Neutron-Rich Nuclei in Heaven and Earth

An accurately calibrated relativistic parametrization is introduced to compute the ground state properties of finite nuclei, their linear response, and the structure of neutron stars. While similar in spirit to the successful NL3 parameter set, it produces an equation of state that is considerably softer -- both for symmetric nuclear matter and for the symmetry energy. This softening appears to be required for an accurate description of several collective modes having different neutron-to-proton ratios. Among the predictions of this model are a symmetric nuclear-matter incompressibility of K=230 MeV and a neutron skin thickness in 208Pb of Rn-Rp=0.21 fm. Further, the impact of such a softening on the properties of neutron stars is as follows: the model predicts a limiting neutron star mass of Mmax=1.72 Msun, a radius of R=12.66 km for a ``canonical'' M=1.4 Msun neutron star, and no (nucleon) direct Urca cooling in neutrons stars with masses below M=1.3 Msun.Comment: 4 pages, 3 tables, and no figure

Insensitivity of the elastic proton-nucleus reaction to the neutron radius of 208Pb

The sensitivity--or rather insensitivity--of the elastic proton-nucleus reaction to the neutron radius of 208Pb is investigated using a non-relativistic impulse-approximation approach. The energy region (Tlab=500 MeV and Tlab=800 MeV) is selected so that the impulse approximation may be safely assumed. Therefore, only free nucleon-nucleon scattering data are used as input for the optical potential. Further, the optical potential includes proton and neutron ground-state densities that are generated from accurately-calibrated models. Even so, these models yield a wide range of values (from 0.13 fm to 0.28 fm) for the poorly known neutron skin thickness in 208Pb. An excellent description of the experimental cross section is obtained with all neutron densities. We have invoked analytic insights developed within the eikonal approximation to understand the insensitivity of the differential cross section to the various neutron densities. As the diffractive oscillations of the cross sections are controlled by the matter radius of the nucleus, the large spread in the neutron skin among the various models gets diluted into a mere 1.5% difference in the matter radius. This renders ineffective the elastic reaction as a precision tool for the measurement of neutron radii.Comment: 17 pages with 5 figure

Parity Violation, the Neutron Radius of Lead, and Neutron Stars

The neutron radius of a heavy nucleus is a fundamental nuclear-structure observable that remains elusive. Progress in this arena has been limited by the exclusive use of hadronic probes that are hindered by large and controversial uncertainties in the reaction mechanism. The Parity Radius Experiment at the Jefferson Laboratory offers an attractive electro-weak alternative to the hadronic program and promises to measure the neutron radius of 208Pb accurately and model independently via parity-violating electron scattering. In this contribution we examine the far-reaching implications that such a determination will have in areas as diverse as nuclear structure, atomic parity violation, and astrophysics.Comment: 5 pages, 5 figures, proceedings to the PAVI06 conferenc

Correction to Relativistic Mean Field binding energy and NpNnN_pN_n scheme

The differences between the experimental and Relativistic Mean Field binding energies have been calculated for a large number of even-even nuclei from A=50 to 220. Excluding certain mass regions, the differences, after suitable corrections for particular isotope chains, are found to be proportional to the Casten factor $P$, chosen as a measure of n-p interaction strength in a nucleus. Results for even-$Z$ odd-$N$ nuclei are also seen to follow the same relation, if the odd-even mass difference is taken into account following the semiempirical formula. This indicates that the n-p interaction is the major contributor to the difference between the calculated and the experimental binding energies

Correlation between muonic levels and nuclear structure in muonic atoms

A method that deals with the nucleons and the muon unitedly is employed to investigate the muonic lead, with which the correlation between the muon and nucleus can be studied distinctly. A "kink" appears in the muonic isotope shift at a neutron magic number where the nuclear shell structure plays a key role. This behavior may have very important implications for the experimentally probing the shell structure of the nuclei far away from the $\beta$-stable line. We investigate the variations of the nuclear structure due to the interaction with the muon in the muonic atom and find that the nuclear structure remains basically unaltered. Therefore, the muon is a clean and reliable probe for studying the nuclear structure. In addition, a correction that the muon-induced slight change in the proton density distribution in turn shifts the muonic levels is investigated. This correction to muonic level is as important as the Lamb shift and high order vacuum polarization correction, but is larger than anomalous magnetic moment and electron shielding correction.Comment: 2 figure

Cluster formation in asymmetric nuclear matter: semi-classical and quantal approaches

The nuclear-matter liquid-gas phase transition induces instabilities against finite-size density fluctuations. This has implications for both heavy-ion-collision and compact-star physics. In this paper, we study the clusterization properties of nuclear matter in a scenario of spinodal decomposition, comparing three different approaches: the quantal RPA, its semi-classical limit (Vlasov method), and a hydrodynamical framework. The predictions related to clusterization are qualitatively in good agreement varying the approach and the nuclear interaction. Nevertheless, it is shown that i) the quantum effects reduce the instability zone, and disfavor short-wavelength fluctuations; ii) large differences appear bewteen the two semi-classical approaches, which correspond respectively to a collisionless (Vlasov) and local equilibrium description (hydrodynamics); iii) the isospin-distillation effect is stronger in the local equilibrium framework; iv) important variations between the predicted time-scales of cluster formation appear near the borders of the instability region.Comment: 27 pages, 11 figures, Submitted to Nuclear Physics A, Nuclear Physics A In press (2008

Equation of state of isospin-asymmetric nuclear matter in relativistic mean-field models with chiral limits

Using in-medium hadron properties according to the Brown-Rho scaling due to the chiral symmetry restoration at high densities and considering naturalness of the coupling constants, we have newly constructed several relativistic mean-field Lagrangians with chiral limits. The model parameters are adjusted such that the symmetric part of the resulting equation of state at supra-normal densities is consistent with that required by the collective flow data from high energy heavy-ion reactions, while the resulting density dependence of the symmetry energy at sub-saturation densities agrees with that extracted from the recent isospin diffusion data from intermediate energy heavy-ion reactions. The resulting equations of state have the special feature of being soft at intermediate densities but stiff at high densities naturally. With these constrained equations of state, it is found that the radius of a 1.4$M_\odot$ canonical neutron star is in the range of 11.9 km$\leq$R$\leq$13.1 km, and the maximum neutron star mass is around 2.0$M_\odot$ close to the recent observations.Comment: 14 pages, 3 figure

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. IX: Constraint of pairing force to 1S0^1S_0 neutron-matter gap

In this latest of our series of Skyrme-HFB mass models, HFB-16, we introduce the new feature of requiring that the contact pairing force reproduce at each density the $^1S_0$ pairing gap of neutron matter as determined in microscopic calculations with realistic nucleon-nucleon forces. We retain the earlier constraints on the Skyrme force of reproducing the energy-density curve of neutron matter, and of having an isoscalar effective mass of $0.8M$ in symmetric infinite nuclear matter at the saturation density; we also keep the recently adopted device of dropping Coulomb exchange. Furthermore, the correction term for the spurious energy of collective motion has a form that is known to favour fission barriers that are in good agreement with experiment. Despite the extra constraints on the effective force, we have achieved a better fit to the mass data than any other mean field model, the rms error on the 2149 measured masses of nuclei with $N$ and $Z \ge$ 8 having been reduced to 0.632 MeV; the improvement is particularly striking for the most neutron-rich nuclei. Moreover, it turns out that even with no flexibility at all remaining for the pairing force, the spectral pairing gaps that we find suggest that level densities in good agreement with experiment should be obtained. This new force is thus particularly well-suited for astrophysical applications, such as stellar nucleosynthesis and neutron-star crusts.Comment: 38 pages, 9 figures accepted for publication in Nuclear Physics

Constraining the Radii of Neutron Stars with Terrestrial Nuclear Laboratory Data

Neutron star radii are primarily determined by the pressure of isospin asymmetric matter which is proportional to the slope of the nuclear symmetry energy. Available terrestrial laboratory data on the isospin diffusion in heavy-ion reactions at intermediate energies constrain the slope of the symmetry energy. Using this constraint, we show that the radius (radiation radius) of a 1.4 solar mass neutron star is between 11.5 (14.4) and 13.6 (16.3) km.Comment: 11 pages, 3 figures; version to be published in Phys. Lett.

Optimization of relativistic mean field model for finite nuclei to neutron star matter

We have optimized the parameters of extended relativistic mean-field model using a selected set of global observables which includes binding energies and charge radii for nuclei along several isotopic and isotonic chains and the iso-scalar giant monopole resonance energies for the $^{90}$Zr and $^{208}$Pb nuclei. The model parameters are further constrained by the available informations on the energy per neutron for the dilute neutron matter and bounds on the equations of state of the symmetric and asymmetric nuclear matter at supra-nuclear densities. Two new parameter sets BSP and IUFSU* are obtained, later one being the variant of recently proposed IUFSU parameter set. The BSP parametrization uses the contributions from the quartic order cross-coupling between $\omega$ and $\sigma$ mesons to model the high density behaviour of the equation of state instead of the $\omega$ meson self-coupling as in the case of IUFSU* or IUFSU. Our parameter sets yield appreciable improvements in the binding energy systematics and the equation of state for the dilute neutron matter. The importance of the quartic order $\omega-\sigma$ cross coupling term of the extended RMF model, as often ignored, is realized.Comment: 22 pages, 11 figures, Nucl. Phys. A (in press