Vol 86, No 3 (2023)

An anomaly in the distribution of Coulomb energies of tin isotopes (Sn anomaly) is determined. This anomaly manifests itself as follows: in the mass-number (@) dependence of @ for the isotopes @ Sn, experimental data on @  show a linear dependence close to a constant. The Coulomb energy difference @ between the Sn–Sb neighboring isobaric nuclei is approximated by a two-parameter expression. The energies of isobaric analog resonances, @, for the isotopes 
Sn are calculated both on the basis of the resulting @ approximation within a @ phenomenological model and on the basis of the microscopic theory of finite Fermi systems. The results are compared with experimental data on 
, and it is found that the phenomenological model describes the energies 
 quite accurately, and so do the new self-consistent relativistic model.

A method for measuring cross sections at  colliders for the case where the center-of-mass frame of colliding particles moves in the laboratory frame is proposed. Within this method, the energy dependence of the cross section is extracted from the angular distribution of interaction products. The method applied to the process is found to be sensitive. This method provides the possibility of studying the fine structure of the cross section near the threshold at scales much less than the energy spread of the beams used. Similar measurements may be implemented in experiments at the Super Charm-Tau Factory.

The contribution of neutrino electromagnetic properties to elastic neutrino–proton scattering is considered in detail. The neutrino electromagnetic properties are introduced via the charge, magnetic, electric, and anapole form factors in the basis of neutrino mass eigenstates. The effects of mixing of three neutrino states are taken into account along with effects of the change in the flavor of a neutrino that moves from the source to the detector. The weak neutral and electromagnetic nucleon form factors are also taken into account. The differential cross section calculated numerically for elastic neutrino–proton scattering obtained with allowance for the neutrino charge radius and magnetic moment are compared with the predictions of the Standard Model for reactor and accelerator neutrinos.

The equations of quantum relativistic hydrodynamics are derived from the Klein–Gordon equation. In the nonrelativistic semiclassical approximation, these equations reduce to the traditional equations of hydrodynamics of a perfect fluid. An analytic solution of hydrodynamic equations in the soliton approximation is found for a collision of nuclear layers in one- and two-dimensional cases. The importance of taking into account nonequilibrium processes is highlighted. The stages of compression, decompression, and expansion are considered by means of a single formula for layers with energies on the order of 10 MeV per nucleon. This reduction of solutions of hydrodynamic equations to soliton solutions was not considered earlier. A generalization to the two-dimensional case leads to the concept of rarefied-bubble formation at the expansion stage. As to the approach itself, it can also be used in other realms of physics in calculations for nonlinear dynamics of vibrations of complex systems.

A variational analysis of the Fayans energy-density functional is performed with allowance for the earlier unused isovector parameters @ in the volume part of the functional. The quality of the previous fit to nuclear densities, masses of nuclei, single-particle levels, and charge radii remains unchanged under the additional condition of description of the giant-dipole-resonance energy in the @Pb nucleus. The effect of variations in the isovector parameter @ on the equations of state for infinite symmetric nuclear matter and pure neutron matter is determined. The density dependence of the symmetry energy @ and of its derivative @ is studied. For the parameter @, a range is established that is consistent with the estimated values of the symmetry energy @ and its derivative @ at the equilibrium density @, which are parameters of the equation of state for symmetric nuclear matter. These values were obtained earlier from a simultaneous analysis of the values of the ‘‘neutron skin’’ @ of @Pb and @Ca nuclei from the PREX-II and CREX experiments, from the results of ab initio calculations of equations of state and ground-state properties of nuclei, and from astrophysical observations and data on the discovery of gravitational waves from the merger of binary neutron stars by the LIGO-Virgo Collaboration in 2017.