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One way to simulate infinite neutron matter is to put a number of neutrons in a box, surround that box with identical boxes, then sum up the forces among all the particles.
One way to simulate infinite neutron matter is to put a number of neutrons in a box, surround that box with identical boxes, then sum up the forces among all the particles.
Image courtesy of Alessandro Lovato

The Science

The matter inside a neutron star consists mostly of neutrons, with a few protons, electrons, and other sub-atomic particles. This matter is so dense that an entire neutron star, with a mass greater than the Sun, would fit inside a city the size of Chicago. To predict the properties of this matter, nuclear physicists consider a theoretical model. This model consists of an infinite system of pure neutrons that interact by the strong, short-range nuclear force. The strong nuclear force is one of the four basic forces in the universe, along with gravity, electromagnetism, and the weak nuclear force. Using sophisticated numerical techniques and supercomputers, scientists calculate the neutron matter equation of state that tells how much weight the star can support before gravity crushes it into a black hole.

The Impact

An equation of state is an equation that describes the state of matter under a set of physical conditions, such as pressure, volume, temperature, or internal energy. In this new research, scientists studied the equation of state of neutron matter using a series of computer-intensive calculations. The strong, short-range force between two neutrons is very complicated and is known only approximately. The numerical techniques for calculating neutron-matter with such forces are also complicated. The scientists used a combination of five different forces and three independent methods to help pin down how well we understand the matter that neutron stars are made of. This, in turn, tells us how large neutron stars can grow and influences what heavy elements are made through nucleosynthesis when two neutron stars merge.


Nuclear theorists made benchmark calculations of the energy per particle of pure neutron matter as a function of the neutron density. The calculations were made for two distinct families of realistic coordinate-space nucleon-nucleon potentials. These force models were all constructed to reproduce nucleon-nucleon scattering data from laboratory experiments. The researchers implemented important technical improvements in a couple of the methods for the first time. They observed good agreement among the five force models and three many-body techniques up to the saturation density typical of the centers of large atomic nuclei. At higher densities, the results diverge gradually as a function of both the force models and the many-body methods. The range of results helps set the limit on how well we can predict the neutron matter equation of state which, in turn, tells us the maximum mass a neutron star can have before it collapses into a black hole.  It also influences the gravitational wave signal generated when two neutron stars merge as well as the amount of heavy elements produced in such a merger.


Alessandro Lovato
Physics Division, Argonne National Laboratory

Robert Wiringa
Physics Division, Argonne National Laboratory  


This research is supported by the Department of Energy Office of Science, Office of Nuclear Physics, including an FRIB Theory Alliance Award as well as the NUCLEI SciDAC program. Computer time at the Argonne Leadership Computing Facility was provided by the INCITE program; computer time was also provided by the Argonne Laboratory Computing Resource Center and by a CINECA-INFN agreement, giving access to resources on MARCONI at CINECA.


Piarulli, M., et al., “Benchmark calculations of pure neutron matter with realistic nucleon-nucleon interactions,”Physical. Review C 101, 045801 (2020) [DOI:10.1103/PhysRevC.101.045801]