Neutron-rich $^{208}$Pb nucleus with delta excitation under compression

The spherical Hartree-Fock approximation is applied to a no-core shell model with a realistic effective baryon-baryon interaction. The ground state properties of a heavy spherical neutron-rich doubly magic 208Pb nucleus under compression are investigated. It is found that the nucleus becomes more bound with the occurrence of Delta resonances. The creation of Delta increases as the compression is continuous. There is a considerable reduction in the compressibility when the Delta degree of freedom is activated. It is found that the Delta particle is the basic component of the 208Pb nucleus besides nucleons at the ground state without any compression. When the nucleus is compressed to about 4.31 times the ordinary density, the Delta component is sharply increased to about 14.4% of all baryons in the system. It is found that there is a radial density distribution for Delta at the ground state of 208Pb nucleus without any compression. The single particle energy levels are calculated and their behaviors are examined under compression too. A good agreement was obtained between the results of the effective Hamiltonian and the phenomenological shell model for the low lying single-particle spectra.