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

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.

Automated summary

The study focused on N identical fermions interacting with a lighter atom via a zero-range attractive potential in one dimension. By using few-body and mean-field theories, the energies, critical mass ratios, and emergence of tetramer, pentamer, and hexamer were determined. The system becomes bound when the heavy-to-light mass ratio exceeds a critical value, which increases as N-3 at large N, and a more sophisticated Hartree-Fock approach was employed for a better description of the cluster's microscopic structure.