Universal description of three two-component fermions

Abstract

A quantum mechanical three-body problem for two identical fermions of mass $m$ and a distinct particle of mass $m_1$ in the universal limit of zero-range two-body interaction is studied. For the unambiguous formulation of the problem in the interval ${\mu }_r<m/m_1\le {\mu }_c$ (${\mu }_r\approx 8.619$ and ${\mu }_c\approx 13.607$) an additional parameter $b$ determining the wave function near the triple-collision point is introduced; thus, a one-parameter family of self-adjoint Hamiltonians is defined. The dependence of the bound-state energies on $m/m_1$ and $b$ in the sector of angular momentum and parity $L^P=1^{-}$ is calculated and analysed with the aid of a simple model.

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Cited by in corpus (11)

• Efimov Physics: a review
• Universal few-body physics and cluster formation
• Five-Body Efimov Effect and Universal Pentamer in Fermionic Mixtures
• Spectral analysis of the 2+1 fermionic trimer with contact interactions
• Few-body states of bosons interacting with a heavy quantum impurity
• Mass-imbalanced fermionic mixture in a harmonic trap
• Universality of isolated $N$-body resonances at large scattering length
• Three-body contact for fermions. I. General relations
• Minlos-Faddeev regularization of zero-range interactions in the three-body problem
• Shallow Trimers of Two Identical Fermions and One Particle in Resonant Regimes
• Mass-ratio condition for non-binding of three two-component particles with contact interactions