Background Coexistence of different geometric shapes at low energies presents a universal struc-

Microscopic signatures of nuclear ground-state shape phase transitions in odd-mass Eu isotopes are explored starting from excitation spectra and collective wave functions obtained by diagonalization of a core-quasiparticle coupling Hamiltonian based on energy density functionals. As functions of the physical control parameter -the number of nucleons -theoretical low-energy spectra, twoneutron separation energies, charge isotope shifts, spectroscopic quadrupole moments, and E2 reduced transition matrix elements accurately reproduce available data, and exhibit more pronounced discontinuities at neutron number N = 90, compared to the adjacent even-even Sm and Gd isotopes. The enhancement of the first-order quantum phase transition in odd-mass systems can be attributed to a shape polarization effect of the unpaired proton which, at the critical neutron number, starts predominantly coupling to Gd core nuclei that are characterized by larger quadrupole deformation and weaker proton pairing correlations compared to the corresponding Sm isotopes.PACS numbers: 21.60. Jz, 21.60.Ev, 21.10.Re, 21.10.Tg Quantum mechanical systems can undergo zerotemperature phase transitions upon variation of a nonthermal control parameter. Quantum phase transitions (QPTs) present a very active field of research and have found a variety of applications in many areas of physics and chemistry [1,2]. Nuclear QPTs, in particular, correspond to shape transitions between competing groundstate phases induced by variation of a non-thermal control parameter (number of nucleons) [3][4][5][6][7]. Most experimental and theoretical studies of first-and second-order nuclear QPTs have considered systems with even numbers of protons and neutrons [8][9][10][11][12][13][14][15][16][17][18][19]. QPTs in odd-A nuclei present a more complex phenomenon because of the coupling between single-particle and collective degrees of freedom. The crucial issues for QPTs in odd-A systems are the influence of the unpaired fermion(s) on the precise location and nature of the phase transition, empirical signatures of QPTs, and the definition and computation of order parameters [20,21]. In recent years phenomenological geometric models with single-or multij state coupling [22][23][24][25], the interacting boson-fermion framework [25][26][27], and microscopic energy density functionals [28,29] have been employed in extensive studies of QPTs in odd-mass nuclei.In this paper we report a microscopic study of QPT in odd-mass Eu isotopes, calculate a series of observables that can be related to order parameters (low-energy spectra, two-neutron separation energies, isotope shifts, spectroscopic quadrupole moments, and reduced transition matrix elements), both for odd-mass nuclei and the adjacent even-even isotopes, and analyze the polarization * zpliphy@swu.edu.cn effect of the unpaired nucleon on the QPT. The choice of Eu isotopes is motivated by the fact that probably the best example of a QPT in atomic nuclei is in the rare earth region with N ≈ 90 neutrons, where a transition b...

Background: Predictions of spectroscopic properties of low-lying states are critical for nuclear structure studies. Theoretical methods can be particularly involved for odd-mass nuclei because of the interplay between the unpaired nucleon and collective degrees of freedom. Only a few models have been developed for systems in which octupole collective degrees of freedom play a role.Purpose: We aim to predict spectroscopic properties of odd-mass nuclei characterized by octupole shape deformation, employing a model that describes single-particle and collective degrees of freedom within the same microscopic framework.Method: A microscopic core-quasiparticle coupling (CQC) model based on the covariant density functional theory is developed, which includes collective excitations of even-mass core nuclei and single-particle states of the odd nucleon, calculated using a quadrupole-octupole collective Hamiltonian combined with a constrained reflection-asymmetric relativistic Hartree-Bogoliubov model.Results: Model predictions for low-energy excitation spectra and transition rates of odd-mass radium isotopes 223,225,227 Ra are shown to be in good agreement with available data.Conclusions: A microscopic CQC model based on covariant density functional theory has been developed for odd-mass nuclei characterized by both quadrupole and octupole shape deformations. Theoretical results reproduce data in odd-mass Ra isotopes and provide useful predictions for future studies of octupole correlations in nuclei and related phenomena.

Background Predictions of the spectroscopic properties of low-lying states are critical for nuclear structure studies, but are problematic for nuclei with an odd nucleon due to the interplay of the unpaired single particle with nuclear collective degrees of freedom.Purpose To predict the spectroscopic properties of odd-mass medium-heavy and heavy nuclei with a model that treats single-particle and collective degrees of freedom within the same microscopic framework.Method A microscopic core-quasiparticle coupling (CQC) model based on the covariant density functional theory is developed that contains the collective excitations of even-mass cores and spherical single-particle states of the odd nucleon as calculated from a quadrupole collective Hamiltonian combined with a constrained triaxial relativistic Hartree-Bogoliubov model. ResultsPredictions of the new model for excitation energies, kinematic and dynamic moments of inertia, and transition rates are shown to be in good agreement with results of low-lying spectroscopy measurements of the axially deformed odd-proton nucleus 159 Tb and the oddneutron nucleus 157 Gd.Conclusions A microscopic CQC model based on covariant density functional theory is developed for odd-mass nuclei and shown to give predictions that agree with measurements of two medium-heavy nuclei. Future studies with additional nuclei are planned. Figure 7 displays the core and single-particle contributions to the intraband B(E2; J → J − 1), B(E2; J → J − 2), and B(M1; J → J − 1) in the ground state bands of 159 Tb and 157 Gd. It is found that the B(E2) transitions are dominated by the core component and present monotonically increasing B(E2; J → J − 2) and monotonically decreasing B(E2; J → J − 1) as functions of spin. This is because the core has the majority of the

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