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Journal Articles Physical Review A Year : 2022

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

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.

Dates and versions

hal-03784730 , version 1 (23-09-2022)

Identifiers

Cite

A. Tononi, J. Givois, D. S. Petrov. Binding of heavy fermions by a single light atom in one dimension. Physical Review A, 2022, 106 (1), pp.L011302. ⟨10.1103/PhysRevA.106.L011302⟩. ⟨hal-03784730⟩
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