Abstract:

The equation of state for asymmetric nuclear matter (NM) is determined
essentially by the isospin dependence of the NN interaction which
isoriginated from the neutron-proton asymmetry in the medium. To explore
isospin effects, asymmetric NM has been studied within the Hartree Fock
formalism using different density-dependent M3Y interactions as well as the
Skyrme (SLy4) and Gogny (D1S, D1N) interactions. While all these
interactions were proven to be quite realistic in the nuclear structure or
reaction studies, they are clearly divided into two families which are
associated with different behaviors of the NM symmetry energy at high
densities. As a consequence, the two families offer two distinct scenarios
for the proton-to-neutron ratio in beta-equilibrium which imply two
drastically different mechanisms for the neutron star cooling. Such an
ambiguity in the NM symmetry energy at high densities remains an open
question due to the experimental evidences favoring either families of the
mean-field interactions.

In finite nuclei, the neutron-proton asymmetry is largest at the surface of
neutron-rich nuclei which can significantly affect the shell evolution of
valence neutrons. To study such effects, a coupled-channel (CC) analysis of
the $^{18,20,22}$O$(p,p')$ data has been performed to determine the neutron
transition strengths of 2$^+_1$ states in $^{18,20,22}$O, using the
microscopic optical potential and inelastic form factor given by the folding
model. With the isospin dependence of the effective interaction carefully
fine-tuned against the data of charge-exchange (p,n) reactions, the
isoscalar (delta_0) and isovector (delta_1) deformation lengths of 2$^+_1$
states in $^{18,20,22}$O were extracted from the CC analysis of (p,p') data.
A specific N dependence of delta_0 and delta_1 has been established which
can be linked to the neutron shell closure occurring at N-> 16. The ratios
of the neutron/proton transition matrix elements (M_n/M_p) determined for
the 2$^+_1$ states in $^{18,20}$O have been compared to those deduced from
the mirror symmetry, using the measured B(E2) values of 2$^+_1$ states in
the proton rich $^{18}$Ne and $^{20}$Mg nuclei, to discuss the isospin
impurity in the $2^+_1$ excitation of the A=18,T=1 and A=20,T=2 isobars.