The calculations are performed within the random-phase approximation and with corrections for the local field. It is shown that the results of the calculations are in good agreement with the experimental data. This indicates that, first, the corrections to the random-phase approximation should be taken into account for metals with a low electron density and, second, the local-field factor approximation is an appropriate approach.     

Nonlinear excitations in the low temperature region of the classical toda lattice

The ideal cnoidal wave gas approximation is presented. It is shown that this approximation is valid for low temperatures.     

On the choice of the condensation pressure in the condensation approximation

The choice of the condensation pressure in the condensation approximation is a rather ambiguous step, and only fortuitously the methods of choice proposed by Harris and by Cerofolini give the same results when applied to the Fowler-Guggenheim isotherm. In fact, the two methods lead to different condensation pressures when considering the Hill-De Boer isotherm. This article is due to the necessity of clarifying what method may be opportunely used: the conclusions of our discussion show that if the condensation approximation is a good approximation, then the obtained distribution function does not depend markedly on the assumed condensation pressure.     

On the validity of the quasi-particle approximation in nuclear physics

The validity of the quasi-particle approximation for the two-point function in nuclear physics is tested by means of one-particle strengths taken from (d, p) reactions. It is found that in general the quasi-particle approximation is not justified.     

Separability of a two-particle t-matrix in the case of the three-body problem

A factorization is proposed in this article of a two-particle t-matrix for the problem of three bodies, the scattering phase and the half-mass amplitude being described exactly for any approximation order. The uniform convergence of the approximation process is also proved.     

Barrier-transmission probability in the extended petrashenfok method

The transmission coefficient of a one-dimensional barrier with a single peak of arbitrary shape is considered via Miller and Good 's [1] approximation, which is found to be very poor in the general case. A method of improving the approximation is presented.     

Projection method of solving the Bogolyubov equation for the generating functional in classical statistical physics

An approximate method is considered for the solution of the Bogolyubov equation, which is characterized from the physical viewpoint by successively taking account of corrections of ever higher order. In the zeroth approximation the known Vlasov equation is obtained, in the first approximation a system of equations for the unary distribution and second-order correlation functions, and in the second approximation, a system of three equations for the appropriate correlation functions. The properties of the first approximation equations are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 95–99, April, 1984.The authors are grateful to É. A. Arinshtein and N. M. Placid for useful discussions.     

Single-polaron properties in the one-dimensional Holstein and SSH models

We study the single-polaron properties of the one-dimensional Holstein and SSH model. The dynamical coherent potential approximation (under the Hartree approximation) is applied to compute the polaron dispersion, the quasi-particle residue, and the polaron?s Green?s functions. We compare our calculated results in comparison with those by the self-consistent Born approximation plus higher-order diagrams.     

二元高斯核模型的相不稳定性研究

从考虑巨势Ω在平衡点附近随密度的微小涨落δρ_α(r)的变化出发，由系统的关联函数可以研究描述高分子链二元系统的相不稳定性.在超网链(HNC)近似下研究了二元高斯核模型的相不稳定性，得到了它的相不稳定线，同时确定此相变是由浓度涨落为主的相不稳定性引起的退混合相变.将HNC近似下的结果与随机相近似下的结果进行了比较. 关键词： 高斯核模型 关联函数 相不稳定性 高分子链     

Nonlinear analysis of the equilibrium shape of a charged drop in the tornado funnel wall

From the pressure balance condition on the free surface of a conducting liquid charged drop, an expression is derived for the equilibrium shape of the drop placed in the field of centrifugal forces acting in the tornado wall. The analysis is carried out in an approximation quadratic in small parameter (the ratio of the deformation amplitude to the radius of the initially spherical drop). In the linear approximation, the drop is a spheroid oblate in the direction normal to the tornado axis. The eccentricity of the spheroid squared is proportional to the angular velocity squared and the radius of the drop cubed. In the quadratic approximation, the equilibrium shape of the drop is other than spheroidal.     

Emission in the final state in processes with the production of charged pions and light leptons

The Drell-Yan form is proposed for the decay widths of heavy quarks and cross sections for high-energy scattering with the production of charged pions and light leptons including radiative corrections in the final state in the leading logarithmic approximation. The corresponding spectral distributions are given in terms of the convolution of the cross section (decay width) in the Born approximation with the structure functions of pions and leptons. The pion structure function is given in the explicit form.     

Strong-coupling method in the kronig-penny model

The strong-coupling approximation is investigated in a model one-dimensional potential. It is shown that even for large values of the overlap integrals S = 0.5 the approximation gives good results when a sufficiently large number of neighbors is taken into account. Otherwise, the approximation can give spurious extrema in the density of states. A modified strong-coupling method is formulated having considerable advantage over the usual method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 27–30, March, 1975.     

The Implementation of Impulse Approximation in the Wave Function and the Response Function of Many-Fermion System

In this work, we investigate the ambiguities proposed by Benhar et al. about different implementation of the impulse approximation (IA) for calculation of the response function of many-Fermion system. The many-Fermion wave-function of composite system is calculated in the framework of impulse approximation by considering the iteration equation of many-Fermion wave-function through the system Hamiltonian propagator, and it is shown that by imposing the plane wave approximation for the struck particle it is possible to remove these ambiguities (the plane wave impulse approximation (PWIA)). Finally it is concluded that in order to get relevant result, one should be careful to perform the IA on the many-Fermion wave function to calculate the response function of the system, since the system response is obviously very sensitive to this quantity.