[Paper Review] Regularity and chaos in the nuclear masses

P. Lebœuf|ArXiv.org|Jun 18, 2004

Quantum chaos and dynamical systems3 references3 citations

TL;DR

This paper proposes that nuclear mass fluctuations arise from both regular and chaotic nucleonic motion, using semiclassical periodic orbit theory to explain shell effects. It shows that deviations of ~500 keV in experimental nuclear masses from global models stem from chaotic dynamics, with a simple spherical cavity model reproducing data within 1.3 MeV RMS error—highlighting kinematic origins of shell effects and coexistence of order and chaos in nuclei.

ABSTRACT

Shell effects in atomic nuclei are a quantum mechanical manifestation of the single--particle motion of the nucleons. They are directly related to the structure and fluctuations of the single--particle spectrum. Our understanding of these fluctuations and of their connections with the regular or chaotic nature of the nucleonic motion has greatly increased in the last decades. In the first part of these lectures these advances, based on random matrix theories and semiclassical methods, are briefly reviewed. Their consequences on the thermodynamic properties of Fermi gases and, in particular, on the masses of atomic nuclei are then presented. The structure and importance of shell effects in the nuclear masses with regular and chaotic nucleonic motion are analyzed theoretically, and the results are compared to experimental data. We clearly display experimental evidence of both types of motion

Motivation & Objective

• To understand how regular and chaotic single-particle motion in nuclei influence shell effects and nuclear mass fluctuations.
• To determine whether experimental nuclear masses can distinguish between regular and chaotic nucleonic dynamics.
• To assess the role of chaotic components in explaining discrepancies between theoretical mass models and experimental data.
• To provide a semiclassical explanation of shell effects without relying on full many-body calculations.
• To investigate the coexistence of regular and chaotic dynamics in the nuclear many-body phase space and its impact on mass structure.

Proposed method

• Applies periodic orbit theory to link classical nucleon motion (regular or chaotic) to quantum shell effects in the single-particle spectrum.
• Uses random matrix theory and semiclassical methods to model statistical fluctuations in the single-particle energy levels.
• Employs a spheroidal cavity potential model to simulate regular motion, with adjustable parameters like Fermi wave number $\bar{k}_{\scriptscriptstyle F}R$ to fit experimental data.
• Introduces a time-scale $\tau_{\text{min}}$ associated with the shortest chaotic orbit to estimate long-range mass modulations via Eq. (67).
• Compares theoretical predictions of mass fluctuations with experimental nuclear masses across the entire mass spectrum.
• Analyzes RMS error between model and data (1.3 MeV) and identifies residual deviations (~500 keV) as signatures of chaotic contributions.

Experimental results

Research questions

• RQ1 Can experimental nuclear masses distinguish between regular and chaotic nucleonic motion?
• RQ2 What is the origin of the ~500 keV deviations observed between global theoretical mass models and experimental data?
• RQ3 How do shell effects and level bunching from short periodic orbits influence the thermodynamic properties of Fermi gases in nuclei?
• RQ4 To what extent can a simple single-particle model with regular motion reproduce the average trend and fluctuations in nuclear masses?
• RQ5 What role do chaotic layers in the many-body phase space play in generating long-range modulations in nuclear mass fluctuations?

Key findings

• The RMS error of the spherical cavity model in reproducing experimental nuclear masses is 1.3 MeV for nuclei with more than 30 neutrons, a factor of two higher than the best global mass fits.
• Deviations of approximately 500 keV between experimental data and theoretical models are interpreted as evidence of chaotic components in the nucleonic dynamics.
• The model shows that shell effects are primarily kinematic in origin, with spin-orbit and other interactions playing a minor role, as confirmed by adjusting $\bar{k}_{\scriptscriptstyle F}R$ phenomenologically.
• Supershell structures—long-range modulations from periodic orbits—are indicated by experimental data, though not unambiguously resolved due to limited particle numbers.
• Chaotic dynamics contribute to mass fluctuations via long-range modulations, estimated using the shortest chaotic orbit time $\tau_{\text{min}}$, consistent with Eq. (67).
• The theory predicts autocorrelations in total energies and observable effects on level density as a function of excitation energy, providing testable signatures of chaos.