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arXiv · 1702.08832

Efimov effect for a three-particle system with two identical fermions

Giulia Basti·Alessandro Teta
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Abstract

We consider a three-particle quantum system in dimension three composed of two identical fermions of mass one and a different particle of mass $m$. The particles interact via two-body short range potentials. We assume that the Hamiltonians of all the two-particle subsystems do not have bound states with negative energy and, moreover, that the Hamiltonians of the two subsystems made of a fermion and the different particle have a zero-energy resonance. Under these conditions and for $m m^*$ the number of negative eigenvalues of $H$ is finite and for $m<m^*$ the number $N(z)$ of negative eigenvalues of $H$ below $z<0$ has the asymptotic behavior $N(z) \sim \mathcal C(m) |\log|z||$ for $z \rightarrow 0^-$. Moreover, we give an upper and a lower bound for the positive constant $\mathcal C(m)$.

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Giulia Basti, Alessandro Teta. 2017-02-28. Efimov effect for a three-particle system with two identical fermions. https://doi.org/10.1007/s00023-017-0608-8

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