Rubish V. Quasiclassical approach for the Dirac equation with scalar-vector coupling in physics of the heavy-light quark systems

The objects of studies are the Dirac equation, heavy-light mesons and baryons with two heavy quarks and the quantum-mechanical problem of two centres with Coulomb and oscillator interactions. The aim of present research is the construction of quasiclassical asymptotics of the Dirac equation in the external spherically symmetric scalar and vector fields and its applications for spectral problems of heavy-light mesons physics and the theory of quasistationary states. The method of research is the asymptotical expansion of quantum-mechanical equation over small parameter ћ (the Planck constant). The generalizations of the Bohr-Sommerfeld quantization rule and the Gamow's formula for the width of quasistationary level with taking into account relativistic effects, spin and Lorentz structure of the interaction potentials are proposed. Analytical formulae for the energy and mass spectra, mean radiuses and wavefunctions of heavy-light mesons are obtained. The relativistic quasiclassical theory of ionization of the Coulomb system in external radial-constant scalar and electric fields are constructed. The group of dynamical symmetry for the model two centre quantum-mechanical problem with Coulomb and oscillator potentials are obtained. The mass spectra of doubly heavy baryons are calculated. The application of obtained results is the calculation of decay widths of heavy-light mesons and doubly heavy baryons as well as calculation of the higher orders corrections in heavy quarks theory.