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تسجيل مستخدم جديدEfimov physics with $1/2$ spin-isospin fermions
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The structure of few-fermion systems having $1/2$ spin-isospin symmetry is studied using potential models. The strength and range of the two-body potentials are fixed to describe low energy observables in the angular momentum $L=0$ state and spin $S=0,1$ channels of the two-body system. Successively the strength of the potentials are varied in order to explore energy regions in which the two-body scattering lengths are close to the unitary limit. This study is motivated by the fact that in the nuclear system the singlet and triplet scattering lengths are both large with respect to the range of the interaction. Accordingly we expect evidence of universal behavior in the three- and four-nucleon systems that can be observed from the study of correlations between observables. In particular we concentrate in the behavior of the first excited state of the three-nucleon system as the system moves away from the unitary limit. We also analyze the dependence on the range of the three-body force of some low-energy observables in the three- and four-nucleon systems.
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In scattering theory, the unitary limit is defined by an infinite scattering-length and a zero effective range, corresponding to a phase-shift pi/2, independent of energy. This condition is satisfied by a rank-1 separable potential V(k,k)=-v(k)v(k) w
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Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by a continuous-scale invariance, which is broken to a discrete one when three or more particles come into play. This symmetry induces a unive
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plitudes is developed, and the expression for calculating $cal{E}$ in a partial-wave amplitude expansion is also given. The case of contact interactions is completely solved and is shown to provide renormalized results, expressed directly in terms of scattering data parameters, within cutoff regularization in a wide class of schemes. $S$- and $P$-wave interactions are considered up to including the first three-terms in the effective-range expansion, paying special attention to the parametric region around the unitary limit.
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