Nucleon Effective E-Mass in Neutron-Rich Matter from the Migdal-Luttinger Jump

The well-known Migdal-Luttinger theorem states that the jump of the single-nucleon momentum distribution at the Fermi surface is equal to the inverse of the nucleon effective E-mass. Recent experiments studying short-range correlations (SRC) in nuclei using electron-nucleus scatterings at the Jefferson National Laboratory (JLAB) together with model calculations constrained significantly the Migdal-Luttinger jump at saturation density of nuclear matter. We show that the corresponding nucleon effective E-mass is consequently constrained to $M_0^{\ast,\rm{E}}/M\approx2.22\pm0.35$ in symmetric nuclear matter (SNM) and the E-mass of neutrons is smaller than that of protons in neutron-rich matter. Moreover, the average depletion of the nucleon Fermi sea increases (decreases) approximately linearly with the isospin asymmetry $\delta$ according to $\kappa_{\rm{p}/\rm{n}}\approx 0.21\pm0.06 \pm (0.19\pm0.08)\delta$ for protons (neutrons). These results will help improve our knowledge about the space-time non-locality of the single-nucleon potential in neutron-rich nucleonic matter useful in both nuclear physics and astrophysics.Comment: Discussions added. Version accepted by PL

High Density Behaviour of Nuclear Symmetry Energy and High Energy Heavy-Ion Collisions

High energy heavy-ion collisions are proposed as a novel means to obtain information about the high density ({\rm HD}) behaviour of nuclear symmetry energy. Within an isospin-dependent hadronic transport model using phenomenological equations of state ({\rm EOS}) for dense neutron-rich matter, it is shown that the isospin asymmetry of the HD nuclear matter formed in high energy heavy-ion collisions is determined mainly by the HD behaviour of nuclear symmetry energy. Experimental signatures in several sensitive probes, i.e., $\pi^-$ to $\pi^+$ ratio, transverse collective flow and its excitation function as well as neutron-proton differential flow, are investigated. A precursor of the possible isospin separation instability in dense neutron-rich matter is predicted to appear as the local minima in the excitation functions of the transverse flow parameter for both neutrons and protons above the pion production threshold. Because of its {\it qualitative} nature unlike other {\it quantitative} observables, this precursor can be used as a unique signature of the isospin dependence of the nuclear {\rm EOS}. Measurements of these observables will provide the first terrestrial data to constrain stringently the HD behaviour of nuclear symmetry energy and thus also the {\rm EOS} of dense neutron-rich matter. Implications of our findings to neutron star studies are also discussed.Comment: 25 pages + 16 figures, Nucl. Phys. A (2002) in pres