Effective nucleon masses in symmetric and asymmetric nuclear matter

The momentum and isospin dependence of the in-medium nucleon mass are studied. Two definitions of the effective mass, i.e., the Dirac mass m*D and the nonrelativistic mass m*NR which parametrizes the energy spectrum, are compared. Both masses are determined from relativistic Dirac-Brueckner-Hartree-Fock calculations. The nonrelativistic mass shows a distinct peak around the Fermi momentum. The proton-neutron mass splitting in isospin asymmetric matter is m*D,nm*NR,p, which is consistent with nonrelativistic approaches.     

The nonrelativistic limit of the relativistic point coupling model

We relate the relativistic finite range mean-field model (RMF-FR) to the point-coupling variant and compare the nonlinear density dependence. From this, the effective Hamiltonian of the nonlinear point-coupling model in the nonrelativistic limit is derived. Different from the nonrelativistic models, the nonlinearity in the relativistic models automatically yields contributions in the form of a weak density dependence not only in the central potential but also in the spin-orbit potential. The central potential affects the bulk and surface properties while the spin-orbit potential is crucial for the shell structure of finite nuclei. A modification in the Skyrme-Hartree-Fock model with a density-dependent spin-orbit potential inspired by the point-coupling model is suggested.     

N‐shell ionization cross sections by proton impact in the BEA

The N‐subshell ionizations cross sections of heavy elements by proton impact have been calculated in the binary‐encounter approximation. The momentum distribution of target electrons is taken into account by the use of the nonrelativistic and relativistic hydrogenic models and the Hartree–Fock–Roothaan and the relativistic Hartree–Fock–Roothaan methods. The obtained subshell ionization cross sections are compared with the experimental data and other theoretical calculations. The electronic relativistic effect and the wave‐function effect on N‐shell ionization cross sections are discussed.     

Quasi-potential approach to the three-quark nucleon wave function

The structure of the nucleon wave function as a coupled system of valence quarks is examined by the quasi-potential method used to describe coupled states with a fixed number of particles. In the momentum approximation, the wave function is reduced to a three-particle state vector component in the Fock space. The spin structure of the wave function is examined by the method of representing a product of irreducible representations of the Lorentz inhomogeneous group in terms of states with fixed momenta. The physical uniqueness of the SU(6) symmetrical solution is its unambiguity in the nonrelativistic limit. The effective mass approximation of relativistic theory with large average quark momentum and small momentum variance is numerically investigated. A relativistic generalization of the nonrelativistic three-particle problem with oscillator forces is suggested.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 27–32, December, 2004.     

Relativistic differential-difference momentum operators and noncommutative differential calculus

The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics (QM) in the Relativistic Configuration Space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated as the independent term of the total Hamiltonian. This relativistic kinetic energy term is not distinguishing in form from its nonrelativistic counterpart. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generating function for the matrix elements of the unitary irreps of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS.     

Nonrelativistic limit of Dirac-Fock codes: the role of Brillouin configurations

We solve a long standing problem with relativistic calculations done with the widely used multiconfiguration Dirac-Fock method. We show, using relativistic many-body perturbation theory (RMBPT), how, even for relatively high-Z, relaxation or correlation causes the nonrelativistic limit of states of different total angular momentum but identical orbital angular momentum to have different energies. We show that only large scale calculations that include all single excitations, even those obeying Brillouin's theorem, have the correct limit. We reproduce very accurately recent high-precision measurements in F-like Ar, and turn then to a precise test of QED. We obtain the correct nonrelativistic limit not only for fine structure but also for level energies and show that RMBPT calculations are not immune to this problem.     

Theory of complete orthonormal sets of relativistic tensor wave functions and Slater tensor orbitals of particles with arbitrary spin in position, momentum and four-dimensional spaces

Using the complete orthonormal basis sets of nonrelativistic and quasirelativistic orbitals introduced by the author in previous papers for particles with arbitrary spin the new analytical relations for the 2(2s+1)-component relativistic tensor wave functions and Slater tensor orbitals in position, momentum and four-dimensional spaces are derived, where s=1/2,1,3/2,2,… . The relativistic tensor function sets are expressed through the corresponding nonrelativistic and quasirelativistic orbitals. The analytical formulas for overlap integrals over relativistic Slater tensor orbitals in position space are also derived.     

Exact flow equation for bound states

We develop a formalism to describe the formation of bound states in quantum field theory using an exact renormalization group flow equation. As a concrete example we investigate a nonrelativistic field theory with instantaneous interaction where the flow equations can be solved exactly. However, the formalism is more general and can be applied to relativistic field theories, as well. We also discuss expansion schemes that can be used to find approximate solutions of the flow equations including the essential momentum dependence.     

Calculations of hyperfine splitting constants taking into account the volume distribution of the nuclear magnetic moment. I. Computational procedure as applied to hydrogen-like ions

A computational algorithm is developed for the magnetic-dipole constant of the hyperfine structure of atomic spectra, which takes into account the distribution of the magnetic moment in the nuclear volume both in the relativistic and in the nonrelativistic formulation. A significant difference between the nonrelativistic approximation, and the pointlike nucleus approximation is the presence of a nonzero contact hyperfine interaction for electrons with nonzero orbital angular momentum in the former case. The procedure is tested in the computation of the Bohr-Weisskopf correction for hydrogen-like spectra.     

Is There Really a Spin Crisis?

The matrix element of quark axial vector current is shown to be different from the nonrelativistic quark spin sum for a nucleon at rest. The nucleon spin content discovered in polarized deep inelastic scattering is shown to be accommodated in a constituent quark model with 15% sea quark component mixing. The relativistic correction and sea quark pair excitation inherently related to quark axial vector current reduce the nucleon axial charge and this reduction is compensated by the relativistic quark orbital angular momentum exactly and in turn keeps the nucleon spin 1/2 untouched. Nucleon tensor charge has similar but smaller relativistic and sea quark pair excitation reduction.     

Some relativistic aspects of nuclear dynamics at the electrodisintegration of nuclei

An approach aimed to extend the applicability range of the nonrelativistic microscopic calculations of electronuclear response functions is reviewed. In the quasielastic peak region these calculations agree with experiment at momentum transfers up to about 0.4 GeV/c, while at higher momentum transfers being beyond 1 GeV/c a disagreement is seen. In view of this, a reference frame where dynamic relativistic corrections are small was employed to calculate the response functions and the results were transformed exactly to the laboratory reference frame. This proved to remove the major part of the disagreement with experiment. All leading-order relativistic corrections to the transition charge operator and to the one-body part of the transition current operator were taken into account in the calculations. Furthermore, a particular model to determine the kinematical inputs of the nonrelativistic calculations was introduced. This model provides the correct relativistic relationship between the reaction final-state energy and the momenta of the knocked-out nucleon and the residual system. The above-mentioned choice of a reference frame in conjunction with this model has led to an even better agreement with experiment.     

Lorentz Boosted Potential for a Two-Body System with Unequal Masses

We produce a Lorentz boosted two-body potential for particles of different mass that is phase equivalent to a given realistic non-relativistic two-body potential. The relativistic potential is related to the nonrelativistic potential using the Coester–Pieper–Serduke scheme, which ensures that the same scattering wave functions are obtained from the relativistic and non-relativistic potentials. This implies that the phase shifts are identical functions of the relative momentum. To construct the potential we use an iterative scheme that generalizes one that has been applied successfully to two-body systems with equal masses.     

Induced electronic interactions in Chern-Simons systems

The induced electronic interactions in (1+2)-dimensional vector Chern-Simons systems are studied by means of path-integral quantization. We consider four cases: relativistic, and nonrelativistic fermion Maxwell-Chern-Simons models, and relativistic and nonrelativistic fermion Chern-Simons models. It is shown that the Chern-Simons term may induce exotic electronic interactions which can be local or nonlocal and small Chern-Simons coupling may have a considerable effect in some cases.     

Algebraic treatment of quantum-mechanical models with modified Coulomb potentials

Nonrelativistic models with modified Coulomb potentials are solved by an algebraic method based on SO(4,2) dynamical group. The nonrelativistic model with Yukawa long-range potential and the Stark effect in the nonrelativistic hydrogen atom in the homogeneous and inhomogeneous external electrostatic fields are studied in details. The algebraic method for the Dirac and Klein-Gordon relativistic hydrogen atom as well as relativistic models with the rotationally symmetric modified Coulomb potentials are also discussed.     

Field-dependent coupling strength for scalar fields

Effective Lagrangians with a nonlinear coupling between the scalar density of the nucleons and the scalar meson field are investigated within the framework of relativistic mean-field theories. This phenomenological coupling acts as a field-dependent coupling strength and is supposed to take into account renormalization effects within a mean-field picture. The parameters of the model are adjusted to saturation properties of nuclear matter and predictions for the real part of the optical potential are compared with experimental data. For that relativistic and nonrelativistic optical model fits are examined and an experimental standard is deduced which covers the energy range from ? 50 MeV to 1000 MeV. A definition for the real part of the optical potential is given which is not linear in the energy but has the proper limits for momentum zero and infinity. It is shown that for a special choice of the field-dependent coupling strength the meanfield theory can describe the nuclear equation of state and the momentum dependence of the single particle energy without further parameters up to momenta where the intrinsic structure of nucleon becomes relevant.     

Single-particle space-momentum angle distribution effect on two-pion HBT correlation in high-energy heavy-ion collisions

We analyze the transverse momentum dependence of HBT radii in relativistic heavy-ion collisions using several source models.Results indicate that the single-particle space-momentum angle distribution plays an important role in the transverse momentum dependence of HBT radii.In a cylinder source,we use several formulas to describe the transverse momentum dependence of HBT radii and the single-particle space-momentum angle distribution.We also make a numerical connection between them in the transverse plane.     

Final state interaction effects in electrodisintegration of the deuteron in the Bethe-Salpeter approach

The electrodisintegration of the deuteron is considered in a relativistic model of nucleon-nucleon interaction based on the Bethe-Salpeter approach with a separable interaction kernel. The exclusive cross section is calculated in the impulse approximation under various kinematic conditions. Final state interactions between the outgoing nucleons are taken into account. The comparison of nonrelativistic and relativistic calculations is presented. Partial-wave states of the neutron-proton pair with total angular momentum J = 0, 1 are considered.