Self-Consistent Single-Particle Spectra with Delta Excitations

Abstract

Single-particle energies of spherical double magic rich-neutron $^{208}Pb$ nucleus are investigated by using a realistic effective baryon-baryon Hamiltonian. The results showed that the computed spectrum followed the expected arrangement of the shell model in the dominant nucleon orbitals. In this spectrum, visible gaps between the shells are clearly shown. By compressed nucleus, the arrangement of single-particle orbitals and their gaps is maintained. When the nucleus is compressed, the general trend of single-particle energies shifts to higher energies. When the orbitals approach the surface, their curvature rises more and more. For $\Delta ^0$ orbitals, in some root mean square radii ($r_{rms}$), some orbitals close together but do not intersect. There is no clear evidence for the gaps in the nuclear shells. However, a gap of about 251.2 MeV was observed between the last dominant neutron orbital and the first predominant $\Delta ^0$ orbitals, in this work. This is attributed to the difference in the rest mass of baryons that are neutron (ns and $\Delta ^0$) particles.