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

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

Selecting fast folding proteins by their rate of convergence

We propose a general method for predicting potentially good folders from a given number of amino acid sequences. Our approach is based on the calculation of the rate of convergence of each amino acid chain towards the native structure using only the very initial parts of the dynamical trajectories. It does not require any preliminary knowledge of the native state and can be applied to different kinds of models, including atomistic descriptions. We tested the method within both the lattice and off-lattice model frameworks and obtained several so far unknown good folders. The unbiased algorithm also allows to determine the optimal folding temperature and takes at least 3--4 orders of magnitude less time steps than those needed to compute folding times

Universal Angular Probability Distribution of Three Particles near Zero Energy Threshold

We study bound states of a 3--particle system in $\mathbb{R}^3$ described by the Hamiltonian $H(\lambda_n) = H_0 + v_{12} + \lambda_n (v_{13} + v_{23})$, where the particle pair $\{1,2\}$ has a zero energy resonance and no bound states, while other particle pairs have neither bound states nor zero energy resonances. It is assumed that for a converging sequence of coupling constants $\lambda_n \to \lambda_{cr}$ the Hamiltonian $H(\lambda_n)$ has a sequence of levels with negative energies $E_n$ and wave functions $\psi_n$, where the sequence $\psi_n$ totally spreads in the sense that $\lim_{n \to \infty}\int_{|\zeta| \leq R} |\psi_n (\zeta)|^2 d\zeta = 0$ for all $R>0$. We prove that for large $n$ the angular probability distribution of three particles determined by $\psi_n$ approaches the universal analytical expression, which does not depend on pair--interactions. The result has applications in Efimov physics and in the physics of halo nuclei