Using symmetric 112Sn+112Sn, 124Sn+124Sn collisions as references, we probe isospin diffusion in peripheral asymmetric 112Sn+124Sn, 124Sn+112Sn systems at an incident energy of E/A=50 MeV. Isoscaling analyses imply that the quasiprojectile and quasitarget in these collisions do not achieve isospin equilibrium, permitting an assessment of isospin transport rates. We find that comparisons between isospin sensitive experimental and theoretical observables, using suitably chosen scaled ratios, permit investigation of the density dependence of the asymmetry term of the nuclear equation of state.

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Multi-fragment decays of 129 Xe, 197 Au, and 238 U projectiles in collisions with Be, C, Al, Cu, In, Au, and U targets at energies between E/A = 400 MeV and 1000 MeV have been studied with the ALADIN forward-spectrometer at SIS. By adding an array of 84 SiCsI(Tl) telescopes the solid-angle coverage of the setup was extended to θ lab = 16 • . This permitted the complete detection of fragments from the projectile-spectator source.The dominant feature of the systematic set of data is the Z bound universality that is obeyed by the fragment multiplicities and correlations. These observables are invariant with respect to the entrance channel if plotted as a function of Z bound , where Z bound is the sum of the atomic numbers Z i of all projectile fragments with Z i ≥ 2. No significant dependence on the bombarding energy nor on the target mass is observed. The dependence of the fragment multiplicity on the projectile mass follows a linear scaling law.The reasons for and the limits of the observed universality of spectator fragmentation are explored within the realm of the available data and with model studies. It is found that the universal properties should persist up to much higher bombarding energies than explored in this work and that they are consistent with universal features exhibited by the intranuclear cascade and statistical multifragmentation models.

A comprehensive description of all single-particle properties associated with the nucleus 40 Ca is generated by employing a nonlocal dispersive optical potential capable of simultaneously reproducing all relevant data above and below the Fermi energy. The introduction of nonlocality in the absorptive potentials yields equivalent elastic differential cross sections as compared to local versions but changes the absorption profile as a function of angular momentum suggesting important consequences for the analysis of nuclear reactions. Below the Fermi energy, nonlocality is essential to allow for an accurate representation of particle number and the nuclear charge density. Spectral properties implied by (e, e ′ p) and (p, 2p) reactions are correctly incorporated, including the energy distribution of about 10% high-momentum nucleons, as experimentally determined by data from Jefferson Lab. These high-momentum nucleons provide a substantial contribution to the energy of the ground state, indicating a residual attractive contribution from higher-body interactions for 40 Ca of about 0.64 MeV/A.PACS numbers: 21.10. Pc,24.10.Ht,11.55.Fv The properties of a nucleon that is strongly influenced by the presence of other nucleons have traditionally been studied in separate energy domains. Positive energy nucleons are described by fitted optical potentials mostly in local form [1,2]. Bound nucleons have been analyzed in static potentials that lead to an independent-particle model modified by the interaction between valence nucleons as in traditional shell-model calculations [3,4]. The link between nuclear reactions and nuclear structure is provided by considering these potentials as representing different energy domains of one underlying nucleon self-energy. This idea was implemented in the dispersive optical model (DOM) by Mahaux and Sartor [5]. By employing dispersion relations, the method provides a critical link between the physics above and below the Fermi energy with both sides being influenced by the absorptive potentials on the other side.The DOM provides an ideal strategy to predict properties for exotic nuclei by utilizing extrapolations of these potentials towards the respective drip lines [6,7]. The main stumbling block so far has been the need to utilize the approximate expressions for the properties of nucleons below the Fermi energy that were developed by Mahaux and Sartor [5] to correct for the normalizationdistorting energy dependence of the Hartree-Fock (HF) potential. By restoring the proper treatment of nonlocality in the HF contribution, it was possible to overcome this problem [8] although the local treatment of the absorptive potentials yielded a poor description of the nuclear charge density and particle number.In the present work we have for the first time treated the nonlocality of these potentials for the nucleus 40 Ca with the aim to include all available data below the Fermi energy that can be linked to the nucleon single-particle propagator [9] while maintaining a correct description of the el...

Recent measurements of pre-equilibrium neutron and proton transverse emission from 112,124 Sn+ 112,124 Sn reactions at 50 MeV/A have been completed at the National Superconducting Cyclotron Laboratory. Free nucleon transverse emission ratios are compared to those of A=3 mirror nuclei. Comparisons are made to BUU transport calculations and conclusions concerning the density dependence of the asymmetry term of the nuclear equation-of-state at sub-nuclear densities are made. The double-ratio of neutron-proton ratios between two reactions is employed as a means of reducing first-order Coulomb effects and detector efficiency effects. Comparison to BUU model predictions indicate a density dependence of the asymmetry energy that is closer to a form in which the asymmety energy increases as the square root of the density for the density region studied. A coalescent-invariant analysis is introduced as a means of reducing suggested difficulties with cluster emission in total nucleon emission. Future experimentation is presented.PACS numbers: 25.70.Mn,21.65.+f,26.62.+c The nuclear symmetry energy increases the masses of nuclei with very different neutron and proton concentrations and limits the neutron concentration and maximum neutron number N of any element. In the interior regions of neutron stars, where neutrons may comprise over 90% of the matter, the symmetry energy may contribute the bulk of the pressure supporting the star [1]. The nuclear equation-of-state at densities of 0.5≤ ρ ρ0 ≤10 (where ρ 0 is the nuclear saturation density) governs many of the neutron star macroscopic properties, including radius, moment of inertia, core structure [2], cooling rates, and the possible collapse of a neutron star into a black hole [3,4,5].Constraints on the symmetry energy at sub-saturation density have been obtained from measurements of the diffusion of neutrons and protons between nuclei of different asymmetry δ = (N-Z)/(N+Z) in peripheral collisions [6,7]. (Here N and Z are the relevant neutron and proton number of the nuclei.) Measurements of nuclear masses, isovector collective excitations and neutron skin measurements may also provide constraints at densities less than ρ 0 . Nevertheless, the density dependence of the symmetry energy is not known well enough to constrain the relevant neutron star properties. Using an alternative approach to improve present constraints, new measurements of the ratios of neutron and proton spectra in central heavy ion collisions are presented and compared to transport theory calculations. These calculations display a strong sensitivity to the density dependence of the symmetry energy, from which additional contraints may ultimately be derived [8] Using proton and neutron densities calculated from the non-linear relativistic mean-field theories as inputs, the dynamics of nucleon-nucleon collisions are calcuated. These calculations utilize nucleonic mean field potentials corresponding to an equation-of-state that can be expressed (at zero temperature) in terms of the mean energy of a nuc...

Neutron elastic-scattering angular distributions were measured at beam energies of 11.9 and 16.9 MeV on 40,48 Ca targets. These data plus other elastic-scattering measurements, total and reaction cross sections measurements, (e, e ′ p) data, and single-particle energies for magic and doubly magic nuclei have been analyzed in the dispersive optical model (DOM) generating nucleon self-energies (optical-model potentials) which can be related, via the many-body Dyson equation, to spectroscopioc factors and occupation probabilities. It is found that for stable nuclei with N ≥ Z, the imaginary surface potential for protons exhibits a strong dependence on the neutron-proton asymmetry. This result leads to a more modest dependence of the spectroscopic factors on asymmetry. The measured data and the DOM analysis of all considered nuclei clearly demonstrates that the neutron imaginary surface potential displays very little dependence on the neutron-proton asymmetry for nuclei near stability (N ≥ Z).

A review of recent developments of the dispersive optical model (DOM) is presented. Starting from the original work of Mahaux and Sartor, several necessary steps are developed and illustrated which increase the scope of the DOM allowing its interpretation as generating an experimentally constrained functional form of the nucleon self-energy. The method could therefore be renamed as the dispersive selfenergy method.The aforementioned steps include the introduction of simultaneous fits of data for chains of isotopes or isotones allowing a data-driven extrapolation for the prediction of scattering cross sections and level properties in the direction of the respective drip lines. In addition, the energy domain for data was enlarged to include results up to 200 MeV where available.An important application of this work was implemented by employing these DOM potentials to the analysis of the (d,p) transfer reaction using the adiabatic distorted wave approximation (ADWA). We review these calculations which suggest that physically meaningful results are easier to obtain by employing DOM ingredients as compared to the traditional approach which relies on a phenomenologically-adjusted bound-state wave function combined with a global (nondispersive) optical-model potential. Application to the exotic 132 Sn nucleus also shows great promise for the extrapolation of DOM potentials towards the drip line with attendant relevance for the physics of FRIB. We note that the DOM method combines structure and reaction information on the same footing providing a unique approach to the analysis of exotic nuclei.We illustrate the importance of abandoning the custom of representing the nonlocal HF potential in the DOM by an energy-dependent local potential as it impedes the proper normalization of the solution of the Dyson equation. This important step allows for the interpretation of the DOM potential as representing the nucleon selfenergy permitting the calculations of spectral amplitudes and spectral functions above and below the Fermi energy. The latter feature provides access to quantities like the momentum distribution, charge density, and particle number which were not available in the original work of Mahaux and Sartor.When employing a non-local HF potential, but local dispersive contributions (as originally proposed by Mahaux and Sartor), we illustrate that it is impossible to Novel applications of the dispersive optical model 2 reproduce the particle number and the measured charge density. Indeed, the use of local absorptive potentials leads to a substantial overestimate of particle number. However from detailed comparisons with self-energies calculated with ab initio manybody methods that include both short-and long-range correlations, we demonstrate that it is essential to introduce non-local absorptive potentials in order to remediate these deficiencies.We review the fully non-local DOM potential fitted to 40 Ca where elastic-scattering data, level information, particle number, charge density and high-momentum-removal (e, e ′ ...

A dispersive-optical-model analysis of p+ 40,42,44,48 Ca and n+ 40 Ca interactions has been carried out. The real and imaginary potentials have been constrained by fitting elastic-scattering data, total and reaction cross sections, and level properties of valence hole states deduced from (e, e p) data. The resulting surface imaginary potential increases with asymmetry for protons, implying that in heavier Ca isotopes, protons experience stronger long-range correlations. Presently, there is not enough data for neutrons to determine their asymmetry dependence. Global optical-model fits usually assume that the neutron asymmetry dependence is equal in magnitude, but opposite in sign, to that for protons. Such a dependence was found to give unphysical results for heavy Ca isotopes. The dispersive optical model is shown to be a useful tool for data-driven extrapolations to the drip lines. Neutron and proton data at larger asymmetries are needed to achieve more reliable extrapolations. The present analysis predicts 60 Ca and 70 Ca to be bound, while the intermediate isotopes are not.