The relativistic interquark potential

A method for the calculation of interaction potentials in a momentum space is proposed which is based on exact calculations of the Lorentz structures of the corresponding interaction amplitudes. With this method the kernel of the QCD-motivated potential of a quark-antiquark relativistic system is obtained for different masses and an arbitrary angular momentum J. The calculation is performed taking into account the anomalous chromodynamic moments of the quarks. The case of the singlet state of a relativistic quark system is considered. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 87–94, November, 2006.     

Cutting DNA: Mechanics of the topoisomerase

The framework of relativistic self-consistent mean-field models is extended to include correlations related to restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The model, currently restricted to axially symmetric shapes, employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a δ-interaction in the pairing channel. Both bulk and spectroscopic nuclear properties are explored.     

Relativistic correction to the dipole polarizability of a hydrogenic ion

The first relativistic correction of orderα ² to the dipole polarizability of a hydrogenic ion has been investigated by using mean excitation energy of the ion within the second-order perturbation theory. The density-dependent mean excitation energy is estimated via Bethe theory for the stopping cross section for a moving point charge interacting with the hydrogenic ion. In this approach only the unperturbed Dirac wavefunctions are required to evaluate the appropriate matrix elements. The first relativistic correction turns out to be − (13/12)(αZ)². This has the correct sign and is within 5% of the exact result which is −(28/27)(αZ)².     

Radial wave functions of a discrete spectrum

The system of equations for radial wave functions is written in a form allowing both relativistic and non relativistic wave functions to be obtained. In the case of a discrete spectrum, an asymptotic solution of this system is obtained for a potential which includes not only a Coulomb term but also terms corresponding to dipole and quadrupole polarization. The normalizing factor of the asymptote is determined in the approximation of the relativistic quantum-defect method, which offers the possibility, in principle, of using the functions in semiempirical calculations analogous to nonrelativistic calculations by the Bates — Damgaard — Seaton method. The calculation scheme is illustrated for the example of the calculation of Si IV wave functions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 39–44, December, 1978.     

The Wigner Functions for a Spin-1/2 Relativistic Particle in the Presence of Magnetic Field

This paper provides a study of Wigner functions for a spin-1/2 relativistic particle in the presence of magnetic field. Since the Dirac equation is described as a matrix equation, it is necessary to describe the Wigner function as a matrix function in phase space. What’s more, this function is then proved to satisfy the Dirac equation with ⋆-product. Finally, by solving the ⋆-product Dirac equation, the energy levels as well as the Wigner functions for a spin-1/2 relativistic particle in the presence of magnetic field are obtained.     

Energy loss of relativistic, multiply charged ions in an electron plasma

A simple equation is derived for calculating the energy loss of a relativistic, multiply charged ion moving in an electron plasma in the region where the Born approximation fails. The contribution of the energy losses from collisions with solitary electrons is calculated using the exact Dirac equation for relativistic Coulomb scattering. Zh. Tekh. Fiz. 68, 9–12 (February 1998)     

Variational wave equations of two fermions interacting via scalar,pseudoscalar, vector,pseudovector and tensor fields

We consider a method for deriving relativistic two-body wave equations for fermions in the coordinate representation. The Lagrangian of the theory is reformulated by eliminating the mediating fields by means of covariant Green's functions. Then, the nonlocal interaction terms in the Lagrangian are reduced to local expressions which take into account retardation effects approximately. We construct the Hamiltonian and two-fermion states of the quantized theory, employing an unconventional “empty” vacuum state, and derive relativistic two-fermion wave equations. These equations are a generalization of the Breit equation for systems with scalar, pseudoscalar, vector, pseudovector and tensor coupling.     

Treatment of Confinement in the Faddeev Approach to Three-Quark Problems

We present a method to solve the Faddeev integral equations of the semirelativistic constituent quark model. In such a model the quark–quark interaction is modeled by an infinitely rising confining potential and the kinetic energy is taken in a relativistic form. We solve the integral equations in Coulomb–Sturmian basis. This basis facilitates an exact treatment of the confining potentials.     

General magnetized Weyl solutions: disks and motion of charged particles

We construct three families of general magnetostatic axisymmetric exact solutions of Einstein-Maxwell equations in spherical coordinates, prolate, and oblates. The solutions obtained are then presented in the system of generalized spheroidal coordinates which is a generalization of the previous systems. The method used to build such solutions is the well-known complex potential formalism proposed by Ernst, using as seed solutions vacuum solutions of the Einstein field equations. We show explicitly some particular solutions among them a magnetized Erez-Rosen solution and a magnetized Morgan-Morgan solution, which we interpret as the exterior gravitational field of a finite dislike source immersed in a magnetic field. From them we also construct using the well known “displace, cut and reflect” method exact solutions representing relativistic thin disks of infinite extension. We then analyze the motion of electrically charged test particles around these fields for equatorial circular orbits and we discuss their stability against radial perturbations. For magnetized Morgan-Morgan fields we find that inside of disk the presence of magnetic field provides the possibility of to find relativist charged particles moving in both prograde and retrograde direction.     

Quasiclassical distribution function of electrons in a homogeneous magnetic field

Vlasov's equation is used to find the classical nonrelativistic and relativistic distribution functions that describe an electron beam of bounded radius in a homogeneous magnetic field. In the quasiclassical approximation, by means of the exact wave functions of an electron in a homogeneous magnetic field, the quantum relativistic distribution function with allowance for the electron spin is found. The mean physical quantities that characterize the radially bounded electron beam are found as functions of the temperature and electron spin.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 50–56, July, 1976.It is a pleasant duty to thank Professor V. G. Bagrov for discussing the results.     

Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

Propagation of a monochromatic electromagnetic plane wave in a medium with nonsimple motion

An exact analytical solution is obtained for the trajectory of the wave vector of a monochromatic electromagnetic plane wave in a medium with nonsimple motion. It is shown that the spatial dragging of the electromagnetic wave by the moving medium can be described correctly in the general case only if relativistic terms of order β ² are taken into account. Zh. Tekh. Fiz. 69, 97–100 (May 1999)     

Structure of nuclei far from the stability in relativistic approach

The recent progress of the relativistic many-body approach by the group at Peking University will be reviewed. In particular, axially deformed relativistic Hartree-Bogoliubov approach in Woods-Saxon basis aiming at halo nucleus, time-odd triaxial RMF approach, the adiabatic and configuration-fixed constrained triaxial RMF approaches, a Reflection ASymmetric RMF (RAS-RMF) approach, and a new relativistic Hartree-Fock (RHF) approach with density-dependent σ,ω,ρ and π meson-nucleon couplings for finite nuclei and nuclear matter, will be highlighted.     

Reliability of the pseudospin symmetry in atomic nuclei

The reliability of the pseudospin symmetry (PSS) in atomic nuclei is analyzed in the framework of the relativistic Hartree approach. We find that the nuclear surface strongly increases the effect of the pseudospin-orbit potential (PSOP), spoiling the possibility of the exact realization of the PSS even in the limit of a vanishing PSOP. It is also shown that the PSS cannot be explained by the fact that Σ_S ≃ - Σ. New arguments to explain the PSS in finite nuclei are given. The important role the spin-orbit interaction plays in the achievement of the PSS is also discussed. Received: 22 July 2002 / Accepted: 18 February 2003 / Published online: 20 May 2003     

Dirac方程的数值解法及其在原子总能量计算中的应用

中心势近似下径向Dirac方程的求解是相对论性原子(离子)结构计算的基础.本文通过相对论性方程中径向波函数大分量与非相对论方程径向波函数的类比,提出了径向Dirac方程的一种数值解法.为了验证数值解法的精度和可靠性,首先将数值结果与类氢势作用下的解析解进行比较.然后,将这种算法扩展到基于解析势的相对论性原子结构计算中,并将计算出的总能量与实验结果和其他方法得到的结果进行对比.     

Quasiclassical approximation with the centrifugal potential excluded

We develop a modification of the WKB method (the modified quantization method, or MQM) for finding the radial wave functions. The method is based on excluding the centrifugal potential from the quasiclassical momentum and changing correspondingly the phase in the Bohr-Sommerfeld quantization condition. MQM is used to calculate the asymptotic coefficients at zero and at infinity. We use the examples of power-law and funnel potentials to show that MQM not only dramatically broadens the possibilities of studying the energy spectrum and the wave functions analytically but also ensures accuracy to within a few percent even when one calculates states with a radial quantum number n _r ∼1, provided that the angular momentum l is not too large. We also briefly discuss the possibility of generalizing MQM to the relativistic case (the spinless Salpeter equation). Zh. éksp. Teor. Fiz. 116, 511–525 (August 1999)     

Relativistic wave functions for single-proton resonant states

With the relativistic boundary condition, single-proton resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean-field (RMF) theory. In this scheme, we investigate the wave functions for l≠ 0 proton resonant states close to the continuum threshold in the stable nuclide ¹²⁰Sn for the first time. Some hints for pseudospin symmetry in the resonant states of nuclei are mentioned as well.