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arXiv:2511.18095

Quantum and classical analyses of intertwined phase transitions in odd-mass Nb isotopes

A. Leviatan

nucl-thquant-phSubmitted Nov 22, 2025• Announced Nov 25, 2025

Abstract

Quantum phase transitions (QPTs) in odd-mass Nb isotopes are investigated in the framework of the interacting boson-fermion model with configuration mixing. A quantum analysis reveals a Type I QPT (gradual shape-evolution within the intruder configuration) superimposed on a Type II QPT (abrupt crossing of normal and intruder states), thus demonstrating the occurrence of intertwined QPTs. A classical analysis highlights the implications for the single particle motion in the deformed field generated by the even-even Zr cores.

Journal reference: EPJ Web of Conferences 342, 01016 (2025)
DOI: 10.1051/epjconf/202534201016
Comments: 8 pages, 9 figures, Proceedings 14th International Spring Seminar on Nuclear Physics: "Cutting-Edge Developments in Nuclear Structure Physics", May 19-23, 2025, Ischia, Italy

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Quantum phase transitions (QPTs) in odd-mass Nb isotopes are investigated in the framework of the interacting boson-fermion model with configuration mixing. A quantum analysis reveals a Type I QPT (gradual shape-evolution within the intruder configuration) superimposed on a Type II QPT (abrupt crossing of normal and intruder states), thus demonstrating the occurrence of intertwined QPTs. A classical analysis highlights the implications for the single particle motion in the deformed field generated by the even-even Zr cores.

Abstract Pronounced structural changes within individual configurations (Type I QPT), superimposed on an abrupt crossing of these configurations (Type II QPT), define the notion of intertwined quantum phase transitions (QPTs). We discuss and present evidence for such a scenario in finite Bose and Bose-Fermi systems. The analysis is based on algebraic models with explicit configuration mixing, where the two types of QPTs describe shape-phase transitions in-between different dynamical symmetries and shape-coexistence with crossing.

We introduce the notion of intertwined quantum phase transitions (IQPTs), for which shape-changes and configuration-changes in the ground state of a system are intertwined. We demonstrate the relevance of IQPTs to the Zr isotopes, where one of the most complex situations encountered in nuclear physics occurs, with coexisting Type I and Type II quantum phase transitions, and ground state shapes changing from spherical to prolate axially deformed and finally to gamma-unstable. Comparison with experimental data provides the first evidence for IQPTs in physical systems.

In this paper‎, ‎we study the nature of the dynamics in second-order Quantum Phase Transition (QPT) between vibrational ( ) and -unstable ( ) nuclear shapes‎. ‎Using a transitional Hamiltonian according to an affine SU(1,1) algebra in combination with a coherent state formalism, Shape Phase Transitions (SPT) in odd-nuclei in the framework of the Interacting Boson Fermion Model (IBFM) are investigated‎. ‎Classical analysis reveals a change in the system along with the transition in a critical point‎. ‎The role of a fermion with angular momentum j at the critical point on quantum phase transitions in bosonic systems is investigated via a semi-classical approach‎. ‎The effect of the coupling of the odd particle to an even-even boson core is discussed along with the shape transition and‎, ‎in particular‎, ‎at the critical point‎. Our study confirms the importance of the odd nuclei as necessary signatures to characterize the occurrence of the phase transition and determine the critical point's precise position‎.