Quantum phase transitions and structural evolution in nuclei

Abstract

Recently, the idea of quantum phase transitions has been applied to equilibrium shape changes in finite atomic nuclei. An introduction to and discussion of this concept, both from the macroscopic perspective and from a microscopic approach, in terms of shell structure and residual interactions is presented. Following this, the quantitative predictions of the critical point symmetries (CPS) X(5) and E(5) are discussed in some detail and compared to the data in a number of nuclei and mass regions. Any successful new model paradigm soon generates modifications to improve the predictions and, likewise, often spawns related models inspired by the original ansatz. This is eminently true of the CPS and we make an effort to briefly discuss this rapidly advancing area in terms of a number of recent modifications to the CPS as well as related models that are couched in a geometrical perspective.

Ground state phase transition in the Nilsson mean-field plus standard pairing model

“…Therefore, our analysis provides a microscopic picture that the ground state phase transitional behaviors may be driven by the competition between the Nilsson mean-field and the pairing interaction based on the present model. It has been recognized that the emergence of the collective phenomena in these nuclei are related to the competition between the pairing interaction and the deformationdriven quadrupole-quadrupole interaction [4,7]. However, the analysis shown in this work is based on the Nilsson meanfield plus standard pairing model, in which the quadrupolequadrupole interaction is replaced by the deformation.…”

“…The two-neutron separation energy has also been taken as an effective order parameter to identify the phase transition, which was investigated extensively in both experimental and theoretical approaches for even-even and odd-A systems [7,8].…”

“…These studies have provided new insights and understanding of the evolution of nuclear shapes and energy level structures in transitional regions [7]. Theoretical studies of the QPTs in nuclei are typically based on the collective model and the interacting boson model [1,4,[8][9][10][11].…”

“…Since a nuclear system is finite, only a crossover may be observed instead of a dramatic and sudden change or discontinuity in these quantities predicted from the classical limit of the theories. [7] Nuclear pairing correlation, as an important part of the residual interactions necessary to augment any nuclear meanfield theory, represents one of the main and longstanding pillars of current understanding of nuclear structure [17]. Particularly, the pairing interaction in the nuclear shell model plays a key role to reproduce ground-state properties of nuclei, such as binding energies, two-neutron (proton) separation energies, odd-even effects, and excitation spectra, etc.…”

Recent progress in theoretical studies of nuclear magnetic moments

“…The transitions in nuclear shapes, also referred as quantum phase transition (QPT) reveal the changes of dominant configurations or distinctly different shapes in nuclear states. In the last decade, QPTs in nuclei have attracted a lot of attention both in theory and experiment [72][73][74][75][76]. Meanwhile, several Chinese groups have published their results on this subject too [77][78][79][80][81][82][83][84][85][86][87].…”