On nonlinear dynamical equations for relativistic nucleons moving near atomic nuclei
Department of Applied Mathematics, HSE Tikhonov Moscow Institute of Electronics and Mathematics, 123458, Moscow, Russia
Accepted: 24 August 2020
Published online: 4 September 2020
Nonlinear dynamical equations for relativistic nucleons moving under the action of nuclear and electromagnetic forces are studied in the classical approximation. In them, the influence of the nuclear potential on the mass of nucleons is taken into account and examined. The dynamical equations are considered in the case of a relativistic nucleon moving near a heavy atomic nucleus at rest. They are examined in polar coordinates, and their first integral is found. As a result, the examined equations are reduced to one nonlinear differential equation of the second order. This equation allows one to describe trajectories of relativistic nucleons in the considered case. Using it, quasi-nuclei are examined in which nucleons or antinucleons move in circular orbits around atomic nuclei.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020