Abstract
The self-consistent-field approximation is applied for the study of the energy spectrum, sound velocity, and correlation function on a one-dimensional, spin-1/2 Fermi system, interacting as rigid rods of length $l$. Two very distinct regions are observed, which are named as low- and high-density behaviors, corresponding to small and large Landau's ${F}_{0}$, respectively. The results are very similar to those obtained for a boson system with the same type of interaction, as one might expect. For the very high densities the energy spectrum approaches the $E(q)=0$ line, indicating the existence of an instability, a liquid to crystal transition, which is very neatly followed by observing the behavior of the pair-correlation function as density increases.
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