In this paper we use a self-consistent scheme proposed by Singwi, Tosi, Land, and Sjo\ifmmode\ddot\else\textasciidieresis\fi{}lander to study a two-dimensional Fermi liquid whose particles interact via a repulsive hard-core potential with or without an attractive tail. We determine the Landau parameters ${\mathit{F}}_{0}^{\mathit{s}}$ and ${\mathit{F}}_{0}^{\mathit{a}}$ , the static structure factors, and we discuss the effect of adding the attractive tail to the hard-core potential.In this paper we use a self-consistent scheme proposed by Singwi, Tosi, Land, and Sjo\ifmmode\ddot\else\textasciidieresis\fi{}lander to study a two-dimensional Fermi liquid whose particles interact via a repulsive hard-core potential with or without an attractive tail. We determine the Landau parameters ${\mathit{F}}_{0}^{\mathit{s}}$ and ${\mathit{F}}_{0}^{\mathit{a}}$, the static structure factors, and we discuss the effect of adding the attractive tail to the hard-core potential.

Physical review. B, Condensed matterAug 1, 19927 citations

Ideal Bose systems

Raj K. Pathria, Paul D. Beale

Elsevier eBooksFeb 21, 20210 citations

Very low temperature properties of bosons with repulsive core and attractive tails

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Positivity of the effective range for finite range attractive potentials with a repulsive core

Davide Germani

In the phenomenological study of exotic hadrons, the sign of the effective range, $r_0$ , is invoked as a criterion to distinguish between compact multiquark configurations (associated with $r_0 < 0$ ) and loosely bound hadronic molecules ( $r_0 > 0$ ). Motivated by this, we investigate the fundamental constraints on the sign of the effective range for single-channel local interactions. We rigorously prove that for finite-range potentials, characterized by an inner repulsive core and an outer attractive tail, the effective range remains strictly positive provided that the scattering length is greater than the range of the potential ( $a > R$ ).In the phenomenological study of exotic hadrons, the sign of the effective range, $r_0$, is invoked as a criterion to distinguish between compact multiquark configurations (associated with $r_0 < 0$) and loosely bound hadronic molecules ($r_0 > 0$). Motivated by this, we investigate the fundamental constraints on the sign of the effective range for single-channel local interactions. We rigorously prove that for finite-range potentials, characterized by an inner repulsive core and an outer attractive tail, the effective range remains strictly positive provided that the scattering length is greater than the range of the potential ($a > R$).

hep-phCross-listedarXiv:2605.18207May 19, 2026

{\mathit{F}}_{0}^{\mathit{s}}

and

{\mathit{F}}_{0}^{\mathit{a}}

, the static structure factors, and we discuss the effect of adding the attractive tail to the hard-core potential.

In the phenomenological study of exotic hadrons, the sign of the effective range,

r_0

, is invoked as a criterion to distinguish between compact multiquark configurations (associated with

r_0 < 0

) and loosely bound hadronic molecules (

r_0 > 0

). Motivated by this, we investigate the fundamental constraints on the sign of the effective range for single-channel local interactions. We rigorously prove that for finite-range potentials, characterized by an inner repulsive core and an outer attractive tail, the effective range remains strictly positive provided that the scattering length is greater than the range of the potential (

a > R