#### Abstract

The effects of neutron excess on the formation of $\Delta \mathrm{}(3,3)\mathrm{}$ resonance states in exotic nuclei at equilibrium and under large amplitude compression have been investigated within the radial constraint spherical Hartree-Fock method. An effective Hamiltonian has been used which includes the $\Delta $ degree of freedom explicitly. Results are presented for ${}^{28}\mathrm{O},$ ${}^{60}\mathrm{Ca},$ and ${}^{70}\mathrm{Ca}$ in a model space of seven major oscillator shells and eight $\Delta $ orbitals. The results show that the formation of the Δ’s depends strongly on the amount of neutron excess in the nuclear system. In contrast to previous work where we found no Δ’s in ${}^{16}\mathrm{O}$ and ${}^{40}\mathrm{Ca}$ at equilibrium, these results show that a significant amount of Δ’s exists at equilibrium in exotic isotopes. In addition, as the nucleus is compressed to a density of 2.5 times the ordinary nuclear density, the percentage of the Δ’s rises to 3%, 5%, and 7% of the total number of all baryons in ${}^{28}\mathrm{O},$ ${}^{60}\mathrm{Ca},$ and ${}^{70}\mathrm{Ca},$ respectively. This suggests a parametrization for the percentage of the Δ’s created at 2.5 times the normal density of the form $0.25\left(N-Z\right)\%.\mathrm{}$ The results are consistent with the theoretical prediction of the formation of Δ matter in neutron-rich matter at high compression.

DOI: http://dx.doi.org/10.1103/PhysRevC.61.014301

- Received 1 June 1999
- Published 23 November 1999

© 1999 The American Physical Society