Isovector deformation and its link to the neutron shell closure

DWBA analysis of the inelastic S(p, p′) and O(p, p′) scattering data measured in the inverse kinematics has been performed to determine the isoscalar (δ0) and isovector (δ1) deformation lengths of the 2+1 excitations in the Sulfur and Oxygen isotopes using a compact folding approach. A systematic N-dependence of δ0 and δ1 has been established which shows a link between δ1 and the neutron-shell closure. Strong isovector deformations were found in several cases, e.g., the 2+1 state in O where δ1 is nearly three times larger than δ0. These results confirm the relation δ1 > δ0 anticipated from the core polarization by the valence neutrons in the open-shell (neutron rich) nuclei. The effect of neutron shell closure at N = 14 or 16 has been discussed based on the folding model analysis of the inelastic O+p scattering data at 46.6 MeV/u measured recently at GANIL. PACS. 2 5.40.Ep, 21.10.Re, 24.10.Eq, 24.10.Ht The neutron and proton contributions to the structure of the lowest 2 excited states are known to be quite different in the neutron-rich nuclei due, in particular, to a strong polarization of the core by valence neutrons [1]. In the distorted-wave Born approximation (DWBA) for the inelastic hadron scattering, the different neutron and proton contributions to the nuclear excitation are explicitly determined by the isospin dependence of the inelastic form factor (FF). In general, the isospin-dependent nucleon optical potential (OP) can be written in terms of the isoscalar (IS) and isovector (IV) components [2] as U(R) = U0(R)± εU1(R), ε = (N − Z)/A, (1) where the + sign pertains to incident neutron and sign to incident proton. While the strength of the Lane potential U1 has been studied since a long time [2] in the (p, p) and (n, n) elastic scattering and (p, n) reaction studies, very few attempts were made to study the isospin dependence of the inelastic FF. Within a collective-model prescription, the inelastic FF for the nucleon-nucleus scattering is obtained by “deforming” the OP (1) with scaling factors δ known as the nuclear deformation lengths