Stability of the 2+2 fermionic system with point interactions

TL;DR

This paper establishes a lower bound on the ground state energy of a 2+2 fermionic system with point interactions, identifying a critical mass ratio for stability, thus advancing understanding of multi-fermion stability conditions.

Contribution

It provides the first known stability criterion for the 2+2 fermionic system with point interactions, revealing a critical mass ratio for bounded energy spectrum.

Findings

System is stable for mass ratios between approximately 0.58 and 1/0.58.

Established a lower bound on the ground state energy.

Supports the stability of more general N+M fermionic systems.

Abstract

We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m_c \approx 0.58 such that the system is stable, i.e., the energy is bounded from below, for m \in [m_c, m_c^{-1}]. So far it was not known whether this 2+2 system exhibits a stable region at all or whether the formation of four-body bound states causes an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our result gives further evidence for the stability of the more general N+M system.