Algebraic and Topological Approaches for Atomic Nuclei and Related Systems

Projektinformationen

AlgeTopo

ID Finanzhilfevereinbarung: 101107805

DOI

10.3030/101107805

Das Projekt endete am 2 Dezember 2024

EK-Unterschriftsdatum 8 Mai 2023

Startdatum 10 September 2023

Enddatum 9 September 2025

Finanziert unter

• Marie Skłodowska-Curie Actions (MSCA)

Gesamtkosten

Keine Daten

EU-Beitrag

€ 211 754,88

Koordiniert durch

COMMISSARIAT A L ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES
France

Periodic Reporting for period 1 - AlgeTopo (Algebraic and Topological Approaches for Atomic Nuclei and Related Systems)

Berichtszeitraum: 2023-09-10 bis 2025-09-09

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

The goal of the project is to shed light on the emergence of “simplicity out of complexity” in atomic nuclei. This will be achieved by means of so-called algebraic methods based on group theory, which is the mathematical theory of symmetry. Group theory is of central importance in physics, in particular in the quantum world, and enables one to derive exact results on the basis of general principles without the knowledge of all intricate details of a physical system such as a nucleus. These goals will be achieved in the context of the interacting boson model (IBM), which considers the nucleus in terms of pairs of neutrons and protons, leading to a tremendous simplification of the problem of many (~50 to more than 200) interacting nucleons. Specifically, quantum phase transitions (QPTs), in which the nucleus undergoes a sudden transition as a function of some interaction parameter, can be conveniently described in the framework of the IBM. They are the focus of the project. QPTs have been studied in many domains of physics and some of the developments in condensed-matter physics related to the topology of the transition will be explored in nuclei. A separate but related objective is the application of the algebraic approach to define a new model of the quark-gluon plasma.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

The project has made significant progress in exploring the emergence of "simplicity out of complexity" in atomic nuclei using algebraic approaches. Key milestones include:
- Detailed studies of quantum phase transitions (QPTs) in odd-mass nuclei, focusing on the zirconium (with Z=40 protons) and niobium (Z=4) isotopes. This work provided new insights into the evolution of nuclear structure, revealing intertwined QPTs in these systems and exploring the influence of single-particle orbitals on collective dynamics with multiple shell-model configurations.
- Initial development of a Monte Carlo code for interacting fermions and bosons (MCFB), which allows for efficient calculations of nuclear structures.

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

The project has achieved results that go beyond the current state of the art in several areas:
- A comprehensive study of quantum phase transitions (QPTs) in odd-mass zirconium (with Z=40 protons) and niobium (Z=4) isotopes has advanced the understanding of intertwined quantum phase transitions (IQPTs). This work demonstrates how complex phenomena in nuclear structure can be explained through detailed algebraic modelling.
- The initial incorporation of the interacting bosons and fermions in conjunction with a Monte Carlo method will enable precise calculations of structural evolution in even-even, odd-mass and odd-odd nuclei, for the entire nuclear chart.
- These studies provide a novel perspective on the interplay between single-particle and collective behaviours in nuclei, offering benchmarks for experimental data and inspiring further research in nuclear-structure physics.