Constraints on the Equation of State for symmetric matter (equal neutron and proton numbers) have been extracted from energetic collisions of heavy ions over a range of energies. Collisions of neutron-deficient and neutron-rich heavy ions now provide initial constraints on the EoS of neutron-rich matter at sub-saturation densities from isospin diffusions and neutron proton ratios. This article reviews the experimental constraints on the density dependence of Symmetry Energy at sub-saturation density.

We report final-state-exclusive measurements of the light charged fragments in coincidence with 26 Ne residual nuclei following the direct two-proton removal from a neutron-rich 28 Mg secondary beam. A Dalitz-plot analysis and comparisons with simulations show that a majority of the triplecoincidence events with two protons display phase-space correlations consistent with the (two-body) kinematics of a spatially-correlated pair-removal mechanism. The fraction of such correlated events, 56(12) %, is consistent with the fraction of the calculated cross section, 64 %, arising from spin S = 0 two-proton configurations in the entrance-channel (shell-model) 28 Mg ground state wave function. This result promises access to an additional and more specific probe of the spin and spatial correlations of valence nucleon pairs in exotic nuclei produced as fast secondary beams. Access to nuclear reactions that can probe the states of pairs of nucleons in an atomic nucleus is a long-standing ambition. Specifically, an ability to probe the spinstructure of nucleon pairs and, for example, to identify and quantify two-nucleon correlations in the [S, T ]=[0, 1] spin-isospin channel, is required. Intermediate-energy reactions that remove two nucleons (2N) suddenly from a fast projectile, in collisions with a light target nucleus, have been shown [1-4] to provide a sensitivity to the 2N configurations near the projectile surface. Experimentally, the importance of nucleon removal reactions derives from their high detection efficiency (forward focusing of the reaction residues) and use of thick reaction targets, increasing the effective luminosity of the relatively low intensity exotic beams. Prior to the present work these 2N removal cross section measurements have been inclusive with respect to the final states of both the target and the removed nucleons but often exclusive with respect to the bound final-states of the forward-traveling projectilelike residues, allowing spectroscopic studies based on the different residue final-state yields and the shapes of their momentum distributions [5][6][7][8][9][10].The present work sacrifices, temporarily, this betterunderstood residue final-state sensitivity to investigate new information that might be forthcoming from more exclusive measurements of the final states of the removed nucleons. The 9 Be( 28 Mg, 26 Ne) reaction was used at an intermediate energy of 93 MeV/u. The chosen reaction was studied previously in a 26 Ne-γ coincidence measurement [10] and was used to confirm the predicted relative populations of the four bound 26 Ne final states [1]. The present data set has also been used [11] to confirm that the measured contributions to the inclusive 2N-removal cross section from each of the possible elastic and inelastic removal mechanisms [1] were consistent with calculations that use eikonal reaction dynamics and sd-shellmodel structure inputs for the 28 Mg to 26 Ne(J π ) 2p overlap functions. There it was shown that only 8(2) % of the inclusive 9 Be( 28 Mg, 26 Ne) reaction cross s...

The two-proton removal reaction from 28 Mg projectiles has been studied at 93 MeV/u at the NSCL. First coincidence measurements of the heavy 26 Ne projectile residues, the removed protons and other light charged particles enabled the relative cross sections from each of the three possible elastic and inelastic proton removal mechanisms to be determined. These more final-state-exclusive measurements are key for further interrogation of these reaction mechanisms and use of the reaction channel for quantitative spectroscopy of very neutron-rich nuclei. The relative and absolute yields of the three contributing mechanisms are compared to reaction model expectations -based on the use of eikonal dynamics and sd-shell-model structure amplitudes.