Signatures of shape phase transitions in odd-mass nuclei

Abstract

Quantum phase transitions between competing ground-state shapes of atomic nuclei with an odd number of protons or neutrons are investigated in a microscopic framework based on nuclear energy density functional theory and the particle-plus-boson-core coupling scheme. The boson-core Hamiltonian, as well as the single-particle energies and occupation probabilities of the unpaired nucleon, are completely determined by constrained self-consistent mean-field calculations for a specific choice of the energy density functional and paring interaction, and only the strength parameters of the particle-core coupling are adjusted to reproduce selected spectroscopic properties of the odd-mass system. We apply this method to odd-A Eu and Sm isotopes with neutron number N ≈ 90, and explore the influence of the single unpaired fermion on the occurrence of a shape phase transition. Collective wave functions of low-energy states are used to compute quantities that can be related to quantum order parameters: deformations, excitation energies, E2 transition rates and separation energies, and their evolution with the control parameter (neutron number) is analysed.

Description of odd-mass nuclei within the interacting boson-fermion model based on the Gogny energy density functional

“…By studying the same isotopes ( 149−155 Eu and 149−155 Sm) as in Refs. [21,23], we demonstrate that the IBFM Hamiltonian based on the Gogny EDF describes the low-lying states in odd-mass nuclei at the same level of accuracy as in the earlier studies of [21,23] based on the relativistic EDF. The Gogny EDF is a successful member of the class of non-relativistic EDF.…”

“…Furthermore, the addition of the γ-soft nuclei, 195 Pt and 195 Au, which have not been included in Refs. [21,23], further confirms the robustness of the procedure.…”

“…Only the strength parameters of the boson-fermion coupling term in the IBFM Hamiltonian have been determined so as to fit the selected experimental data. The validity of the method has been confirmed in the axially-deformed odd-mass Eu isotopes [21] and further applied to study shape phase transitions between nearly spherical and axially deformed shapes in the oddmass Eu and Sm isotopes [23], and between nearly spherical and γ-soft shapes in the mass A ≈ 130 region [24].…”

Intertwined quantum phase transitions in the Zr isotopes

“…The 40 Zr isotopes have been recently the subject of several experimental investigations [9][10][11][12][13][14][15] and theoretical studies, including mean-field based methods [16][17][18], the Monte-Carlo shell-model (MCSM) [19] and algebraic methods [8,20]. We adapt here the algebraic approach of the Interacting Boson Model (IBM) [21], with bosons representing valence nucleon pairs counted from the nearest closed shells.…”

Intertwined quantum phase transitions in the Zr chain

“…The 40 Zr isotopes have been recently the subject of several experimental [6][7][8][9][10] and theoretical investigations, including mean-field based methods [11][12][13] and the Monte-Carlo shell-model (MCSM) [14]. We adapt here the algebraic approach of the Interacting Boson Model (IBM) [15], with bosons representing valence nucleon pairs counted from the nearest closed shells.…”