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Physics of Atomic Nuclei

, Volume 80, Issue 5, pp 976–982 | Cite as

Phenomenological description of relativistic-quark interaction on the basis of the Dirac equation with the Cornell potential

  • A. J. Silenko
  • O. V. Teryaev
Proceedings of LXVI International Conference on Nuclear Spectroscopy and Atomic Nuclei Structure October 11–14, 2016, Sarov, Russia/Elementary Particles and Fields Theory
  • 37 Downloads

Abstract

Relativistic-quark interaction is described phenomenologically on the basis of the Dirac equation with the Cornell potential. A general form of the initial equation involving the vector and scalar components of the Cornell potential is used for the case of an arbitrary relation between them. The Hamiltonian in the Foldy–Wouthuysen representation is derived in a general form with allowance for electromagnetic interaction. In contrast to earlier investigations, it is relativistic and exact for the zeroth- and first-order terms in the Planck constant and also for those second-order terms that describe contact interactions. General quantum-mechanical equations of motion for the momentum and spin are derived, and the classical limit of the Hamiltonian and for the equations of motion is found for the first time. A relation between the angular velocity of quark spin precession and the force acting on the quark is obtained. The energy of spin–orbit interaction is rather high (on the order of 100 MeV). Terms that describe spin–orbit and contact interactions have opposite signs for the vector and scalar components of the Cornell potential. The evolution of the quark helicity and the spin–spin interaction of the quarks are also calculated.

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Research Institute for Nuclear ProblemsBelarusian State UniversityMinskBelarus
  2. 2.Joint Institute for Nuclear ResearchDubna, Moscow oblastRussia

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