Dmitry K. Gridnev, Stefan Schramm, Walter Greiner, Konstantin Gridnev
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. The obtained results partly change the paradigm, in which the stability of neutron stars is attained through the Pauli principle; the strong repulsive core in the nucleon interactions is by no means less important.
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http://arxiv.org/abs/1306.5573
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