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This white paper informs the nuclear astrophysics community and funding agencies about the scientific directions and priorities of the field and provides input from this community for the 2015 Nuclear Science Long Range Plan. It summarizes the outcome of the nuclear astrophysics town meeting that was held on August 21–23, 2014 in College Station at the campus of Texas A&M University in preparation of the NSAC Nuclear Science Long Range Plan. It also reflects the outcome of an earlier town meeting of the nuclear astrophysics community organized by the Joint Institute for Nuclear Astrophysics (JINA) on October 9–10, 2012 Detroit, Michigan, with the purpose of developing a vision for nuclear astrophysics in light of the recent NRC decadal surveys in nuclear physics (NP2010) and astronomy (ASTRO2010). The white paper is furthermore informed by the town meeting of the Association of Research at University Nuclear Accelerators (ARUNA) that took place at the University of Notre Dame on June 12–13, 2014. In summary we find that nuclear astrophysics is a modern and vibrant field addressing fundamental science questions at the intersection of nuclear physics and astrophysics. These questions relate to the origin of the elements, the nuclear engines that drive life and death of stars, and the properties of dense matter. A broad range of nuclear accelerator facilities, astronomical observatories, theory efforts, and computational capabilities are needed. With the developments outlined in this white paper, answers to long standing key questions are well within reach in the coming decade.

Recent developments in the theory of pure neutron matter and experiments concerning the symmetry energy of nuclear matter, coupled with recent measurements of high-mass neutron stars, now allow for relatively tight constraints on the equation of state of dense matter. We review how these constraints are formulated and describe the implications they have for neutron stars and core-collapse supernovae. We also examine thermal properties of dense matter, which are important for supernovae and neutron star mergers, but which cannot be nearly as well constrained at this time by experiment. In addition, we consider the role of the equation of state in medium-energy heavy-ion collisions., Comment: 87 pages, 20 figures, Accepted for Phys. Rep (Gerald E. Brown's Memorial Volume)

Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of non-relativistic and relativistic models of hot and dense matter currently used in nuclear physics and astrophysics (supernovae, proto-neutron stars and neutron star mergers) as well as in condensed matter physics. We consider the general case of arbitrary dimensionality of momentum space and an arbitrary degree of relativity (for relativistic mean-field theoretical models). For non-relativistic zero-range interactions, knowledge of the Landau effective mass suffices to compute next-to-leading order effects, but in the case of finite-range interactions, momentum derivatives of the Landau effective mass function up to second order are required. Numerical computations are performed to compare results from our analytical formulas with the exact results for zero- and finite-range potential and relativistic mean-field theoretical models. In all cases, inclusion of next-to-leading order temperature effects substantially extends the ranges of partial degeneracy for which the analytical treatment remains valid., 28 pages, 8 figures

We investigate how current and proposed observations of neutron stars can lead to an understanding of the state of their interiors and the key unknowns: the typical neutron star radius and the neutron star maximum mass. A theoretical analysis of neutron star structure, including general relativistic limits to mass, compactness, and spin rates is made. We consider observations made not only with photons, ranging from radio waves to X-rays, but also those involving neutrinos and gravity waves. We detail how precision determinations of structural properties would lead to significant restrictions on the poorly understood equation of state near and beyond the equilibrium density of nuclear matter., 70 pages, 19 figures, submitted to Hans Bethe Centennial Physics Reports

The role of the equation of state in the structure of neutron stars is summarized. At densities beyond a few times the normal nuclear saturation density, the neutron-proton-electron sea can be supplemented with more exotic matter, usually involving strangeness, such as hyperons, kaon or pion condensates, and deconfined quark matter. In the case of a boson condensate or deconfined quark matter, the exotic matter may form a mixed-phase region with the hadronic matter. Global aspects of neutron stars, such as radii, moments of inertia and the maximum mass, can be related to specific properties of matter at selected density ranges. Recent observations of isolated neutron stars and pulsars in binaries are beginning to yield significant constraints on structural properties of neutron stars and hence on the properties and composition of neutron-rich nuclear matter.

We investigate the effects of very strong magnetic fields upon the equation of state of dense bayonic matter in which hyperons are present. In the presence of a magnetic field, the equation of state above nuclear density is significantly affected both by Landau quantization and magnetic moment interactions, but only for field strengths $B>5\times10^{18}$ G. The former tends to soften the EOS and increase proton and lepton abundances, while the latter produces an overall stiffening of the EOS. Each results in a supression of hyperons relative to the field-free case. The structure of a neutron star is, however, primarily determined by the magnetic field stress. We utilize existing general relativistic magneto-hydrostatic calculations to demonstrate that maximum average fields within a stable neutron are limited to values $B\le 1-3 \times10^{18}$ G. This is not large enough to significantly influence particle compositions or the matter pressure, unless fluctuations dominate the average field strengths in the interior or configurations with significantly larger field gradients are considered., 12 pages, 3 figures. To be submitted to Phys. Lett. B

The presence of quark matter in neutron star interiors may have distinctive signatures in basic observables such as (i) masses and radii [1], (ii) surface temperatures versus age [2], (iii) spin-down rates of milli-second pulsars [3], and (iv) neutrino luminosities from future galactic core collapse supernovae [4]. I highlight recent developments in some of these areas with a view towards assessing how theory may be confirmed by $\nu-$signals from future galactic supernovae in detectors like SuperK, SNO and others under consideration, including UNO [5], and by multi-wavelength photon observations with new generation satellites such as the HST, Chandra, and XMM., Comment: 4 pages, 2 figures. To appear in the proceedings of QM 2001. Uses fleqn.sty and espcrc1.sty

A first order phase transition at high baryon density implies that a mixed phase can occupy a significant region of the interior of a neutron star. In this article we investigate the effect of a droplet phase on neutrino transport inside the core. Two specific scenarios of the phase transition are examined, one having a kaon condensate and the other having quark matter in the high density phase. The coherent scattering of neutrinos off the droplets greatly increases the neutrino opacity of the mixed phase. We comment on how the existence of such a phase will affect a supernova neutrino signal., Comment: 7 pages, 4 figures

A protoneutron star is formed immediately after the gravitational collapse of the core of a massive star. At birth, the hot and high density matter in such a star contains a large number of neutrinos trapped during collapse. Trapped neutrinos generally inhibit the presence of exotic matter — hyperons, a kaon condensate, or quarks. However, as the neutrinos diffuse out in about 10–15 s, the threshold for the appearance of strangeness is reduced; hence, the composition and the structure of the star can change significantly. The effect of exotic, negatively-charged, strangeness-bearing components is always to soften the equation of state, and the possibility exists that the star collapses to a black hole at this time. This could explain why no neutron star has yet been seen in the remnant of supernova SN1987A, even though one certainly existed when neutrinos were detected on Feb. 23, 1987. With new generation neutrino detectors it is feasible to test different theoretical scenarios observationally.

Based on the Kaplan-Nelson Lagrangian, we investigate kaon condensation in dense neutron star matter allowing for the explicit presence of hyperons. Using various models we find that the condensate threshold is sensitive to the behavior of the scalar density; the more rapidly it increases with baryon density, the lower is the threshold for condensation. The presence of hyperons, particularly the $\Sigma^-$, shifts the threshold for $K^-$ condensation to a higher density. In the mean field approach, with hyperons, the condensate amplitude grows sufficiently rapidly that the nucleon effective mass vanishes at a finite density and a satisfactory treatment of the thermodynamics cannot be achieved. Thus, calculations of kaon-baryon interactions beyond the mean field level appear to be necessary., Comment: 13 pages, latex, 3 figures by fax/mail from ellis@physics.spa.umn.edu

The structure of newborn hot neutron stars is compared with that of cold catalyzed configurations. The role of the nuclear equation of state on the structural changes is investigated and some of the astrophysical consequences are briefly discussed.

The correlation between the compression modulus and the skewness coefficient of the nuclear matter ground state implied by the breathing mode data is compared with predictions of the relativistic Hartree approximation (RHA). Retaining explicit dependence on the renormalization scale μ, employed in the RHA, this correlation, together with other considerations, suggests a value for μ/M ⋍ 1.2 .

The space—time evolution of matter produced in high energy nuclear collisions is explored using a three dimensional hydrodynamic model. A significant coupling between longitudinal and transverse hydrodynamic flows is observed. This coupling of flows may be used to infer the degree of stopping in heavy ion experiments. These results are illustrated by qualitative fits to the CERN NA35 data for S+S collisions at 200 GeV nucleon .

The equilibration of hot hadronic matter is studied in the framework of relativistic kinetic theory. Various non-equilibrium properties of a mixture comprised of pions, kaons and nucleons are calculated in the dilute limit for small deviations from local thermal equilibrium. Interactions between these constituents are specified through the empirical phase shifts. The properties calculated include the relaxation/collision times, momentum and energy persistence ratios in elastic collisions, and transport properties such as the viscosity, the thermal conductivity, and the diffusion and thermal diffusion coefficients. The Chapman-Enskog formalism is extended to extract relaxation times associated with shear and heat flows, and drag and diffusion flows in a mixture. The equilibrium number concentration of the constituents is chosen to mimic those expected in the mid-rapidity interval of CERN and RHIC experiments. In this case, kaons and nucleons are found to equilibrate significantly more slowly than pions. These results shed new light on the influence of collective flow effects on the transverse momentum distributions of kaons and nucleons versus those of pions in ultra-relativistic nuclear collisions.

We study hadronic matter at temperatures close to the pion mass. In the dilute-gas stage, the relativistic virial expansion is used with empirical phase shifts to investigate the thermodynamic properties of an interacting gas of pions, kaons and nucleons. The interplay between the attractive and repulsive interactions which governs the size of the interacting contributions is discussed. In the dense gas stage characterized by the presence of many massive resonances, schematic models that include the effects of repulsive interactions are analysed. Limits on the size of repulsive interactions are established by causality constraints. The causal behaviour of some of the conventional excluded-volume approaches is examined. Since our work is also aimed at studying those equations of state which may be used in dynamical simulations of heavy-ion collisions, phase diagrams are constructed including the thermodynamics of the quark-gluon phase.

The correlation between the compression modulus and the skewness coefficient of the nuclear matter ground state implied by the breathing mode data is compared with predictions of the relativistic Hartree approximation (RHA). Retaining explicit dependence on the renormalization scale, μ, employed in the RHA, this correlation, together with other considerations, suggests a value for μ M ⋍ 1.2 .

We calculate the speed of sound in a pion gas including interactions between pions using the results of chiral perturbation theory as well as a relativistic virial expansion with experimental phase shifts. Our result is that the speed of sound is considerably less than that for the corresponding ideal, relativistic gas. The ramifications of this result in the description of heavy-ion collisions at ultrarelativistic energies are noted.

We calculate the maximum keplerian frequencies of stars containing strange matter that are in uniform rotation. We consider both self-bound stars and stars containing quark matter cores but normal surfaces. For both cases studied, use of perturbative QCD results for the equation of state of quark matter implies a limit on the maximum keplerian frequency of ∼1×104s−1.

We analyze the quark mass dependence of the chiral parameters calculated from an SU(2) Nambu-Jona-Lasinio model in the context of chiral perturbation theory. We find that in the mean-field approximation the model is unable to reproduce, within the experimental bounds, two parameters of the low-energy SU(2) effective lagrangian of Gasser and Leutwyler. Our results suggest that the model is not suited to give quantitative predictions concerning quark mass dependences. We also comment on the strange quark mass dependence of the chiral parameters in the SU(3) version of the model.

We first discuss calculations in the Nambu-Jona-Lasinio model which show that the mass of the σ-meson, mσ, decreases with increasing density at the same rate as nucleon effective mass m ∗ N , i.e. m ∗ σ (ρ)/m σ = m ∗ N /m N . We next discuss linear response theory in which Δ-particle, nucleon-hole insertions are put into pion lines; then masses of all the mesons seem to decrease with increasing density. To the extent that all of the masses scale in the same way, the common scale can be taken out of the hamiltonian, giving a new hamiltonian which involves only vacuum masses. The nucleon effective mass is calculated in the Dirac-Brueckner Hartree-Fock formalism, with inclusion of nucleon one-loop terms. The latter tend to keep m ∗ N /m N large , ∼0.9 . Finally, a full DBHF calculation is carried out, including the nucleon one-loop term and density dependent meson masses. With inclusion of the latter, conventional mechanisms in nuclear physics for saturation disappear and a density dependent two loop term ΔUσ(ρ) must be introduced. We motivate its introduction by empirical as well as formal arguments. In the discussion it is pointed out that the scaled meson masses can be considered, for a convenient density, as renormalization points.

We present results of microscopic calculations of the drift and diffusion coefficients in deep inelastic heavy ion collisions. Assuming the two nuclei to interact weakly, we make use of first-order perturbation theory (Golden Rule) for nucleon transfer and take into account the Pauli blocking effect. The nucleon transfer probability from one nucleus to the other is obtained using single particle wave functions. The results obtained are consistent with empirical estimates.

We extend the relativistic Brueckner-Hartree-Fock approach for nuclear matter to dense neutron matter. Special attention is devoted to contributions arising from tensor interactions due to the exchange of π-and ϱ-mesons and the dependence upon neutron-proton asymmetry. The role of the symmetry energy in studies of beta-stable neutron stars is also discussed.

An equation of state for cold nuclear matter for the region of densities ρnm−4ρnm, where ρnm is empirical nuclear-matter density, is constructed. We begin from the detailed calculation of Day and Wiringa for the two-body interactions; these give a saturation density of ∼2ρnm. This density is brought down to ρnm by the addition of relativistic corrections. Additional binding is obtained from three-body forces. A reasonable picture is obtained with the Day-Wiringa compression modulus for the two-body calculation, but the picture can be further improved by choosing this to be smaller. Our equation of state is similar to that of Friedman and Pandharipande in the region of nuclear matter denstiy ρnm, but, due to higher-order terms in the loop correction, is substantially softer at high density. Basically what happens is that the many-body effects saturate with increasing density, leaving only the two-body interactions. With this equation of state, prompt supernova explosions are very powerful when the compression modulus of neutron-rich matter (twice as many neutrons as protons) is ∼150 MeV, which corresponds to Knm ∼ 190 MeV for symmetric nuclear matter. Analysis shows that hot nuclear matter formed in heavy ion collisions demands a very stiff equation of state. We understand this as arising from the strong velocity dependence in the real part of the optical model potential which follows chiefly from the Lorentz character of the interactions, the vector mean field growing with increasing density and the scalar one decreasing. This gives a substantial repulsive contribution to the energy per particle and produces a stiff effective equation of state for several hundred MeV heavy-ion collisions. With increasing degree of equilibration the magnitude of the repulsive energy decreases since equilibration decreases the effective momentum. Given the strong velocity dependence in the interaction, the hot equation of state can be reconciled with the cool one.

The influence of momentum and frequency dependence of the nuclear mean field Σ on the level density parameter a is studied. By introducing a local quasiparticle effective mass we determine the volume, surface and curvature coefficients of a, expressed as a = a V A + a S A 2 3 + a c A 1 3 . It is found that the magnitude of ac is significant due to the very nature of the surface. A purely momentum dependent field Σ determined from the nonlocality of the optical potential gives a level density close to a self-consistent Thomas-Fermi description with Skyrme III forces. An explicit frequency dependence of Σ mainly influences as, enhancing it considerably for medium and heavy nuclei.

We derive analytic expressions for the Wigner transform (WT) of the one-body density matrix of a system of independent fermions in an N-dimensional harmonic oscillator (HO) potential. Considerable simplification is obtained for closed-shell configurations (all degenerate states occupied), when the Wigner transform (WT) depends only on the energy. Illustrative examples for one- and three-dimensional cases are discussed.

Using smoothed single-particle occupation numbers, the contribution of shell and surface effects to the static Wigner phase-space distribution function for non-interacting nucleons in an external, spherical, harmonic oscillator potential well is determined. The smoothing procedure illustrates clearly the strong quantum oscillations of the distributions function around the constant value for an infinite Fermi gas, and allows the separation of the contributions arising from shell effects connected with the structure of the single-particle level spectrum near the Fermi surface, and surface effects associated with single reflections of nucleons from the surface of the potential well. The temperature dependence of these effects in the distribution function is also investigated and a thermodynamical definition of the shell contribution to the kinetic energy density is suggested.

A simple model which includes the effects of primary degradation is shown to be able to reproduce FERMILAB data for transverse energy production in pA collisions of 800 GeV protons on all targets from protons to 208 Pb.

We examine the application of transition-state theory for fission-fragment angular distributions to composite nuclei near the limits of stability. The possible roles of saddle-point and scission-point configurations are explored. For many heavy-ion reactions that involve large angular momenta, the observed anisotropies are between the predictions of the saddle-point and scisson--point models. Empirical correlations are shown between the effective moments of inertia and the spin and Z 2 A of the compound nucleus. These correlations provide evidence for a class of transition-state nuclei intermediate between saddle- and scission-point configurations. An important indication of these patterns is that the speed of collective deformation toward fission may well be slow enough to allow for statistical equilibrium in the tilting mode even for configurations well beyond the saddle point.

Charmonium bound states immersed in a coherent chromo-electric field are easily ripped apart for field strengths comparable to the QCD string tension. Estimates based on flux tube models suggest that field strengths of such magnitude may be achieved in heavy-ion collisions at ultrarelativistic energies. Our results suggest that charmonium suppression would not discriminate between a coherent and a thermalized post collision state in relativistic heavy-ion collisions.

We study the flow of matter, momentum and energy in low energy heavy-ion collisions. This is done by using the Wigner phase space distribution function to calculate quantum mechanical analogs of the classical distributions of the observables. We apply the Wigner transformation to time dependent Hartree-Fock calculations of 16O + 16O and 40Ca + 40Ca reactions. Both static and dynamic features of the distribution functions are demonstrated.

A number of difficult problems are encountered in attempts to incorporate the strange quark into hadronic structure by generalizing from two to three flavors because the mass of the strange quark m s ≈ 175 MeV ≈ Λ QCD . This mass is neither small nor large. A question of particular interest is as to the ss content of the nucleon. If it is large, it is likely that strangeness condensation will occur at densities ϱ ≈ 3 ϱ o , where ρ o is nuclear matter density. In order to gain insight into the mechanism for strangeness condensation, s-wave neutral pion condensation is first investigated. Then the analogous problem of strangeness condensation, once the SU(3) × SU(3) problem is reduced to an SU(2) × SU(2) one by using V spin, can be simply investigated. The role of the strange quark mass in quark condensates is investigated, employing the Nambu-Jona-Lasinio formalism. In the large N c limit, the quark flavors decouple, but in order 1/N c are strongly mixed by the determinantal interaction between quarks which arises once instantons are integrated out. This suggests a possible mechanism for the strange quark mass to affect the nucleon energy and for the ss content of the nucleon to be large.

By calculating the inclusive cross sections for Δ -hole and nucleon -hole excitations in peripheral nucleus-nucleus collisions, pion production cross sections are estimated. An intermediate energies, this collective mechanism may be verified by coincidence measurements.

Charmonium bound states immersed in a coherent chromo-electric field are easily ripped apart for field strengths comparable to the QCD string tension. Estimates based on flux tube models suggest that field strengths of such magnitude may be achieved in heavy-ion collisions at ultrarelativistic energies. Our results suggest, that charmonium suppression would not discriminate between a coherent and a thermalized post collision state in rela.tivistic heavy-ion collisions.

The stress-energy tensor and entropy are calculated for non-interacting quarks and gluons confined to a slab of thickness L at finite temperature T . Slab propagators for quarks and gluons are constructed. For T = 200 MeV corrections to the Stefan-Boltzmann results are less than 10% if L ⩾ 1.5 fm. If L is less than this, corrections become substantial, for example, pressures exhibit marked directional asymmetries. Implications for the calculation of the evolution of quark-gluon plasmas expected in heavy-ion collisions are discussed.

It is found that for level schemes obtained from a folded Yukawa potential, the Strutinsky smearing procedure for the evaluation of the shell correction to the total potential energy of nuclei does not lead to a unique value for nuclear shapes near and beyond the outer fission barrier deformations and consequently introduces uncertainties in the relative fission barrier heights.