Effective field theory approach to nuclear matter

Effective field theory provides a systematic approach to hardon physics and few-nucleon systems. It allows one to determine the effective two-, three-, and more-nucleon interactions which are consistent with each other. We present a project to derive bulk properties of nuclei from the effective nucleonic interactions. The text was submitted by the authors in English.     

Effective nuclear force of a realistic potential: A selfconsistent approach

Core polarization corrections to the Tabakin realistic nucleon-nucleon potential have been calculated by a selfconsistent method. The derived residual interaction is demonstrated by the example of the tin isotope spectroscopy.     

Spin-adapted vector method: An alternative to the conventional configuration interaction approach

A number of refinements have been incorporated in the vector method. The refinements include utilization of spin-adapted configurations, partitioning the steps in the calculation, and determining the connection of this spin-adapted vector method and standard configuration interaction techniques. To this end, the spin-adapted vector method can be used to generate an integral inverted formula tape commonly used by standard configuration interaction. Sample calculations on LiH are used to compare standard C1 and the spin-adapted vector method.     

Effective models for nearly ideal Dirac semimetals

Topological materials (TMs) have gained intensive attention due to their novel behaviors compared with topologically trivial materials. Among various TMs, Dirac semimetal (DSM) has been studied extensively. Although several DSMs have been proposed and verified experimentally, the suitable DSM for realistic applications is still lacking. Thus finding ideal DSMs and providing detailed analyses to them are of both fundamental and technological importance. Here, we sort out 8 (nearly) ideal DSMs from thousands of topological semimetals in Nature 566(7745), 486 (2019). We show the concrete positions of the Dirac points in the Brillouin zone for these materials and clarify the symmetryprotection mechanism for these Dirac points as well as their low-energy effective models. Our results provide a useful starting point for future study such as topological phase transition under strain and transport study based on these effective models. These DSMs with high mobilities are expected to be applied in fabrication of functional electronic devices.     

Effective dimensionality approach to the RKKY interaction in multilayer systems

We consider RKKY interaction in a quasi 2D system with nonparabolic dispersion. In our paper we calculate the RKKY range function assuming the in-layer confinement via effective dimensionality approach. We show, that indirect magnetic exchange in our system can be modelled by the effective spectral dimension which equals one.     

Two-body Dirac equation versus KDP equation

A brief review of two-body Dirac and Kemmer-Duffin-Petiau approaches for the bound state problem of two fermions is presented from an algebraic point of view in a comparative manner. Reduction of the direct product of two Dirac spaces is discussed.Work supported by the T.B.T.A.K. under TBAG/CG-1.     

A Dirac algebraic approach to supersymmetry

The power of the Dirac algebra is illustrated through the Kähler correspondence between a pair of Dirac spinors and a 16-component bosonic field. The SO(5, 1) group acts on both the fermion and boson fields, leading to a supersymmetric equation of the Dirac type involving all these fields.     

The single-particle interaction in nuclear matter via the relativistic Dirac-Brueckner approach

Within the relativistic Dirac-Brueckner approach and starting from a one-boson-exchange interaction, the nucleon selfenergy is calculated above the nuclear-matter Fermi sea. The effects of Pauli blocking and energy dispersion are studied. At low energy we see a dominance of the Pauli blocking whereas at nucleon energies up to 250 MeV the dispersive effect still has a very large influence on the single-particle interaction. From the selfenergy a Schrödinger optical potential is deduced, for which the DB results nicely agree with empirical values. The density dependence of this optical potential compares well with earlier calculations.     

Consistency of nuclear Dirac phenomenology with meson-nucleon interactions

The phenomenological relativistic theory of nuclear single-particle dynamics is reviewed and its salient characteristics discussed. The phenomenological (relativistic) potential strengths necessary to secure agreement with the usual low-energy properties of nuclei are determined. These phenomenological potentials are then related to the time-independent meson fields generated by nuclei, and it is shown by direct calculation that the potential strengths predicted on the basis of renormalized meson-nucleon couplings (as measured in, say, NN scattering) are consistent with those deduced empirically. Thus the phenomenological theory is shown to be consistent with a more microscopic approach, in agreement with the work of previous authors. The role of the ρ-meson is then examined, and it is shown that the time-independent ρ-field leads to isovector terms in both the central and spin-orbit terms of the equivalent Schrödinger potential. The signs and magnitudes of these terms agree with those determined from fits to the isobaric analogue (p, n) reactions, or to the systematics of single-particle energies.     

A new approach to stroboscopic resonance measurements of the nuclear quadrupole interaction

A new stroboscopic resonance method for the measurement of the quadrupole interaction of long-lived nuclear isomers excited by pulsed beams with a fixed repetition frequency is demonstrated. The method utilizes the phenomenon of beats which occurs when a magnetic perturbation is introduced in the presence of a pure quadrupole interaction. The nuclear precession is thus controlled by the beat frequencies which can be varied by the external magnetic field which is oriented parallel to the symmetry axis of the crystal. Stroboscopic resonance can be achieved by varying thebeat frequency to be an integral multiple of the beam pulsing frequency. The method is demonstrated using the 398 keV level of⁶⁹Ge excited and recoil implanted into a single crystal of tin by means of a heavyion reaction.Supported in part by the National Science Foundation.     

Stationary states of the nonlinear Dirac equation: A variational approach

In this paper we prove the existence of stationary solutions of some nonlinear Dirac equations. We do it by using a general variational technique. This enables us to consider nonlinearities which are not necessarily compatible with symmetry reductions.     

Generalized phase factors and the interaction of Dirac particles

The nonintegrable phase factor approach to interactions is generalized in the case of a Dirac particle. The results differ significantly from those obtained in the Schrödinger theory and allow Dirac particles to be characterized by two fundamental couplings.     

RKKY interaction in three-dimensional tilted Dirac and Weyl semimetals

We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities of the tilted Dirac and Weyl semimetals in three dimensions. In accordance with the untilted scenario, the RKKY interaction contains three terms, namely the Heisenberg term, the Ising term, and the Dzyaloshinsky-Moriya term. The main influence of tilt on the RKKY Hamiltonian is a modulation to the oscillation frequencies of range functions. Our results enrich the knowledge of the magnetic properties of materials with tilted Dirac cones and may see an important application in spintronics.     

Spin structures, spinors and the Dirac operator: real versus complex manifolds

We describe the relation between spin-structures, spinors and the Dirac operator on a (real) manifold and the analogous definitions in complex holomorphic terms. This may be useful for physicists interested in the algebraic geometric approach to superstrings.     

The effect of conventional nuclear binding on nuclear structure functions

We show that Fermi motion (including the effect of nucleon binding energy), together with a simple ansatz for the dependence of the nucleon structure function on its invariant mass, can explain the major features of recent nuclear structure function data. The close relationship of this work to the earlier explanations of the EMC effect based on an enhancement of the virtual pion field of the nucleus is discussed.