Use of quantality in nuclei and many-body systems

TL;DR

This paper explores the concept of quantality in nuclei and many-body systems, analyzing its relation to system behavior, length scales, and various physical effects, highlighting nuclei's unique position among many-body systems.

Contribution

It introduces and analyzes the role of quantality and related dimensionless parameters in understanding many-body systems, especially nuclei, and proposes new generalized quantities.

Findings

Quantality indicates whether a system behaves like a crystal or quantum liquid.

Nuclei are unique with all dimensionless quantities near unity.

The relation between quantality, scattering length, and length scales is established.

Abstract

The use of quantality is discussed in the case of nuclei and other many-body systems such as atomic electrons. This dimensionless quantity is known to indicate when a many-body system behaves like a crystal or a quantum liquid. Its role is further analyzed by showing its relation to the scattering length. The emergence of a fundamental lengthscale, the limit radius, is also shown. It corresponds to the hard-core of the nucleon-nucleon interaction in the case of nucleons, and to a value close to the Bohr radius in the case of atomic electrons. The occurrence of a cluster phase in nuclei is analyzed using the quantality through its relation to the localization parameter, allowing for the identification of both the number of nucleons and the density as control parameters for the occurrence of this phase. The relation of the quantality to the magnitude of the interaction also exhibits a third dimensionless parameter, monitoring the magnitude of the spin-orbit effect in finite systems, through the realization of the pseudo-spin symmetry. The impact of quantality on the spin-orbit effect is compared in various many-body systems. The role of quantality in the relative effect of the binding energy and the shell one is also analyzed in nuclei. Finally, additional dimensionless quantities are proposed from the generalization of the quantality. Nuclei are found to be exceptional systems because all their dimensionless quantities are close to the order of unity, at variance with other many-body systems.