Neutron Stars and Nuclei in the Modified Relativistic Hartree Approximation

We have examined the properties of neutron-rich matter and finite nuclei in the modified relativistic Hartree approximation for several values of the renormalization scale, $\mu$, around the standard choice of $\mu$ equal to the nucleon mass $M$. Observed neutron star masses do not effectively constrain the value of $\mu$. However for finite nuclei the value $\mu/M=0.79$, suggested by nuclear matter data, provides a good account of the bulk properties with a sigma mass of about 600 MeV. This value of $\mu/M$ renders the effective three and four body scalar self-couplings to be zero at 60\% of equilibrium nuclear matter density, rather than in the vacuum. We have also found that the matter part of the exchange diagram has little impact on the bulk properties of neutron stars.Comment: 33 pages, Latex, 8 figures (available from authors by fax), Minnesota preprint NUC-MINN-93/7-

Monopole giant resonances and nuclear compressibility in relativistic mean field theory

Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field (RMF) theory. Excitation energies and the structure of eigenmodes are determined from a Fourier analysis of dynamical monopole moments and densities. The generator coordinate method, with generating functions that are solutions of constrained RMF calculations, is also used to calculate excitation energies and transition densities of giant monopole states. Calculations are performed with effective interactions which differ in their prediction of the nuclear matter compression modulus K_nm. Both time-dependent and constrained RMF results indicate that empirical GMR energies are best reproduced by an effective force with K_nm \approx 270 MeV.Comment: 30 pages of LaTeX, 18 PS-figure

Meson mixing amplitudes in asymmetric nuclear matter

Using a purely hadronic model, we study the charge-symmetry-breaking $\rho$-$\omega$, $\sigma$-$\delta$, $\sigma$-$\rho$ and $\delta$-$\omega$ mixing amplitudes in isospin asymmetric nuclear matter. The basic assumption of the model is that the mixing amplitude is generated by nucleon and anti-nucleon loops and hence driven entirely by the difference between proton and neutron Fermi momenta and the proton-neutron mass difference. We find that the behavior of the mixing amplitude is very complicated in the spacelike region and quite sensitive to the proton fraction of nuclear medium and nuclear density. In particular, in neutron rich nuclei (like Pb) and/or neutron stars the mixing amplitudes become about 10 $\sim$ 100 times as large as those in typical mirror nuclei.Comment: 13 pages, 9 ps figure

Statistical Model for a Complete Supernova Equation of State

A statistical model for the equation of state (EOS) and the composition of supernova matter is presented with focus on the liquid-gas phase transition of nuclear matter. It consists of an ensemble of nuclei and interacting nucleons in nuclear statistical equilibrium. A relativistic mean field model is applied for the nucleons. The masses of the nuclei are taken from nuclear structure calculations which are based on the same nuclear Lagrangian. For known nuclei experimental data is used directly. Excluded volume effects are implemented in a thermodynamic consistent way so that the transition to uniform nuclear matter at large densities can be described. Thus the model can be applied at all densities relevant for supernova simulations, i.e. rho=10^5 - 10^15 g/cm^3, and it is possible to calculate a complete supernova EOS table. The model allows to investigate the role of shell effects, which lead to narrow-peaked distributions around the neutron magic numbers for low temperatures. At larger temperatures the distributions become broad. The significance of the statistical treatment and the nuclear distributions for the composition is shown. We find that the contribution of light clusters is very important and is only poorly represented by alpha-particles alone. The results for the EOS are systematically compared to two commonly used models for supernova matter which are based on the single nucleus approximation. Apart from the composition, in general only small differences of the different EOSs are found. The differences are most pronounced around the (low-density) liquid-gas phase transition line where the distribution of light and intermediate clusters has an important effect. Possible extensions and improvements of the model are discussed.Comment: 33 pages, 22 page

Surface Symmetry Energy

Binding energy of symmetric nuclear matter can be accessed straightforwardly with the textbook mass-formula and a sample of nuclear masses. We show that, with a minimally modified formula (along the lines of the droplet model), the symmetry energy of nuclear matter can be accessed nearly as easily. Elementary considerations for a macroscopic nucleus show that the surface tension needs to depend on asymmetry. That dependence modifies the surface energy and implies the emergence of asymmetry skin. In the mass formula, the volume and surface and (a)symmetry energies combine as energies of two connected capacitors, with the volume and surface capacitances proportional to the volume and area, respectively. The net asymmetry partitions itself into volume and surface contributions in proportion to the capacitances. A combination of data on skin sizes and masses constrains the volume symmetry parameter to 27 MeV < alpha < 31 MeV and the volume-to-surface symmetry-parameter ratio to 2.0 < alpha/beta < 2.8. In Thomas-Fermi theory, the surface asymmetry-capacitance stems from a drop of the symmetry energy per nucleon S with density. We establish limits on the drop at half of normal density, to 0.57 < S(rho_0/2)/S(rho_0) < 0.83. In considering the feeding of surface by an asymmetry flux from interior, we obtain a universal condition for the collective asymmetry oscillations, in terms of the asymmetry-capacitance ratio.Comment: 29 pages, 16 figures; final version - Nuclear Physics A, in pres

The long journey from the giant-monopole resonance to the nuclear-matter incompressibility

Differences in the density dependence of the symmetry energy predicted by nonrelativistic and relativistic models are suggested, at least in part, as the culprit for the discrepancy in the values of the compression modulus of symmetric nuclear matter extracted from the energy of the giant monopole resonance in 208Pb. ``Best-fit'' relativistic models, with stiffer symmetry energies than Skyrme interactions, consistently predict higher compression moduli than nonrelativistic approaches. Relativistic models with compression moduli in the physically acceptable range of K=200-300 MeV are used to compute the distribution of isoscalar monopole strength in 208Pb. When the symmetry energy is artificially softened in one of these models, in an attempt to simulate the symmetry energy of Skyrme interactions, a lower value for the compression modulus is indeed obtained. It is concluded that the proposed measurement of the neutron skin in 208Pb, aimed at constraining the density dependence of the symmetry energy and recently correlated to the structure of neutron stars, will also become instrumental in the determination of the compression modulus of nuclear matter.Comment: 9 pages with 2 (eps) figure

Probing Mechanical and Chemical Instabilities in Neutron-Rich Matter

The isospin-dependence of mechanical and chemical instabilities is investigated within a thermal and nuclear transport model using a Skyrme-type phenomenological equation of state for neutron-rich matter. Respective roles of the nuclear mean field and the 2-body stochastic scattering on the evolution of density and isospin fluctuations in either mechanically or chemically unstable regions of neutron-rich matter are investigated. It is found that the mean field dominates overwhelmingly the fast growth of both fluctuations, while the 2-body scattering influences significantly the later growth of the isospin fluctuation only. The magnitude of both fluctuations decreases with the increasing isospin asymmetry because of the larger reduction of the attractive isoscalar mean field by the stronger repuslive neutron symmetry potential in the more neutron-rich matter. Moreover, it is shown that the isospin fractionation happens later, but grows faster in the more neutron-rich matter. Implications of these results to current experiments exploring properties of neutron-rich matter are discussed.Comment: 18 pages & 15 figures, Nuclear Physics A (2001) in pres

On fluctuations of closed string tachyon solitons

We discuss fluctuations on solitons in the dilaton/graviton/tachyon system using the low energy effective field theory approach. It is shown that closed string solitons are free of tachyons in this approximation, regardless of the exact shape of the tachyon potential.Comment: 13 pages, 1 figure, uses JHEP3.cl

Admission to hospital following head injury in England: Incidence and socio-economic associations

BACKGROUND: Head injury in England is common. Evidence suggests that socio-economic factors may cause variation in incidence, and this variation may affect planning for services to meet the needs of those who have sustained a head injury. METHODS: Socio-economic data were obtained from the UK Office for National Statistics and merged with Hospital Episodes Statistics obtained from the Department of Health. All patients admitted for head injury with ICD-10 codes S00.0–S09.9 during 2001–2 and 2002–3 were included and collated at the level of the extant Health Authorities (HA) for 2002, and Primary Care Trust (PCT) for 2003. Incidence was determined, and cluster analysis and multiple regression analysis were used to look at patterns and associations. Results: 112,718 patients were admitted during 2001–2 giving a hospitalised incidence rate for England of 229 per 100,000. This rate varied across the English HA's ranging from 91–419 per 100,000. The rate remained unchanged for 2002–3 with a similar magnitude of variation across PCT's. Three clusters of HA's were identified from the 2001–2 data; those typical of London, those of the Shire counties, and those of Other Urban authorities. Socio-economic factors were found to account for a high proportion of the variance in incidence for 2001–2. The same pattern emerged for 2002–3 at the PCT level. The use of public transport for travel to work is associated with a decreased incidence and lifestyle indicators, such as the numbers of young unemployed, increase the incidence. CONCLUSION: Head injury incidence in England varies by a factor of 4.6 across HA's and PCT's. Planning head injury related services at the local level thus needs to be based on local incidence figures rather than regional or national estimates. Socio-economic factors are shown to be associated with admission, including travel to work patterns and lifestyle indicators, which suggests that incidence is amenable to policy initiatives at the macro level as well as preventive programmes targeted at key groups

Generator Coordinate Calculations for the Breathing-Mode Giant Monopole Resonance in Relativistic Mean Field Theory

The breathing-mode giant monopole resonance (GMR) is studied within the framework of the relativistic mean-field theory using the Generator Coordinate Method (GCM). The constrained incompressibility and the excitation energy of isoscalar giant monopole states are obtained for finite nuclei with various sets of Lagrangian parameters. A comparison is made with the results of nonrelativistic constrained Skyrme Hartree-Fock calculations and with those from Skyrme RPA calculations. In the RMF theory the GCM calculations give a transition density for the breathing mode, which resembles much that obtained from the Skyrme HF+RPA approach and also that from the scaling mode of the GMR. From the systematic study of the breathing-mode as a function of the incompressibility in GCM, it is shown that the GCM succeeds in describing the GMR energies in nuclei and that the empirical breathing-mode energies of heavy nuclei can be reproduced by forces with an incompressibility close to $K = 300$ MeV in the RMF theory.Comment: 27 pages (Revtex) and 5 figures (available upon request), Preprint MPA-793 (March 1994