Nuclear interactions with modern three-body forces lead to the instability of neutron matter and neutron stars

TL;DR

The paper demonstrates that modern three-body nuclear forces cause neutron matter and neutron stars to become unstable and collapse, unlike older force models which prevent this issue.

Contribution

It provides a mathematical proof that certain modern three-body forces lead to neutron matter instability and suggests modifications to prevent collapse.

Findings

Modern three-body forces cause neutron matter to be unstable.

The energy of neutron systems diverges rapidly with particle number.

Adding a strong repulsive term can prevent neutron matter collapse.

Abstract

It is shown that the neutron matter interacting through Argonne V18 pair-potential plus modern variants of Urbana or Illinois three-body forces is unstable. For the energy of $N$ neutrons $E(N)$, which interact through these forces, we prove mathematically that $E(N) = -cN^3 + \mathcal{O}(N^{8/3})$, where $c>0$ is a constant. This means that: (i) the energy per particle and neutron density diverge rapidly for large neutron numbers; (ii) bound states of $N$ neutrons exist for $N$ large enough. The neutron matter collapse is possible due to the form of the repulsive core in three-body forces, which vanishes when three nucleons occupy the same site in space. The old variant of the forces Urbana VI, where the phenomenological repulsive core does not vanish at the origin, resolves this problem. We prove that to prevent the collapse one should add a repulsive term to the Urbana IX potential, which should be larger than 50 MeV when 3 nucleons occupy the same spatial position.