We will hold an International Collaborations in Nuclear Theory program at FRIB in East Lansing, Mich. from July 15 to Aug. 9, 2013 -- focusing on the symmetry energy at a variety of densities, accessed through heavy ion collisions, other nuclear experiments, and through astrophysical observations. The program will critically examine past and future experiments and their theoretical interpretations aiming at determination of the symmetry energy. In addition, we will discuss implications of the symmetry energy for astrophysics and for dense QCD.
The symmetry energy describes how the energy of symmetric matter rises as one moves away from equal numbers of neutrons and protons. It is crucially important in astrophysics to enable extrapolating known nuclear information to very neutron rich systems present in supernovae and neutron stars. At low densities, i.e. nuclear density and below, we presently have a number of heavy ion collision and nuclear structure observables that constrain the symmetry energy. At high densities, above nuclear density, we have much less information on the symmetry energy, but a number of heavy ion experiments are planned for the near future.
The first week of the program (July 15-19) will focus on the symmetry energy at subnuclear densities and related nuclear structure. Astrophysical topics include the neutrino sphere region in core collapse supernovae and the formation of nuclear pasta. NuSYM13, the third International Symposium on Symmetry Energy will be held during the second week (July 22-26) of the program. The symposium will cover topics on the symmetry energy at both low and high densities as well as its applications in astrophysics. The third week (July 29-Aug. 2) will focus on the symmetry energy at high densities. Astrophysical topics will include neutron star masses and radii and neutron star cooling. Finally the fourth week of the program (Aug. 5-9) will map out plans for future theoretical and experimental work on the symmetry energy. These plans, along with the present status of the field, will be written up in a final report.
This program is timely due to the availability of exotic heavy ion beams at energies above 200 MeV per nucleon to study the symmetry energy at high density. Participants are encouraged to come for as long as possible including the second-week workshop. While the focus of the first week is low densities and nuclear structure, and the third week is high densities, participants will be welcome to join the program at any time, or to come just for the workshop.
Symmetry energy at low density and related nuclear structure
There are a variety of heavy ion and nuclear structure observables that constrain the symmetry energy at nuclear density and below.
Symmetry energy at very low density
At very low densities nucleons can cluster into alpha particles and other light nuclei. This leads to rich nuclear dynamics that makes the symmetry energy dependent on matter constitution and not just average density, with different results emerging for a fully clustered matter and in simple mean-field models. A warm gas of low density nucleons and light nuclei can be produced in heavy ion collisions and a variety of observables such as fragment yields have been measured.
In astrophysics, the symmetry energy at very low densities is important for core collapse supernova simulations. Here, the core of a massive star collapses to form a proto-neutron star. This hot, lepton-rich, neutron star radiates tremendous numbers of neutrinos that are thought to reenergize a shock and eject the outer 90% of the star causing a great explosion. Much of the action in a supernova takes place near the neutrinosphere, the surface of last scattering. The neutrinosphere, where neutrino mean free paths become comparable to the system size, represents very low nucleon densities of 10-4 to 10-3 fm-3 and warm temperatures near 5 MeV. The symmetry energy near the neutrinoshere impacts a number of neutrino interactions important for the observable neutrino spectrum of a galactic supernova and for nucleosynthesis in the neutrino driven wind above the proto-neutron star.
Warm nuclear matter at very low densities can be described with a virial expansion that relates thermodynamic properties to known nucleon-nucleon, nucleon-nucleus, and nucleus-nucleus phase shifts. This provides a model independent benchmark that should be reproduced by theoretical models applicable at higher densities. Effective theories are by construction anchored at low densities and progressively enter more treacherous domains as the density increases.
Symmetry energy at just below nuclear density
Recently, substantial progress in our understanding of the symmetry energy has been made both experimentally and theoretically, in particular at nuclear (saturation) ρ0 and just below nuclear densities. Initial constrains on the symmetry energy have been obtained from a variety of reaction observables, from neutron-to-proton yield ratios and isospin diffusions in heavy ion collisions (HIC), and structure measurements, such as the neutron skin deduced from either parity violating electron scattering or the dipole polarizability. In addition the symmetry energy has been inferred from the Pygmy Dipole Resonance, masses of Isobaric Analog States, and nuclear masses in the Finite Range Droplet Model. To cross-compare results relying on such a wide variety of experiments, 2-D constraints formed from the symmetry energy, S0, and its slope, L, at saturation density, ρ0, have been deduced. The results are consistent within experimental and theoretical uncertainties and provide a constraint centered around (S0, L) ≈ (32.5 ± 1.5 MeV, 70 ± 35 MeV). Tighter constraints can be obtained from improved experiments or from improved theoretical models. Effective chiral theory has made impressive progress calculating the symmetry energy from soft elementary interactions. One of the goals in the first week of the program is to focus on improving the constraints on S0 and L. In addition, the program will discuss the impact of the symmetry energy, near nuclear density, on a variety of neutron star crust properties such as the crust core transition density and the extent of nuclear pasta phases.
Symmetry energy at high density
Heavy-ion (HI) collisions, with both stable and radioactive beams, offer a unique opportunity to study high baryon density neutron rich matter in the laboratory. This motivates a variety of new accelerators and detectors, throughout the world, that will soon provide data of unprecedented quality. These projects include the Active Target-Time Projection Chamber (AT-TPC) at the Facility for Rare Isotope Beams (FRIB), the SAMURAI-TPC detector at the Radioactive Ion Beam Facility (RIBF) in Japan, Nuclotron-based Ion Collider fAcility (NICA) at Dubna in Russia, the Cooler Storage Ring (CSR) in China, the compressed baryon matter (CBM) experiment at the Facility for Antiproton and Ion Research (FAIR) in Germany, and many others. As we learned from experiments at sub-nuclear density, HI collisions are complex. In order to exploit the potential of these facilities, there is a critical need to carefully choose experimental observables and to develop refined theoretical formalisms and interpretations.
Many of these facilities are under construction and will soon take data. For example the first SAMURAI-TPC experiment is expected in 2014. The program should help optimize the experimental conditions and choice of observables along with their theoretical interpretations in order to provide the most reliable and model independent information on the symmetry energy.
In the meantime, pertinent important developments have been taking place on the astrophysical side. Recently a 1.97±0.04 solar-mass neutron-star was discovered. Another 2-solar-mass neutron-star observation is on the eve of being declared. These immediately imply that the equation of state of dense matter is stiff enough (with high enough pressure) to support a 2-solar mass neutron star against collapse to a black hole. However the observation does not directly tell us the composition of dense matter, be it of neutrons and protons, hyperons, or quarks, that depends on the symmetry energy and on other aspects of the equation of state, and that may be reflected in star cooling. The program will critically examine combining of laboratory observations pertaining to the equation of state, emphasizing symmetry energy, together with astronomical observations of neutron star cooling, in order to determine the dense matter composition in QCD. In addition, the frequency and damping of gravitational waves emitted by neutron stars can depend on the symmetry energy.
Neutron stars cool by neutrino emission from their dense interiors. Beta decays of a number of different hadrons can rapidly cool a star. The beta decay of neutrons, called the direct URCA process, is typically forbidden by energy and momentum conservation unless there is a large proton fraction stemming from a large symmetry energy. If astrophysicists establish that some neutron stars cool quickly, and nuclear physicists can rule out (or in!) the direct URCA process by determining the high-density symmetry energy, then one can demonstrate that the dense QCD matter contains additional hadrons. The program will explore both sides of this problem and see how close we are to proving that dense matter contains more than just neutrons and protons.
While quite a number of observables have been proposed (see above) and exploited to test the symmetry energy at sub-nuclear densities in HI collisions, those to test the energy at supra-nuclear densities still remain relatively few. One of those has been the ratio of subthreshold negative-to-positive pion yields that was a motivating factor in proposing to construct the AT-TPC and SAMURAI-TPC detectors. Differential flow of mirror fragments can give information on high density matter. Finally, the ratio of kaon K0/K+ yields can play a similar role to the pion ratio. The program will stimulate proposals of refinements and new observables for the high-density symmetry energy.
In a broader perspective, comprehending the symmetry energy at high densities is a part of the wider efforts to map out the nuclear matter equation of state (EOS) in various regions of control parameters including temperature, baryonic density, as well as the isospin density. Tying results from HI collisions at lower energies to the very high energy results from the Relativistic Heavy Ion Collider (RHIC) represents a particularly important avenue for laying out the dependence of the EOS on these parameters, particularly on baryonic and isospin densities. The EOS dependence on baryonic density has recently been intensively investigated (mainly through higher-order fluctuation measurements) within the Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC) with the lowest center-of-mass energy of about 7GeV.
Similarly, the isospin dependence of the EOS can be explored for a range of RHIC energies. This is a new and very interesting territory to the BES program, and shall supplement other even lower energy facilities (e.g. FAIR in Germany and Cooler Storage Ring (CSR) in China) to map out a full picture of the EOS dependence on isospin at various temperature and density regimes. Even though the nuclear matter created in collisions at those energies may not be directly linked to the astrophysical dense matter, such important experimental input will be an essential lever arm for testing our understanding of the EOS and for constraining various microscopic models applied to the very high density regime. We feel it is valuable to involve the RHIC BES community into this program.
In addition, there are growing interests and efforts from the lattice QCD community in studying dense nuclear matter and the related symmetry energy (and EOS in general), from first principles. While this is currently not mature enough to make fully quantitative predictions, with ever-growing computational power this is certainly an important direction for the future. We also hope to involve and encourage further lattice QCD studies at this program.