Constraining the symmetry energy in the nuclear equation of state

The nuclear equation of state is a thermodynamic description of the average behavior of a large volume of nuclear matter in exact analogy to the equation of state of a gas or any other phase of matter. The nuclear symmetry energy is a component of the nuclear equation of state that describes the variation of the nuclear binding energy as a function of proton (Z) and neutron (N) numbers. While the range of neutron-to-proton number is relatively small in nuclei, neutron stars are thought to be close to pure neutron matter. In this case the nature and stability of phases within the star, the composition and the thickness of its inner crust, the frequencies of vibrations of the crust and its radius, among other properties, depend strongly on the symmetry energy and its density dependence.


Representation of theconstraints on the symmetry energy for pressure in neutron matter as a functionof the symmetry energy in neutron matter. Open rectangles were obtained from the properties of individual nucleiand the hatched area from recent analyses of nuclear collisions.


Attempts have been made in the past to extract the symmetry energy from the properties of individual nuclei. For example, the open region in the accompanying figure labeled “IAS” indicates the constraints from analyses of corresponding states in nuclei with a constant mass (so-called isobaric analog states, IAS). The region labeled “PDR” results from analyses of a special vibrational mode in neutron-rich nuclei called the pygmy dipole resonance. However, there is some disagreement between the results. Scientists at the National Superconducting Cyclotron Laboratory (NSCL) on the campus of Michigan State University have recently developed a consistent theoretical interpretation of a range of data from violent collisions between tin nuclei previously measured at the NSCL. The crosshatched region of the graph shows the allowed region of pressure for pure neutron matter that they extracted as a function of the symmetry energy at saturation. Interestingly, the new constraints lie in-between and span the earlier work with individual nuclei. Some shifts in the boundaries of the constrained region can be expected with improvements in the precision of the experimental data and with the evolution of the theory. Nevertheless, the consistency among the different probes of the symmetry energy and the possibility of probing higher densities with nucleus-nucleus collisions suggests that the symmetry energy will soon be well defined.