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arXiv:1509.02059 · EPJ Web of Conferences

Weakly bound states with spin-isospin symmetry

Alejandro Kievsky, M. Gattobigio

Published Jan 1, 2016• 3 citations
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Abstract

We discuss weakly bound states of a few-fermion system having spin-isospin symmetry. This corresponds to the nuclear physics case in which the singlet, a0, and triplet, a1, n − p scattering lengths are large with respect to the range of the nuclear interaction. The ratio of the two is about a0/a1 ≈ −4.31. This value defines a plane in which a0 and a1 can be varied up to the unitary limit, 1/a0 = 0 and 1/a1 = 0, maintaining its ratio fixed. Using a spin dependant potential model we estimate the three-nucleon binding energy along that plane. This analysis can be considered an extension of the Efimov plot for three bosons to the case of three 1/2-spin-isospin fermions.

DOI
10.1051/epjconf/201611303001

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We discuss weakly bound states of a few-fermion system having spin-isospin symmetry. This corresponds to the nuclear physics case in which the singlet, a0, and triplet, a1, n − p scattering lengths are large with respect to the range of the nuclear interaction. The ratio of the two is about a0/a1 ≈ −4.31. This value defines a plane in which a0 and a1 can be varied up to the unitary limit, 1/a0 = 0 and 1/a1 = 0, maintaining its ratio fixed. Using a spin dependant potential model we estimate the three-nucleon binding energy along that plane. This analysis can be considered an extension of the Efimov plot for three bosons to the case of three 1/2-spin-isospin fermions.
\nWe discuss weakly bound states of a few-fermion system having spin-isospin symmetry. This corresponds to the nuclear physics case in which the singlet, a0, and triplet, a1, n − p scattering lengths are large with respect to the range of the nuclear interaction. The ratio of the two is about a0/a1 ≈ −4.31. This value defines a plane in which a0 and a1 can be varied up to the unitary limit, 1/a0 = 0 and 1/a1 = 0, maintaining its ratio fixed. Using a spin dependant potential model we estimate the three-nucleon binding energy along that plane. This analysis can be considered an extension of the Efimov plot for three bosons to the case of three 1/2-spin-isospin fermions.\n
The equal mass three-fermion system having 1/2 spin-isospin symmetry is study around the unitary limit. The two body system has two different scattering lengths, a 0 and a 1 , corresponding to the spin singlet state S = 0 and the spin triplet state S = 1, respectively. The unitary limit is defined when the two quantities a 0 , a 1 → ∞ . The three-nucleon system is located very close to this limit, the singlet and triplet n − p scattering lengths are large with respect to the range of the nuclear interaction. The ratio of the two is about a 0 / a 1 ≈ −4.31. This value defines a plane in which a 0 and a 1 can be varied. Using a nucleon-nucleon spin dependent potential with variable strength it is possible to study the behavior of the three-nucleon binding energy along that plane. This analysis can be considered an extension of the Efimov plot for three bosons to the case of three 1/2-spin-isospin fermions.
We show that there exist two types of universal phenomena for three-boson systems with isospin degrees of freedom. In the isospin symmetric limit, there is only one universal three-boson bound state with the total isospin one, whose binding energy is proportional to that of the two-boson bound state. With large isospin symmetry breaking, the standard Efimov states of three identical bosons appear at low energies. Both phenomena can be realized by three pions with the pion mass appropriately tuned in lattice QCD simulations, or by spin-one bosons in cold atom experiments. Implication to the in-medium softening of multi-pion states is also discussed.
The three-body system inside the unitary window is studied for three equal bosons and three equal fermions having 1/21/21/2 spin-isospin symmetry. We perform a Gaussian characterization of the window using a Gaussian potential to define trajectories for low-energy quantities as binding energies and phase shifts. On top of this trajectories experimental values are placed or, when not available, quantities calculated using realistic potentials that are known to reproduce experimental values. The intention is to show that the Gaussian characterization of the window, thought as a contact interaction plus range corrections, captures the main low-energy properties of real systems as for example three helium atoms or three nucleons. The mapping of real systems on the Gaussian trajectories is taken as indication of universal behavior. The trajectories continuously link the physical points to the unitary limit allowing for the explanation of strong correlations between observables appearing in real systems and which are known to exist in that limit. In the present study we focus on low-energy bound, scattering, and virtual states.
Gaussian characterization of the unitary window for N=3N=3N=3: bound, scattering and virtual states
The three-body system inside the unitary window is studied for three equal bosons and three equal fermions having 1/21/21/2 spin-isospin symmetry. We perform a gaussian characterization of the window using a gaussian potential to define trajectories for low-energy quantities as binding energies and phase shifts. On top of this trajectories experimental values are placed or, when not available, quantities calculated using realistic potentials that are known to reproduce experimental values. The intention is to show that the gaussian characterization of the window, thought as a contact interaction plus range corrections, captures the main low-energy properties of real systems as for example three helium atoms or three nucleons. The mapping of real systems on the gaussian trajectories is taken as indication of universal behavior. The trajectories continuously link the physical points to the unitary limit allowing for the explanation of strong correlations between observables appearing in real systems and which are known to exist in that limit. In the present study we focus on low-energy bound, scattering and virtual states.