# Localisation and dimensionless studies in nuclei and many-body systems

## TL;DR

This paper explores how dimensionless ratios like the localisation parameter reveal universal properties and phase transitions in many-body systems such as nuclei, emphasizing delocalisation effects and their relation to other quantities.

## Contribution

It introduces a generalized localisation parameter and discusses its implications for understanding nuclear saturation, phase transitions, and the role of delocalisation in many-body systems.

## Key findings

- Localization parameter helps identify phase states in nuclei
- Delocalisation impacts nuclear saturation and phase transitions
- Quantum fluidity and mobility concepts are introduced

## Abstract

Dimensionless ratios characterizing many-body systems are a powerful tool to reveal the main universal quantities involved. The recently-introduced localisation parameter allow to study the occurrence of crystal, clusterisation, and quantum liquid states in many-body systems such as nuclei. Its concomitant use with other dimensionless quantities such as the quantality, allows to pinpoint fundamental lengthscales and dimensionless ratios at work in nuclei. Within the present approach, the impact of delocalisation on nuclear saturation is discussed. The transition from a homogeneous to a clusterised state in low density systems is studied. The spin-orbit effect in nuclei and fermionic systems is also reviewed in the light of this analysis. A generalised localisation parameter is derived, showing that the delocalisation properties are not always driven by the quantality. The concepts of quantum fluidity and mobility are finally introduced.