Abstract
We consider the evolution of the neutron-nucleus scattering length for the lightest nuclei. We show that, when increasing the number of neutrons in the target nucleus, the strong Pauli repulsion is weakened and the balance with the attractive nucleon-nucleon interaction results into a resonant virtual state in ^{18}18B. We describe ^{19}19B in terms of a ^{17}17B-nn-nn three-body system where the two-body subsystems ^{17}17B-nn and nn-nn are unbound (virtual) states close to the unitary limit. The energy of ^{19}19B ground state is well reproduced and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be extended to describe the recently discovered resonant states in ^{20,21}20,21B.
Highlights
One of the most interesting things one can study in experimental and theoretical nuclear physics is the very low energy (S-wave) scattering of neutrons (n) on a nuclear target (A)
We would like to emphasize that due to our ignorance of the aS value we cannot predict a precise value for E(19B), but it is worth noticing that in all the domain of aS that we have considered, including the full unitary limit, the results provided by this simple model are compatible with the experimental value E=-0.14 ± 0.39 MeV
In our previous work [29] we have introduced a spin-dependent interaction and find the robustness of the 17B-n-n model in what concerns the predictions of the 19B bound state: the 17B-n-n ground state remains bound unless we introduce a spin-spin dependence at the level of Vn17B one order of magnitude greater than the one displayed in figure 2
Summary
One of the most interesting things one can study in experimental and theoretical nuclear physics is the very low energy (S-wave) scattering of neutrons (n) on a nuclear target (A). The Pauli principle – imposing an antisymmetric wave function – acts as if there was a repulsive interaction among n’s This has dramatic consequences in the 3n and 4n systems: the 3n Hamiltonian, has a ground state bound by ≈ 1 MeV but this state is symmetric in particle exchange and not realised in Nature. When arriving at the 17B, a particle stable nuclei with ground state Jπ=3/2−, the balance between the attraction and repulsion is so fine-tuned that the scattering length become huge, indicating the presence of 17B virtual state extremely close to the n-17B threshold. The main results, published in [29], are summarized
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