Highly accurate measurement of symmetry energy in nickel isotopes advances nuclear models
In two studies published in the journals Physics Letters B and Physical Review C, the international INDRA-FAZIA collaboration announces that it has established new constraints on a property known as “symmetry energy,” which is related to the weakening of the binding energy of nuclei with an excessive imbalance between their number of neutrons and protons. By measuring with unprecedented precision the nucleon transfers that occur during collisions between nickel isotopes at GANIL, the collaboration has succeeded in refining models describing the behavior of nuclear matter under extreme conditions, models that will one day lead to a better understanding of certain violent astrophysical phenomena.
Understanding how nuclear matter behaves when pushed to extreme densities or temperatures is one of the great challenges facing physics today. Atomic nuclei are complex quantum systems composed of protons and neutrons. At extremely high densities or temperatures, such as in neutron stars or during stellar explosions, the dynamics of their constituents become even more complicated and differ from those characteristic of more ordinary conditions. To better understand these little-known dynamics, experiments are being conducted at GANIL using heavy ion collisions to generate, for very short periods of time, droplets of nuclear matter with properties similar to those found, for example, inside a neutron star or during the merger of two neutron stars.
A recent experiment conducted using the INDRA-FAZIA particle detector duo has shed new light on the mechanisms at work: the international team of scientists has succeeded in better constraining the way in which the energy linked to the imbalance between protons and neutrons in the nucleus, known as symmetry energy, varies according to the density of nucleons.
Nuclear matter is more stable when the number of protons and neutrons is the same (symmetrical matter). However, moving away from this balance between protons and neutrons incurs an energy cost that corresponds to the symmetry energy. Indeed, within the framework of the equation of state of nuclear matter and within the limits of a parabolic approximation of the binding energy with neutron-proton asymmetry, the symmetry energy can be defined as the difference in energy between symmetric matter and purely neutron matter. Characterizing this energy is crucial in the study of neutron stars, which, as their name suggests, have a striking imbalance between very numerous neutrons and rare protons. In order to accurately predict the structure of neutron stars and interpret their properties and the signals emitted during the merger of two such stars, it is therefore necessary to know precisely how this symmetry energy evolves as a function of the density of nuclear matter. Even today, many uncertainties remain. Nuclear physics experiments capable of probing this term at densities close to those of astrophysical interest remain limited, while astrophysical observations provide global constraints that are difficult to relate directly to the different properties of nuclear matter and nuclei and to use to constrain nuclear interaction. It is in this context that the experiment conducted in 2019 with GANIL's INDRA-FAZIA detectors represents a major breakthrough.
To constrain the evolution of symmetry energy, scientists chose to study collisions between two stable nickel isotopes: 58Ni, the most common nickel isotope with almost the same number of protons and neutrons, and 64Ni, which is much rarer and rich in neutrons. By colliding these nuclei in two inverted configurations (58Ni+64Ni and 64Ni+58Ni) and then comparing the emitted fragments, it becomes possible to measure a factor known as "isospin scattering," which describes how neutrons and protons move from one nucleus to another during the collision in order to rebalance the initial asymmetry. It is from the measurement of isospin scattering that scientists are able to deduce the density dependence of symmetry energy.
The INDRA-FAZIA detector duo is ideal for this task. INDRA, designed in the 1990s, offers exceptional angular coverage, enabling it to detect almost all of the particles emitted. FAZIA, in operation since 2015, provides unmatched isotopic resolution: its telescope structure, stacking several layers of detectors, allows the precise identification of the mass and charge of heavy fragments and thus their proton and neutron content. Combining data from the two detectors allows for a complete and reliable reconstruction of events.
Thanks to this precision, researchers were able to directly measure the neutron-proton ratio resulting from each asymmetric reaction in the quasi-projectiles, the heavy fragments of nuclear matter produced by the collision. At the same time, the information provided by INDRA on the multiplicity of light particles enabled an experimental estimate of the impact parameter—i.e., the degree of centrality of the collision—an essential step in comparing the data with theoretical models.
The result is unambiguous: the more head-on the particles collide, the more similar the quasi-projectiles from the two asymmetric reactions become, indicating a gradual rebalancing of the number of protons and neutrons in the fragments. This measurement is the most accurate ever obtained for this phenomenon.
Such precision paves the way for a detailed comparison with theoretical models describing the evolution of the system during the collision. Theorists from LPC Caen and VECC (India) used a theoretical model called BUU@VECC-McGill, which simulates the dynamics of hundreds of nucleons subjected to microscopic interactions, incorporating different assumptions for the symmetry energy. By comparing the data from the experiment conducted at GANIL with their model, the scientists were able to favor the hypothesis that predicts a moderate increase in symmetry energy with nuclear matter density. In other words, at higher densities, having many more neutrons than protons in nuclear matter becomes energetically more costly, as expected, but this increase is gradual and reasonable, neither too weak nor as violent as some alternative models predicted.
By tightening the constraints on symmetry energy, the INDRA-FAZIA experiment provides crucial information for dense matter models used in astrophysics. These results can be directly integrated into advanced statistical analyses combining laboratory data and gravitational wave observations—an approach that has become increasingly widespread since the first detection of a neutron star merger in 2017. This provides a means of interpreting gravitational wave data more accurately in order to understand the mechanisms at work in neutron stars.