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Register a new userModeling $^{19}$B as a $^{17}$B-n-n three-body system in the unitary limit
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We present a model description of the bound $^{17}$B isotope in terms of a $^{17}$B-n-n three-body system where the two-body subsystems $^{17}$B-n and n-n are unbound (virtual) states close to the unitary limit. The $^{17}$B ground state is well described in terms of two-body potentials only, and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be naturally used to describe the recently discovered resonant states in $^{20,21}$B.
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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 $^{18}$B. We describe $^{19}$B in terms of a $^{17}$B-$n$-$n$ three-body system where the two-body subsystems $^{17}$B-$n$ and $n$-$n$ are unbound (virtual) states close to the unitary limit. The energy of $^{19}$B 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 $^{20,21}$B.
For $N=Z$ odd-odd nuclei, a three-body model assuming two valence particles and an inert core can provide an understanding of pairing correlations in the ground state and spin-isospin excitations. However, since residual core-nucleon interactions can have a significant impact on these quantities, the inclusion of core excitations in the model is essential for useful calculation to be performed. The effect of core excitations must be included in order to gain a detailed understanding of both the ground state and spin-isospin properties of these systems. To this end, we include the vibrational excitation of the core nucleus in our model. We solve the three-body core-nucleon-nucleon problem including core vibrational states to obtain the nuclear ground state as well as spin-isospin excitations. The spin-isospin excitations are examined from the point of view of SU(4) multiplets. By including the effect of core excitation, several experimental quantities of $N=Z$ odd-odd nuclei are better described, and the root mean square distances between proton and neutron and that between the center of mass of proton and neutron and core nucleus increase. Large $B$($M1$) and $B$(GT) observed for $^{18}$F and $^{40}$Ca were explained in terms of the SU(4) symmetry. The core nucleus is meaningfully broken by the residual core-nucleon interactions, and various quantities concerning spin-isospin excitations as well as the ground state become consistent with experimental data. Including the core excitation in the three-body model is thus important for a more detailed understanding of nuclear structure.
We discuss the binding mechanism of 11Li based on an extended three-body model of Li+n+n. In the model, we take into account the pairing correlation of p-shell neutrons in 9Li, in addition to that of valence neutrons outside the 9Li nucleus, and solve the coupled-channel two- and three-body problems of 10Li and 11Li, respectively. The results show that degrees of freedom of the pairing correlation in 9Li play an important role in the structure of 10Li and 11Li. In 10Li, the pairing correlation in 9Li produces a so-called pairing-blocking effect due to the presence of valence neutron, which degenerates s- and p-wave neutron orbits energetically. In 11Li, on the other hand, the pairing-blocking effect is surpassed by the core-n interaction due to two degrees of freedom of two valence neutrons surrounding 9Li, and as a result, the ground state is dominated by the p-shell closed configuration and does not show a spatial extension with a large r.m.s. radius. These results indicate that the pairing correlation is realized differently in odd- and even-neutron systems of 10Li and 11Li. We further improve the tail part of the 9Li-n interaction, which works well to reproduce the observed large r.m.s. radius in 11Li.
We consider a model of relativistic three-body scattering with a bound state in the two-body sub-channel. We show that the naive K-matrix type parametrization, here referred to as the B-matrix, has nonphysical singularities near the physical region. We show how to eliminate such singularities by using dispersion relations and also show how to reproduce unitarity relations by taking into account all relevant open channels.
We investigate the three-body Coulomb breakup of a two-neutron halo nucleus $^{11}$Li. We use the coupled-channel $^9$Li + $n$ + $n$ three-body model, which includes the coupling between last neutron states and the various $2p$-$2h$ configurations in $^9$Li due to the tensor and pairing correlations. The three-body scattering states of $^{11}$Li are described by using the combined methods of the complex scaling and the Lippmann-Schwinger equation. The calculated breakup cross section successfully reproduces the experiments. The large mixing of the s-state in the halo ground state of $^{11}$Li is shown to play an important role in explanation of shape and strength of the breakup cross section. In addition, we predict the invariant mass spectra for binary subsystems of $^{11}$Li. It is found that the two kinds of virtual s-states of $^9$Li-$n$ and $n$-$n$ systems in the final three-body states of $^{11}$Li largely contribute to make low-lying peaks in the invariant mass spectra. On the other hand, in the present analysis, it is suggested that the contributions of the p-wave resonances of $^{10}$Li is hardly confirmed in the spectra.
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