Binding of heavy fermions by a single light atom in one dimension

TL;DR

This paper investigates how a single light atom can bind multiple heavy fermions in one dimension, revealing critical mass ratios for cluster formation and comparing different theoretical approaches.

Contribution

It introduces a combined few-body and mean-field framework to analyze binding thresholds and cluster structures in one-dimensional heavy-light fermion systems.

Findings

Critical mass ratios for tetramer, pentamer, hexamer formation identified.

Mean-field and Hartree-Fock approaches yield consistent energies.

System becomes bound when heavy-to-light mass ratio exceeds a size-dependent critical value.

Abstract

We consider the problem of $N$ identical fermions interacting via a zero-range attractive potential with a lighter atom in one dimension. Using the few-body approach based on the Skorniakov and Ter-Martirosian equation, we determine the energies and the critical mass ratios for the emergence of the tetramer, pentamer, and hexamer. For large $N$, we solve the problem analytically by using the mean-field theory based on the Thomas-Fermi approximation. The system becomes bound when the heavy-to-light mass ratio exceeds a critical value which grows as $N^3$ at large $N$. We also employ a more sophisticated Hartree-Fock approach, which turns out to be equivalent to the Thomas-Fermi approximation for determining the energies, but provides a better description of the microscopic structure of the clusters.