Universal description of three two-component fermions

TL;DR

This paper investigates the universal properties of a three-body quantum system with two identical fermions and a third particle, introducing a parameter to define self-adjoint Hamiltonians and analyzing bound states across mass ratios.

Contribution

It introduces a parameterized family of self-adjoint Hamiltonians for the three-fermion system and analyzes bound states in the universal limit of zero-range interactions.

Findings

Bound-state energies depend on mass ratio and parameter b.

A one-parameter family of Hamiltonians is established.

Analysis covers the angular momentum sector L^P = 1^-.

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.