Noam Gavrielov

Lifetimes of excited states of the nucleus Zr 96 were studied with the Doppler-shift attenuation method following the Zr 94 ( O 18 , O 16 ) Zr 96 two-neutron transfer reaction. The obtained B ( E 2 ; 2 2 + → 0 2 + ) and B ( E 2 ; 4 1 + → 2 2 + ) transition strengths, amounting to 26 ( 2 ) and 39 ( 7 ) W . u . , respectively, firmly attribute the 2 2 + and 4 1 + states to the collective intruder band built on top of the 0 2 + state. The nature of this structure is discussed against predictions of the collective model using the Bohr Hamiltonian, the interacting boson model with configuration mixing, and the quasiparticle vacua shell model. The collective, interband B ( E 2 ; 4 1 + → 2 1 + ) = 11.2 ( 8 ) W . u . transition strength, refuting the previously assumed purity of both structures, is reproduced in the calculations. The quasiparticle vacua shell model predicts, in agreement with a simple two-state model based on experimental E 2 transition strengths, considerable mixing between the normal and intruder 2 + states.

A detailed analysis of odd-mass Nb isotopes, in the framework of the interacting boson-fermion model with configuration mixing, discloses the effects of an abrupt crossing of states in normal and intruder configurations (Type II QPT), on top of which superimposed a gradual evolution from spherical- to deformed-core shapes within the intruder configuration (Type I QPT). The pronounced presence of both types of QPTs demonstrates, for the first time, the occurrence of intertwined QPTs in odd-mass nuclei.

The evolution of shape in the even-even zirconium (Zr) isotopes has been the subject of study for many years. However, the odd-mass isotopes have not been investigated as extensively due to limited experimental accessibility and computational challenges. This work, employing the interacting boson-fermion model with configuration mixing, examines the effect of rapid shape evolution and normal-intruder configuration crossing, both identified as quantum phase transitions, alongside evolution in single particle energies, on the positive-parity spectrum of odd-mass 93 -- 103 Zr isotopes. Calculated energy levels, magnetic moments, B ( E 2 ) values, and quadrupole moments are compared to experimental data, showing good agreement. This agreement emphasizes the unique role of the odd neutron in the data. The special case of Zr 99 , which lies near the critical point of both quantum phase transitions, is also addressed, offering a new interpretation of the 7 / 2 1 + isomeric state and the occurrence of the type II shell evolution, in light of recent debates.

Nuclei in the A ≈ 100 region exhibit intricate shape-evolution and configuration crossing signatures. Exploring both even–even and their adjacent odd-mass nuclei gives further insight on the emergence of deformation and shape-phase transitions. We employ the algebraic frameworks of the interacting boson model with configuration mixing and the new interacting boson-fermion model with configuration mixing in order to investigate the even–even zirconium with neutron number 52–70 (⁴⁰Zr) and odd-mass niobium (₄₁Nb) isotopes with 52–62. We compare between the evolution in energy levels, configuration and symmetry content of the wave functions, two neutron separation energies and E2 transition rates, alongside comparison with the experimental data. The comparisons between the two chains of isotopes denote the occurrence of two types of QPTs, a crossing of normal and intruder configurations (named Type II QPT), and a shape-evolution of the intruder configuration (named Type I QPT). The latter QPT begins from spherical shape to axially deformed rotor in the Zr isotopes and from weak to strong coupling scenario in the Nb isotopes. This occurrence, named intertwined quantum phase transitions (IQPTs), in the even–even Zr chain is thus demonstrated to persists when coupling a proton to the boson core for the odd-mass Nb chain, even as deformation increases.

A detailed analysis of odd-mass Nb isotopes, in the framework of the interacting boson-fermion model with configuration mixing, discloses the effects of an abrupt crossing of states in normal and intruder configurations (Type~II QPT), on top of which superimposed a gradual evolution from spherical- to deformed-core shapes within the intruder configuration (Type~I QPT). The pronounced presence of both types of QPTs demonstrates, for the first time, the occurrence of intertwined QPTs in odd-mass nuclei.

The algebraic framework of the interacting boson model with configuration mixing is employed to demonstrate the occurrence of intertwined quantum phase transitions (IQPTs) in the _{40} 40 Zr isotopes with neutron number 52-70. The detailed quantum and classical analyses reveal a QPT of crossing normal and intruder configurations superimposed on a QPT of the intruder configuration from U(5) to SU(3) and a crossover from SU(3) to SO(6) dynamical symmetries.