abstract

The binding energy of a two nucleon system is calculated from the relativistic Weinberg equation with spin, and from its nonrelativistic limit. We get that the interaction of nucleons inside deuteron is largely different from that of nonrelativistic particles, in spite of the fact that the binding energy is very small. The relativistic interaction is much less attractive than the nonrelativistic one. An inclusion of spin introduces significant dynamical effects. The light front dynamics, used in our calculations, has unique advantages over other existing approaches. The practical virtues of this scheme, including the invariant spinor representation, are presented in full detail.

abstract

Considering a baryon to be surrounded by meson cloud, we calculate the magnetic moments. We observe that in the presence of quark structure of the baryon, moments agree well with experiment.

abstract

The influence of viscosity is investigated on the monopole density of the Universe. The result is that if the bulk viscosity coefficient in the GUT continuum after symmetry breaking exceeds a critical value, then viscosity can drive an exponential expansion diluting monopoles below the observational limit. This critical value of the viscosity coefficient means a lower bound for the energy scale parameter of the GUT, somewhere above 10\(^{15}\) GeV. Nevertheless, since the behaviour of the GUT continuum near the phase transition is not yet reliably known, the exact value of this lower bound cannot be precisely calculated.

abstract

A reinvestigation is given for classical motion of colored test particles in the Prasad–Sommerfield monopole field, a problem that was treated already by J. Schechter soon after the discovery of the monopole. The equation used by us can be obtained from the Wong equation if one regards the Higgs field as a component of a five dimensional translation invariant Yang–Mills potential and reinterpret the motion in the fifth direction appropriately. Its nonrelativistic limit is treated for the static, SO(3) symmetrical monopole of unit charge with SU(2) as gauge group. The total angular momentum is conserved, though the particle’s mass is variable. For large distances the space motion is not simply that of an electric pole in a Dirac monopole field, as Schechter has stated neglecting the coupling to the Higgs field. The asymptotical solution at large distances proves that beyond unbounded scattering solutions there exist bounded orbits too, caused by long range forces which arise from the zero mass Higgs field. The bounded motion takes place on a closed, periodical trajectory between two meridian circles of a cone, whose axis is the total angular momentum vector.

abstract

An approximate model is constructed for a system of three Dirac particles of equal masses interacting mutually through a universal static two-body potential. The introduced approximation corresponds to characteristic features of the Lagrange exact solutions to the classical three-body problem, where three distances between three particles are kept equal all the time, although they are, in general, varying. Wave equations are found for the internal motion in the cases of spin 1/2 and spin 3/2. Radial equations are derived.

abstract

It is shown that an improper gauge transformation, similar to that applied by Dirac in his theory of magnetic monopoles but performed in a null plane, produces a finite electric charge provided the shape of the corresponding string is appropriately chosen.

abstract

A model for the unified treatment of rotations and thermal excitations is proposed, in which the single particle (s.p.) level density \(g(\varepsilon )\) is renormalized with respect to the liquid drop (LDM) density \(g_{\rm LDM}(\varepsilon )\). In this way the erroneous behaviour of the smoothed s.p. level density \(\tilde g(\varepsilon )\) as a function of the deformation of the nucleus is removed. This is particularly important in the range of large deformations as encountered in fissioning nuclei. The model is then applied to nuclei in the actinide region to study their shape and their stability against fission. The structure of the fission barriers of rotating, heated nuclei is studied in detail. The shell corrections to the energy, free energy and angular momentum are calculated by means of a deformed Saxon–Woods (SW) potential.