Shape/phase transitions in atomic nuclei have first been discovered in the framework of the Interacting Boson Approximation (IBA) model. Critical point symmetries appropriate for nuclei at the transition points have been introduced as special solutions of the Bohr Hamiltonian, stirring the introduction of additional new solutions describing wide ranges of nuclei. A short review of these recent developments will be attempted.
In typical microscopic approaches, particularly when pairing correlations are present, nuclei and nuclear fragments do not have well defined quantum numbers and symmetries should be restored. I present here a formalism for the simultaneous projection of total particle numbers of a nucleus, particle number of reaction fragments, and of the reaction fragment intrinsic spins and of their correlation, and also for their symmetry restored densities and total energies. These new formulas for the symmetry restored quantities, are free of any singularities, unlike those in the previously introduced pr…
Global symmetries and symmetry breaking patterns of QCD with light quarks, in particular chiral symmetry, provide basic guidance not only for low-energy hadron physics but also for nuclear forces and the nuclear many-body problem. Recent developments of Chiral Effective Field Theory applications to nuclear and neutron matter are summarized, with special emphasis on a (non-perturbative) extension using functional renormalisation group methods. Topics include: nuclear thermodynamics, extrapolations to dense baryonic matter and constraints from neutron star observables.
We present recent developments obtained in the so-called N2LO extension of the usual Skyrme pseudo-potential. In particular, we discuss the isovector splitting mass in infinite nuclear matter and the pairing gaps of selected semi-magic even-even nuclei.
This review presents some of the challenges in constructing models of atomic nuclei starting from theoretical descriptions of the strong interaction between nucleons. The focus is on statistical computing and methods for analyzing the link between bulk properties of atomic nuclei, such as radii and binding energies, and the underlying microscopic description of the nuclear interaction. The importance of careful model calibration and uncertainty quantification of theoretical predictions is highlighted.
Origin of octupole deformation softness in atomic nuclei
Center for Exotic Nuclear Studies, Institute for Basic Science (IBS)（基础科学研究所）；Department of Physics, Ho Chi Minh City University of Education（胡志明市教育大学物理系）；Department of Theoretical Physics, Faculty of Physics and Engineering Physics, University of Science（理科大学物理与工程物理学院理论物理系）；Vietnam National University, Ho Chi Minh City（胡志明市越南国立大学）；Rare Isotope Science Project, Institute for Basic Science（基础科学研究所稀有同位素科学项目）；School of Physics and Astronomy, Tel Aviv University（特拉维夫大学物理与天文学学院）
We present a new statistical tool based on random sampling to assess the confidence interval of Pearson's and Spearman's correlation coefficients. These estimators are then used to quantify the statistical correlations among the neutron skin thickness of atomic nuclei and the slope of the symmetry energy in the infinite nuclear medium.
The quantum phases of superconductivity and superfluidity are characterised mathematically by the Yang concept of Off-Diagonal Long Range Order (ODLRO), related to the existence of a large eigenvalue of the density matrix. We analyse how the Yang criterion applies for various Hamiltonians commonly employed to describe superfluid-type correlations in atomic nuclei. For like-particle pairing Hamiltonians the behaviour of the largest eigenvalue of two-body density matrix shows a clear evidence for a transition between a normal to a paired phase. However, this is not the case for the isoscalar pro…
The Pauli exclusion principle induces a repulsion between composite systems of identical fermions such as colliding atomic nuclei. Our goal is to study how heavy-ion fusion is impacted by this "Pauli repulsion". We propose a new microscopic approach, the density-constrained frozen Hartree-Fock method, to compute the bare potential including the Pauli exclusion principle exactly. Pauli repulsion is shown to be important inside the barrier radius and increases with the charge product of the nuclei. Its main effect is to reduce tunnelling probability. Pauli repulsion is part of the solution to th…
Spontaneous symmetry breaking in non-relativistic quantum systems has previously been addressed in the framework of effective field theory. Low-lying excitations are constructed from Nambu-Goldstone modes using symmetry arguments only. We extend that approach to finite systems. The approach is very general. To be specific, however, we consider atomic nuclei with intrinsically deformed ground states. The emergent symmetry breaking in such systems requires the introduction of additional degrees of freedom on top of the Nambu-Goldstone modes. Symmetry arguments suffice to construct the low-lying …
The role of discrete (or point-group) symmetries in alpha-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the alpha-particles. Particular attention is paid to the discrete symmetry of the geometric arrangement of the alpha-particles, and the consequences for the structure of the corresponding rotational bands. The method is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in a simple way as a consequence of the underlying discrete symmetry that characterizes the geometric…
Description of a nuclear system in its ground state and at low excitations based on the equation of state (EoS) around normal density is presented. In the expansion of the EoS around the saturation point additional spin polarization terms are taken into account. These terms, together with the standard symmetry term, are responsible for appearance of the $α$-like clusters in the ground state configurations of the N=Z even-even nuclei. At the nuclear surface these clusters can be identified as alpha particles. A correction for the surface effects is introduced for atomic nuclei. Taking into acco…
First order quantum phase transition (QPT) between spherical and axially deformed nuclei shows coexisting, but well-separated regions of regular and chaotic dynamics. We employ a Hamiltonian of the Arima-Iachello Interacting Boson Model (IBM) with an arbitrarily high potential barrier separating the phases. Classical and quantum analyses reveal markedly distinct behavior of the two phases: Deformed phase is completely regular, while the spherical phase shows highly chaotic dynamics, similar to the Hénon-Heiles system. Rotational bands with quasi-SU(3) characteristics built upon the regular vib…
Quantum Monte Carlo methods are powerful numerical tools to accurately solve the Schrödinger equation for nuclear systems, a necessary step to describe the structure and reactions of nuclei and nucleonic matter starting from realistic interactions and currents. These ab-initio methods have been used to accurately compute properties of light nuclei -- including their spectra, moments, and transitions -- and the equation of state of neutron and nuclear matter. In this work we review selected results obtained by combining quantum Monte Carlo methods and recent Hamiltonians constructed within chir…
It is shown, that the Gamow-like model with only one adjustable parameter - radius constant is able to reproduce well the alpha-decay half-lives for all even-even nuclei with the proton number larger than 50. The systematics for odd-A and odd-odd isotopes can be also well described when ones introduces an additional hindrance factor. Similar model based on the W. J. Swiatecki idea from 1955 is developed to reproduce the spontaneous fission half-lives of transactinide nuclei. The achieved accuracy of reproduction of the data is better than that obtained in more advanced theories.
sp(4,R)-systematics of atomic nuclei. F-multiplets and nuclear structure
本文在核子数$A = Z + N$和质子中子差$F = Z - N$的框架下考虑原子核的系统学。分类方案是由非紧代数$sp(4,R)$。在这个方案中，原子核被排列成同量异位的多重态，其中$A={fix}$，以及F-多重态，其中$F={fix}$。在$F$ -多重态中，研究了质量过剩$Δ$、第一激发态$E_{2^+}$和比值$R_2=E_{4^+}/E_{2^+}$对核子数$A$的依赖性.适当的过滤器用于研究质量过剩的性质。观察到许多结构效应。对于具有相同的$A$值和相反的$F$值的原子核的能级，清楚地表明了镜像对称性。
原子核动力学的一个有趣的方面是规则态和混沌态在原子核中的共存。在本工作的第一部分中，我们回顾了核动力学的艺术状态，并使用一个示意性的壳模型来显示一个非常简单和示意性的核子-核子相互作用可以产生一个有序的$\to$混沌过渡。第二部分是专门讨论的波函数的行为和混沌状态的衰减使用一些简单的模型（将发表在Rivista Nuovo Cimento）。
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband $E2$ transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
We show that distinct emergent symmetries, such as partial dynamical symmetry and quasi dynamical symmetry, can occur simultaneously in the same or different eigenstates of the Hamiltonian. Implications for nuclear spectroscopy in the rare-earth region and for first-order quantum phase transitions between spherical and deformed shapes, are considered.
Starting from a Skyrme interaction with tensor terms, the $β$-decay rates of $^{52}$Ca have been studied within a microscopic model including the $2p-2h$ configuration effects. We observe a redistribution of the strength of Gamow-Teller transitions due to the $2p-2h$ fragmentation. Taking into account this effect results in a satisfactory description of the neutron emission probability of the $β$-decay in $^{52}$Ca.
Random one plus two-body hamiltonians invariant with respect to $O({\cal N}_1) \oplus O({\cal N}_2)$ symmetry in the group-subgroup chains $U({\cal N}) \supset U({\cal N}_1) \oplus U({\cal N}_2) \supset O({\cal N}_1) \oplus O({\cal N}_2)$ and $U({\cal N}) \supset O({\cal N}) \supset O({\cal N}_1) \oplus O({\cal N}_2)$ chains of a variety of interacting boson models are used to investigate the probability of occurrence of a given $(ω_1 ω_2)$ irreducible representation (irrep) to be the ground state in even-even nuclei; $[ω_1]$ and $[ω_2]$ are symmetric irreps of $O({\cal N}_1)$ and $O({\cal N}_…
The influence of the diffuse surface layer of a finite nucleus on the mean square radii and their isotopic shift is investigated. We present the calculations within the Gibbs-Tolman approach using the experimental values of the nucleon separation energies. Results are compared with that obtained by means of direct variational method based on Fermi-like trial functions.
The moment of inertia of even-even deformed nuclei which are derived on the basis of hydrodynamical model yield values that are too small compared with the experimental [Davidson 1965] ones. We expect that these contradictions come from the consideration only the first term in $R$- expansion in spite of not containing parameters indicating deformity of the nucleus, and neglecting all other terms which include the deformation parameters $αλμ$. In this work, the first three terms in $R$- expansion are taken into account. The results are more realistic and too much better the previous ones.
We discuss the role of QCD symmetries in understanding the eta and etaprime mesons in nuclear media. Recent results on the etaprime mass in nuclei from the CBELSA/TAPS collaboration are very similar to the prediction of the Quark Meson Coupling model.
The algebraic cluster model is is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle for 12C, and a regular tetrahedron for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles.
