Role of incompressibility in enhanced Friedel oscillations

Determine whether the correlation between nuclear incompressibility and the pronounced Friedel oscillations observed in semi-infinite nuclear matter is causal rather than accidental, independently disentangling the effects of incompressibility and the relative contribution of the Fock term by constructing a dedicated family of Gogny interactions.

Background

The paper finds that several Gogny parametrizations—particularly D260, D280, and D300, and to a lesser extent D3G3M—produce enhanced Friedel oscillations and correspondingly larger discrepancies between semiclassical and fully self-consistent Hartree–Fock surface-energy coefficients. These interactions also exhibit relatively large nuclear incompressibilities and differing relative Fock-term contributions.

The reported data do not establish whether the observed association between incompressibility and enhanced density oscillations is causal or accidental. Resolving this issue would require constructing new Gogny parametrizations in which incompressibility is varied independently while the relative Fock contribution is controlled, followed by a systematic analysis of the resulting surface densities and semiclassical accuracy.

References

With the present data set, however, it is not possible to determine whether this correlation is merely accidental or whether the incompressibility is indeed responsible for the pronounced density oscillations. Addressing this question would require the construction of a dedicated family of Gogny interactions in which the incompressibility could be varied independently while carefully controlling the relative contribution of the Fock term. Such an investigation lies beyond the scope of the present work and is left for future studies.

— Nuclear surface energy in a semiclassical Extended Thomas-Fermi approach with finite-range interactions  (2608.28043 - Davesne et al., 28 Aug 2026) in Section IV.C, “Discussion of Friedel oscillations”