By analyzing collisions between several combinations of tin nuclei, researchers at the Michigan State University National Superconducting Cyclotron Laboratory (NSCL) have refined understanding of the symmetry energy. Their work marks the first successful theoretical explanation of the common symmetry energy-related observables – including isospin diffusion and differences in neutron and proton emitted spectra – in heavy-ion experiments. The result should help in discerning the properties of neutron stars, particularly in the crust region.

On the average, the nuclear attraction between a neutron and a proton is stronger than that between two protons or two neutrons. The nuclear contribution to the difference between the binding energy of a system of all neutrons and another with equal numbers of protons and neutrons is known as the symmetry energy. Nuclear mass formulae include a symmetry energy term. This term often takes a form that assumes the symmetry energy to be independent of density, even though its value inside the nucleus, at normal density, should exceed its value at the surface, where the density is lower and the ratio of proton to neutron densities differs from that for the nuclear interior.

The symmetry energy of a stable nucleus reflects typical nuclear densities of about 2-3x10^{14} g/cm^{3}, contributes modestly to the binding energy and influences significantly the stability of nuclei against beta decay. Despite the sensitivity of nuclear masses to its average value, the precise understanding of its dependence on density has proved elusive, leading to large uncertainties in the theoretical predictions for properties of very neutron-rich nuclei, such as their masses or neutron skin thicknesses. The effects of the symmetry energy loom even larger in environments with unusual ratios of protons to neutrons and much larger ranges of density, such as in neutron stars. There, the dependence of the symmetry energy upon density is one of the most uncertain parts of the mathematical palette describing forces at play in such stars. Absent access to this palette, physicists' equations can only paint the broadest outlines of these enigmatic stellar environments.

Now, Betty Tsang, Bill Lynch, Pawel Danielewicz and colleagues have helped to constrain understanding of density dependency of symmetry energy by studying how it affects heavy-ion reactions studied at NSCL’s Coupled Cyclotron Facility (Tsang et al. 2009). In two experiments, the researchers collided various beams of tin nuclei with a stationary tin targets. The four combinations included a tin-124 beam on a tin-124 target, tin-112 on tin-112, tin-124 on tin-112, and tin-112 on tin-124. Use of heavy ions with different neutron to proton ratios– the NSCL facility can accelerate protons through uranium isotopes– allowed the research team to create and study nuclear matter with different neutron to proton ratios at a range of densities that can be varied by adjusting the energy of the beam and the centrality of the collisions.

* Mike Famiano, assistant professor at Western Michigan University and NSCL user, discusses the result in a six-minute Q-and-A.*

Data on several observables were collected. One observable, termed isospin diffusion, probed the neutron over proton ratio of neutron-rich projectile nuclei after collisions with neutron-deficient target nuclei. During grazing collisions at relative velocities of one-third the speed of light, a neck region with reduced density can formed between projectile and target nuclei through which these nucleons diffuse. The stronger the symmetry energy is in this neck region, the more likely the neutron to proton ratios in the projectile and target nuclei will equilibrate and become equal. A second observable involved comparisons of neutron and proton energy spectra in central head-on collisions. In this case the symmetry energy expelled neutrons from the central overlap region of the projectile and target nuclei; the ratio of neutron over proton emission provides a probe of the variation in the symmetry energy as the system compresses and expands during the collision.

By comparing the experimental data to results obtained with theoretical models the researchers obtained an allowed region of symmetry energy and density from normal down to a third of the nuclear matter density. The result will help to describe the inner crust of neutron stars where the density of nuclear matter ranges from 1 x10^{14} to 2x10^{14} g/cm^{3}. The role of the symmetry energy at the cores of such stars, where the density of nuclear matter reaches 8x10^{14} g/cm^{3}, is associated with the largest uncertainty. As high density regions are formed, albeit fleetingly, in head-on heavy ion collisions, the results suggest that symmetry energy can be studied in at higher energy in new and planned accelerator facilities in Japan (RIKEN), Germany (FAIR) and the United States (FRIB).

**Further reading**

M.B. Tsang et al. 2009 *Phys. Rev. Lett.* 102 122701