Liquid Drop Model for Nuclear Matter in the Low Density Limit
ABSTRACT We consider the liquid drop model with a positive background density in the thermodynamic limit. We prove a two‐term asymptotics for the ground state energy per unit volume in the dilute limit. Our proof justifies the expectation that optimal configurations consist of droplets of unit size that arrange themselves according to minimizers for the Jellium problem for point particles. In particular, we provide the first rigorous derivation of what is known as the gnocchi phase in astrophysics.
Authors
- Rupert L. Frank (ORCID: https://orcid.org/0000-0001-7973-4688)
- Robert Seiringer (ORCID: https://orcid.org/0000-0002-6781-0521)
- Mathieu Lewin (ORCID: https://orcid.org/0000-0002-1755-0207)
Institutions
- California Institute of Technology (US)
- Centre National de la Recherche Scientifique (FR)
- Institute of Science and Technology Austria (AT)
- Centre de Recherche en Mathématiques de la Décision (FR)
- LMU Klinikum (DE)
- Munich Center for Quantum Science and Technology (DE)
- Université Paris Dauphine-PSL (FR)
- Ludwig-Maximilians-Universität München (DE)
Publication Details
- Journal
- Communications on Pure and Applied Mathematics
- Published
- 2026-05-22
- DOI
- https://doi.org/10.1002/cpa.70039
- Primary Topic
- High-Energy Particle Collisions Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Deutsche Forschungsgemeinschaft