International Journal of Modern Physics E

Shell model calculations of nuclear energies and wave functions of nucleons outside closed shells interacting by effective two-body forces yield good agreement with much experimental data. Many attempts have been made to calculate nuclear energies ab initio, by starting from some form of an interaction between free nucleons. Recent results of such calculations claim to obtain reasonable agreement with measured energies. These results, however, are obtained for wave functions which are very complicated. It is difficult to see how such wave functions are consistent with independent nucleon motion, the very essence of the shell model. In some of those calculations, 3-body interactions play a very important role. This is puzzling since nuclear energies are accurately obtained in shell model calculations by using only effective two-body interactions. In this paper, some examples of simple shell model calculations are reviewed. They exhibit good agreement with experiment and the apparent absence of the need for effective 3-body interactions.

A schematic but systematic study is presented for p- and sd-shell nuclei to investigate the position of the first opposite-parity state relative to the ground state. This approach rests on the assumption that a probe using a dominant quadrupole-quadrupole interaction and observing the Pauli principle is sufficient to trace qualitatively the position of these states. It is argued that even if the SU(3) symmetry is broken, the lowest states in each shell have contributions from the dominant SU(3) states only, and therefore their relative energies are not influenced significantly by the mixing. It is shown that the global properties and trends of the above-mentioned energy difference are governed by the allowed SU(3) configurations including a pronounced odd-even staggering effect. In some regions, strongly prolate 2ℏω states are found to appear at energies comparable to that of 0ℏω states, indicating that in realistic calculations mixing to excited configurations might become important, and this can explain the anomalous properties of some neutron-rich nuclei. An analysis of the available quadrupole moments is also presented, and a qualitative agreement between calculated and experimental values is found.

Self-dual Yang–Mills theory is presented and the associated equations are derived. An isospectral linear problem whose compatibility condition yields the self-dual Yang–Mills system is formulated. A characterization of the system in terms of a Lie-algebra valued current is given. Finally, several explicit reductions to specific integrable systems are derived.

The behavior of the relativistic charged particle multiplicities and the pseudorapidity distributions for 4.5A and 14.5A GeV/c²⁸Si-nucleus interactions are investigated in terms of the number of emitted relativistic hadrons in the backward hemisphere, (relativistic charged particles emitted with space angle θ_s such that θ_s lies in the interval 90°≤θ_s≤270°). The η distribution of relativistic charged particles for the interactions with are found to be quite nicely fitted by a single Gaussian distribution (GD), while it is fitted by two distinct GD's when the interactions are not accompanied by backward relativistic hadrons. This, in turn, suggests that in the production of events having probably two different mechanisms operate.

In this paper, the general structure of leptonic decay constants of vector mesons is evaluated in the framework of the Bethe–Salpeter equation under the Covariant Instantaneous Ansatz (CIA), which is a Lorentz-invariant generalization of Instantaneous Approximation (IA). The numerical values of f_V in this CIA framework are on the low side in comparison to recent calculations of these quantities. However, the overall asymptotic behavior of f_V is in conformity with QCD predictions.

We argue that it is the effect of non-commutative geometry of spacetime that leads to the generation of mass, thus pleasingly complementing earlier results.

Violations in Lorentz symmetry at very high energies are being discussed by Glashow, Coleman, the author and others. The motivation comes from certain observed events pertaining to ultra high energy cosmic rays, and also from theoretical quantum gravity studies, which require a discrete spacetime at the Planck scale. We examine the modification to the usual energy momentum relation, and in light of this, deduce a modified Dirac equation and examine some consequences.

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

An analytical expression is obtained for the Λ-nucleus potential in the folding model for a finite range of the ΛN force. The effect of ΛN force range on the Λ-binding energy of medium and heavy nuclei is studied. However, more reliable information on ΛN force range may be obtained from the study of light hypernuclei.

Using a generalized mean field theory, we have studied relations among effective meson masses, effective meson–nucleon couplings and equations of state (EOS) in asymmetric nuclear matter. If the effective ω-meson mass becomes smaller at high density, the EOS becomes stiffer. However, if we require that the ω-meson mean field is proportional to baryon density, the effective ω–nucleon coupling also becomes smaller at the same time as the effective ω-meson mass becomes smaller. Consequently, the EOS becomes softer. A similar relation is found for the effective ρ-meson mass and the effective ρ–nucleon coupling. We have also studied relations among effective meson masses, effective meson–nucleon couplings and a radius R of a neutron star. R depends somewhat on the value of the effective ω-meson mass and the effective ω–nucleon coupling.