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

## 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.

- Authors:

- Belarusian State University, Research Institute for Nuclear Problems (Belarus)
- Joint Institute for Nuclear Research (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22759638

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Atomic Nuclei

- Additional Journal Information:
- Journal Volume: 80; Journal Issue: 5; Other Information: Copyright (c) 2017 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7788

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR VELOCITY; DIRAC EQUATION; ELECTROMAGNETIC INTERACTIONS; EQUATIONS OF MOTION; HAMILTONIANS; HELICITY; L-S COUPLING; MEV RANGE 10-100; QUANTUM MECHANICS; QUARKS; RELATIVISTIC RANGE; SCALARS; SPIN; VECTORS

### Citation Formats

```
Silenko, A. J., E-mail: alsilenko@mail.ru, and Teryaev, O. V., E-mail: teryaev@theor.jinr.ru.
```*Phenomenological description of relativistic-quark interaction on the basis of the Dirac equation with the Cornell potential*. United States: N. p., 2017.
Web. doi:10.1134/S1063778817050234.

```
Silenko, A. J., E-mail: alsilenko@mail.ru, & Teryaev, O. V., E-mail: teryaev@theor.jinr.ru.
```*Phenomenological description of relativistic-quark interaction on the basis of the Dirac equation with the Cornell potential*. United States. doi:10.1134/S1063778817050234.

```
Silenko, A. J., E-mail: alsilenko@mail.ru, and Teryaev, O. V., E-mail: teryaev@theor.jinr.ru. Fri .
"Phenomenological description of relativistic-quark interaction on the basis of the Dirac equation with the Cornell potential". United States. doi:10.1134/S1063778817050234.
```

```
@article{osti_22759638,
```

title = {Phenomenological description of relativistic-quark interaction on the basis of the Dirac equation with the Cornell potential},

author = {Silenko, A. J., E-mail: alsilenko@mail.ru and Teryaev, O. V., E-mail: teryaev@theor.jinr.ru},

abstractNote = {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.},

doi = {10.1134/S1063778817050234},

journal = {Physics of Atomic Nuclei},

issn = {1063-7788},

number = 5,

volume = 80,

place = {United States},

year = {2017},

month = {9}

}