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The relativistic mean-field framework, extended to include correlations related to restoration of broken symmetries and to fluctuations of the quadrupole deformation, is applied to a study of shape transitions in Nd isotopes. It is demonstrated that the microscopic self-consistent approach, based on global effective interactions, can describe not only general features of transitions between spherical and deformed nuclei, but also the singular properties of excitation spectra and transition rates at the critical point of quantum shape phase transition.
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The analysis of shape transitions in Nd isotopes, based on the framework of relativistic energy density functionals and restricted to axially symmetric shapes in Ref. cite{PRL99}, is extended to the region $Z = 60$, 62, 64 with $N approx 90$, and includes both $beta$ and $gamma$ deformations. Collective excitation spectra and transition probabilities are calculated starting from a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The results reproduce available data, and show that there is an abrupt change of structure at N=90 that can be approximately characterized by the X(5) analytic solution at the critical point of the first-order quantum phase transition between spherical and axially deformed shapes.
A systematic analysis of low-lying quadrupole and octupole collective states is presented, based on the microscopic energy density functional framework. By mapping the deformation constrained self-consistent axially symmetric mean-field energy surfaces onto the equivalent Hamiltonian of the $sdf$ interacting boson model (IBM), that is, onto the energy expectation value in the boson condensate state, the Hamiltonian parameters are determined. The study is based on the global relativistic energy density functional DD-PC1. The resulting IBM Hamiltonian is used to calculate excitation spectra and transition rates for the positive- and negative-parity collective states in four isotopic chains characteristic for two regions of octupole deformation and collectivity: Th, Ra, Sm and Ba. Consistent with the empirical trend, the microscopic calculation based on the systematics of $beta_{2}$-$beta_{3}$ energy maps, the resulting low-lying negative-parity bands and transition rates show evidence of a shape transition between stable octupole deformation and octupole vibrations characteristic for $beta_{3}$-soft potentials.
Based on the results of a previous paper (Paper I), by performing the geometrical mapping via coherent states, phase transitions are investigated and compared within two algebraic cluster models. The difference between the Semimicroscopic Algebraic Cluster Model (SACM) and the Phenomenological Algebraic Cluster Model (PACM) is that the former strictly observes the Pauli exclusion principle between the nucleons of the individual clusters, while the latter ignores it. From the technical point of view the SACM is more involved mathematically, while the formalism of the PACM is closer to that of other algebraic models with different physical content. First- and second-order phase transitions are identified in both models, while in the SACM a critical line also appears. Analytical results are complemented with numerical studies on {alpha}-cluster states of the neon-20 and magnesium-24 nuclei.
We present first-principle predictions for the liquid-gas phase transition in symmetric nuclear matter employing both two- and three-nucleon chiral interactions. Our discussion focuses on the sources of systematic errors in microscopic quantum many body predictions. On the one hand, we test uncertainties of our results arising from changes in the construction of chiral Hamiltonians. We use five different chiral forces with consistently derived three-nucleon interactions. On the other hand, we compare the ladder resummation in the self-consistent Greens functions approach to finite temperature Brueckner--Hartree--Fock calculations. We find that systematics due to Hamiltonians dominate over many-body uncertainties. Based on this wide pool of calculations, we estimate that the critical temperature is $T_c=16 pm 2$ MeV, in reasonable agreement with experimental results. We also find that there is a strong correlation between the critical temperature and the saturation energy in microscopic many-body simulations.
The past two decades have witnessed tremendous progress in the microscopic description of atomic nuclei. The Topical Review `The Future of Nuclear Structure aims at summarizing the current state-of-the-art microscopic calculations in Nuclear Theory and to give a useful reference for young researches who wish to learn more about this exciting discipline.
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