Diquark confinement in an extended NJL model

In a Nambu-Jona-Lasinio model supplemented with an infrared cutoff in addition to the ultraviolet cutoff we study the issue whether diquarks are confined when the model is extended beyond the rainbow-ladder approximation. The gap equation, obtained in a truncation scheme motivated via a non-trivial quark-gluon vertex function, is solved to determine the constituent quark mass if chiral symmetry is spontaneously broken. In a second step, the Bethe-Salpeter equations for mesons and diquarks beyond the ladder approximation are derived, taking care to preserve Goldstone's theorem in the pion channel. While the obtained masses of pseudo-scalar and vector mesons are only moderately shifted compared to the values in the ladder approximation, we observe that scalar diquarks disappear from the physical spectrum and therefore are confined. For axial-vector diquarks we observe indications that the same mechanism may also work, but the NJL model allows no conclusive answer in this channel.     

Compton scattering of an X-ray photon by an open-shell atom

A nonrelativistic quantum theory for the nonresonant Compton scattering of an X-ray photon by a free many-electron atom with an open shell in the ground state has been constructed in the single-configuration Hartree-Fock approximation outside the impulse approximation widely used in the literature. The transition to an atom with closed shells reproduces the results obtained previously in [6, 7]. The results of a test calculation for atoms with open (Ti, Fe) and closed (Zn) 3d core shells are presented. The effects of the radial relaxation of one-electron states in the field of core vacancies have been taken into account. The results of the calculation agree well with the experimental results [15, 16]. It has been established that the results of the impulse approximation in the investigated X-ray photon energy ranges disagree with those of our theory not only quantitatively but also qualitatively. In particular, the impulse approximation near the elastic (Thomson and Rayleigh) scattering line leads to a gross overestimation of the contributions from the deep atomic shells involved in the inelastic photon scattering only virtually to the scattering probability. The presented theory is general in character and its applicability to a particular element of the Mendeleev table with an open core shell or to a many-electron atomic ion is limited only by the requirement that the nonrelativistic Hartree-Fock approximation be properly used in describing the scattering-state wave functions.     

Poissonian Behavior of Ising Spin Systems in an External Field

We apply the Stein–Chen method for Poisson approximation to spin-half Ising-type models in positive external field which satisfy the FKG inequality. In particular, we show that, provided the density of minus spins is low and can be expanded as a convergent power series in the activity (fugacity) variable, the distribution of minus spins is approximately Poisson. The error of the approximation is inversely proportional to the number of lattice sites (we obtain upper and lower bounds on the total variation distance between the exact distribution and its Poisson approximation). We illustrate these results by application to specific models, including the mean-field and nearest neighbor ferromagnetic Ising models.     

Pair creation by a photon in an electric field

The process of pair creation by a photon in a constant and homogeneous electric field is investigated basing on the polarization operator in the field. The total probability of the process is found in a relatively simple form. At high energy the quasiclassical approximation is valid. The corrections to the standard quasiclassical approximation (SQA) are calculated. In the region of relatively low photon energies, where SQA is unapplicable, the new approximation is used. It is shown that in this energy interval the probability of pair creation by a photon in electric field exceeds essentially the corresponding probability in a magnetic field. This approach is valid at the photon energy much larger than the “vacuum” energy in electric field: ω?eE/m. For smaller photon energies the low energy approximation is developed. At ω?eE/m the found probability describes the absorption of soft photon by the particles created by an electric field.     

The partition function of an interacting many body system

Based on the path integral approach the partition function of a many body system with separable two body interaction is calculated in the sense of a semiclassical approximation. The commonly used Gaussian type of approximation, known as the perturbed static path approximation (PSPA), breaks down near a crossover temperature due to instabilities of the classical mean field solution. It is shown how the PSPA is systematically improved within the crossover region by taking into account large non-Gaussian fluctuations and an approximation applicable down to very low temperatures is carried out. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin-Meshkov-Glick model. The extensions should have applications in finite systems at low temperatures as in nuclear physics and mesoscopic systems, e.g. for gap fluctuations in nanoscale superconducting devices previously studied within a PSPA type of approximation. Received 28 March 2002 Published online 17 September 2002     

Theoretical investigations of the vapour-liquid equilibrium and dielectric properties of dipolar Yukawa fluids in an external field

In a low field approximation, using the dipolar Yukawa fluid model (in mean spherical approximation as a reference system) a consistent field-dependent free energy expression is proposed for the calculation of the vapour-liquid equilibrium of polar fluids in an applied electric field. A perturbation theory high field approximation expression of the free energy is also proposed to study the field-dependent properties of fluids. In the high field approximation, equations for the field-dependent polarization and for the nonlinear dielectric constant (or Piekara constant) are also predicted. It has been discussed that our approximations are appropriate to describe the vapour-liquid-like phase equilibria and the magnetization curves of magnetic fluids.     

Quasiclassical green function in an external field and small-angle scattering processes

A representation is obtained for the quasiclassical Green functions of the Dirac and Klein-Gordon equations allowing for the first nonvanishing correction in an arbitrary localized potential which generally possesses no spherical symmetry. This is used to obtain a solution of these equations in an approximation similar to the Furry-Sommerfeld-Maue approximation. It is shown that the quasiclassical Green function does not reduce to the Green function obtained in the eikonal approximation and has a wider range of validity. This is illustrated by calculating the amplitude of small-angle scattering of a charged particle and the amplitude of Delbrück forward scattering. A correction proportional to the scattering angle was obtained for the amplitude of charged particle scattering in a potential possessing no spherical symmetry. The real part of the Delbrück forward scattering amplitude was calculated in a screened Coulomb potential.     

Scaling Variat ion-Truncat ion Approximation in an Operator Form

An operator form of scaling variational method combining truncation approximation is propoied to solve the energy eigenvalue problem of the onedimensional polynomial potential, in which the scaling parameters of the Hamiltonian are determined by variational principle, followed by a truncation approximation. As examples, the energy values of onedimensional anharnionic and pure quartic oscillators are calculated. The results axsimple in form and have high accuracy. Moreover, the operator method and two-step approximation are combined in a unified treatment on the ground of scaling variational method in an operator form.     

Theoretical Analysis of the Resonance Cone in an Inhomogeneous Magnetoplasma Column

The three-dimensional behavior of the high-frequency resonance cone is investigated using an inhomogeneous slab magnetoplasma model under the quasi-static approximation and neglecting ion motion. The effects of finite ky and electron thermal motion are considered numerically, revealing that the cone angle is shifted to a slightly smaller angle and the reflection point is also shifted toward the high density region compared with results under the cold plasma approximation.     

Diagram technique in an improved nonsymmetrized self-consistent field method

The free energy of a strongly anharmonic crystal is expanded in powers of a small parameter which is the ratio between the mean amplitude of thermal atom vibrations and the interatomic spacing, where the main contribution of the principal anharmonic terms is included in the zeroth approximation (the nonsymmetrized self-consistent field approximation). A diagram representation is used to calculate the corrections. As an illustration of the method, the corrections to the free energy of a strongly anharmonic monatomic linear chain are obtained.Translated from Izvestiya Vysshlkh Uchebnykh Zavedenii, Fizika, No. 6, pp. 67–72, June, 1984.     

Quasiclassic wave functions of an electron in a periodic magnetic field

Wave functions of the Klein-Gordon and Dirac equations are determined in the quasiclassical approximation. These wave functions allow one to obtain results of the axial approximation as a particular case and to take into account in the emission problem quantum corrections related to both the dynamic of electron motion and quantum recoil during phonon emission.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 38–41, January, 1985.     

Adiabatic Approximation in Interaction Between Two-Level Atom in an External Potential V(χ) and Optical Field

In discussion about the detection of the BoseEinstein condensation, the adiabatic approximation method was taken. According to the perturbation theory, this approximation is studied in detail by a single atom model in this paper.     

Study of the P1 approximation in an inverse scattering problem

We examine the validity of the P₁ approximation in determining the albedo and asymmetry factor of a scattering medium from the hemispherical transmittance data. For this purpose, an analytical expression of the hemispherical transmittance is derived with the P₁ approximation and then fitted to hemispherical transmittance data of a scattering medium using three methods. These include the asymptotic expansion method, the unconstrained least mean-squares method and the constrained least mean-squares method. We find that estimation of radiative properties with the P₁ approximation is effective only for high albedos. Only the constrained least mean-squares method yields physically resonable values for the radiative properties in all cases.     

Optical properties of an echelette grating in the short-wave approximation

The problem of plane-wave scattering by an echelette grating with a right angle is considered in the case of high-frequency approximation (the wavelength is assumed to be small compared with the period of grating). We present the results of short-wave asymptotic analysis for a ray optical solution to the problem that was derived on the basis of the method of summation of multiple diffracted fields that is well known in the geometric theory of diffraction. A new effect of perfect blazing for an echelette grating in the high-frequency approximation is also discussed.     

Many-particle effects in resonant inelastic scattering of an X-ray photon by an atom

The influence of many-particle effects on the shape and values of the double differential cross section for the resonant inelastic scattering of a linearly polarized X-ray photon by a free atom near the K and KL₂₃ ionization thresholds has been theoretically analyzed for the neon atom. The calculations have been performed using the nonrelativistic Hartree-Fock approximation for single-electron wavefunctions and the dipole approximation for the anomalous dispersion component of the cross section. The analytical structure of the contact part of the scattering cross section has been obtained beyond the dipole approximation. The effects of the radial relaxation of electron shells, spin-orbit and multiplet splitting, and configuration interaction in the doubly excited atomic states, as well as the Auger and radiative decays of the produced vacancies, are taken into account. The nature and role of the effect of correlation amplitudes, which is responsible for the appearance of the nonzero amplitudes of nonradiative transitions between intermediate and final single-electron states of the same symmetry that are obtained in different Hartree-Fock fields, have been analyzed also. The calculations are predictive and, for an incident-photon energy of 5.41 keV, agree well with experimental results for the Kα X-ray emission spectrum of the neon atom.     

Adiabatic description of impenetrable particles in an infinitely deep potential well

In the framework of adiabatic approximation the energy spectrum and wave functions of two impenetrable particles in an infinitely deep potential well are considered for two cases of approximation of the effective confining potential of the ??slow?? subsystem. In case of the quadraticterm approximation the obtained energy spectrum is equidistant. The probability distribution in the range of ??fast?? particle has a symmetric shape while that in the range of the ??slow?? particle is asymmetric and the peak of localization of the system in its ground state is shifted towards the ??fast?? particle. In the first excited state the center of the probability distribution of the ??slow?? particle is shifted towards the impenetrable wall.     

Discrete breathers in a two-dimensional Morse lattice with an on-site harmonic potential

Two-dimensional discrete breathers in a two-dimensional Morse lattice with on-site harmonic potentials are investigated. Under the harmonic approximation, the linear dispersion relations for the triangular and the square lattices are discussed. The existence of discrete breathers in a two-dimensional Morse lattice with on-site harmonic potentials is proved by using local inharmonic approximation and the numerical method. The localization and amplitude of two-dimensional discrete breathers correlate closely to the Morse parameter a and the on-site parameter κ.