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. The complementarity of the IBA and geometrical approaches will be demonstrated by three examples. First, it will be shown that specific special solutions of the Bohr Hamiltonian correspond to the borders of the critical region of the IBA. Second, it will be demonstrated that the distinct patterns exhibited in different transitional regions by the experimental energy staggering in gamma-bands can be reproduced both by the IBA and by special solutions of the Bohr Hamiltonian. Third, a first attempt to obtain a IBA SU(3) level scheme from a special solution of the Bohr Hamiltonian will be presented.
The ground states of some nuclei are described by densities and mean fields that are spherical, while others are deformed. The existence of non-spherical shape in nuclei represents a spontaneous symmetry breaking.
Metz et al PRL (83), 1542 (1999) have presented evidence for supersymmetry in atomic nuclei but their model Hamiltonian fails to distinguish between irreducible representations that occur with multiplicities greater than one. This failure raises serious questions as to the validity of the evidence.
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.
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.
The relation of the shell, collective and cluster models of the atomic nuclei is discussed from the viewpoint of symmetries. In the fifties the U(3) symmetry was found as their common part for a single shell problem. For multi major-shell excitations, considered here, the U(3)$\otimes$U(3) dynamical symmetry turns out to be their intersection.
This review consists of three parts: (a) what every atomic physicist needs to know about the physics of light nuclei; (b) what nuclear physicists can do for atomic physics; (c) what atomic physicists can do for nuclear physics. A brief qualitative overview of the nuclear force and calculational techniques for light nuclei will be presented, with an emphasis on debunking myths and on recent progress in the field. Nuclear quantities that affect precise atomic measurements will be discussed, together with their current theoretical and experimental status. The final topic will be a discussion of t…
Atomic experiments bring meaningful and valuable information on fundamental symmetries. The hypothesis of a large ($\sim 100$ eV) P-odd weak matrix element between single-particle states in heavy nuclei is inconsistent with the results of atomic PNC experiments. Upper limits on CP-violation obtained in atomic and molecular spectroscopy are as informative as those established in neutron physics. Very strict upper limits on T-odd, P-even interactions (nucleon-nucleon, electron-nucleon, electron-electron, and $β$-decay) are derived from the same atomic and neutron experiments.
The spectral statistics of low--lying states of several $fp$ shell nuclei are studied with realistic shell--model calculations. For Ca isotopes, we find significant deviations from the predictions of the random--matrix theory which suggest that some spherical nuclei are not as chaotic in nature as the conventional view assumes.
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）
The incompressibility of finite fermionic systems is investigated using analytical approaches and microscopic models. The incompressibility of a system is directly linked to the zero-point kinetic energy of constituent fermions, and this is a universal feature of fermionic systems. In the case of atomic nuclei, this implies a constant value of the incompressibility in medium-heavy and heavy nuclei. The evolution of nuclear incompressibility along Sn and Pb isotopic chains is analyzed using global microscopic models, based on both non-relativistic and relativistic energy functionals. The result…
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…
We discuss the role of the broken symmetries in the connection of the shell, collective and cluster models. The cluster-shell competition is described in terms of cold quantum phases. Stable quasi-dynamical U(3) symmetry is found for specific large deformations for a Nilsson-type Hamiltonian.
The DIRHB package consists of three Fortran computer codes for the calculation of the ground-state properties of even-even atomic nuclei using the framework of relativistic self-consistent mean-field models. Each code corresponds to a particular choice of spatial symmetry: the DIRHBS, DIRHBZ and DIRHBT codes are used to calculate nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes, respectively. Reflection symmetry is assumed in all three cases. The latest relativistic nuclear energy density functionals are implemented in the codes, thus ena…
To show the existence of precursor phenomena of the transition order$\ to$chaos in atomic nuclei a simple analysis has been made, based on a recent criterion proposed by Pavli\-chenkov. The basic idea is that nonlinear effects in rotational bands should lead to bifurcation, which qualitatively changes the spectrum for one of the nuclear excitation branches. Experimental data concerning the isotopes of Er, Hf, Yb, Os, Dy, W strongly support the above criterion.
Nuclear mean-field models are briefly reviewed to illustrate its foundation and necessity of state dependence in effective interactions. This state dependence is successfully taken into account by the density dependence, leading to the energy density functional. Recent results for photoabsorption cross sections in spherical and deformed Nd isotopes are shown.
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 …
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…
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.
A systematics of the atomic nuclei in the frame of the nucleon number $A = Z + N$ and the proton-neutron difference $F = Z - N$ is considered. The classification scheme is provided by means of the non-compact algebra $sp(4,R)$. In this scheme the nuclei are ordered into isobaric multiplets, for which $A={fix}$, as well as in F-multiplets, for which $F={fix}$. The dependence of the mass excess $Δ$, the first exited states $E_{2^+}$ and the ratio $R_2=E_{4^+}/E_{2^+}$ on the nucleon number $A$ is empirically investigated within the $F$-multiplets. Appropriate filters are used to study the proper…
The spectroscopic strengths of two-nucleon transfer reactions constitute a stringent test for two-nucleon correlations in the nuclear wave functions. A comparison between the recently measured 198Hg(d,alpha)196Au reaction and the predictions from the nuclear quartet supersymmetry lends further support to the validity of supersymmetry in nuclear physics.
An interesting aspect of nuclear dynamics is the co--existence, in atomic nuclei, of regular and chaotic states. In the first part of the present work, we review the state of the art of nuclear dynamics and use a schematic shell model to show how a very simple and schematic nucleon--nucleon interaction can produce an order$\to$chaos transition. The second part is devoted to a discussion of the wave function behaviour and decay of chaotic states using some simple models (to be published in Rivista Nuovo Cimento).
The degrees of freedom associated with shape fluctuations and space orientation of atomic nuclei are analyzed with effective forces and large configuration spaces. A pedagogical theoretical introduction to the topic of symmetries restoration broken in the mean field approach as well as to the concept of generator coordinate is presented. We discuss global properties, like binding energies, two neutron separation energies and quadrupole moments, as well as spectroscopic ones like excitation energies or transition probabilities. The analysis covers selected examples of light and heavy nuclei, as…
A systematic analysis of the spherical-to-deformed shape phase transition in even-even rare-earth nuclei from $_{58}$Ce to $_{74}$W is carried out in the framework of the interacting boson model. These results are then used to calculate nuclear radii and electric monopole (E0) transitions with the same effective operator. The influence of the hexadecapole degree of freedom ($g$ boson) on the correlation between radii and E0 transitions thus established, is discussed.
The charge-dependent realistic nuclear Hamiltonian for a nucleus, composed of neutrons and protons, can be successfully approximated by a charge-independent one. The parameters of such a Hamiltonian, i.e., the nucleon mass and the NN potential, depend upon the mass number A, charge Z and isospin quantum number T of state of the studied nucleus.
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.
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.
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 nonlinear model of pionic condensate in nuclei by G. Preparata can be efficiently verified by investigation of the quasielastic knockout process of pions out of nuclei by high energy electrons. First, a momentum distribution (MD) of the collective pions has a bright maximum at q=0.3 Gev.Second the excitation spectrum of a recoil nucleus is concentrated at low energies E lesser than 1MeV. The results for the pion knockout from mesonic clouds of individual nucleons are absolutely different. The latter results are presented both for pion and rho-meson clouds localized on nucleons.
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.
The dynamics of monopole giant resonances in nuclei is analyzed in the time-dependent relativistic mean-field model. The phase spaces of isoscalar and isovector collective oscillations are reconstructed from the time-series of dynamical variables that characterize the proton and neutron density distributions. The analysis of the resulting recurrence plots and correlation dimensions indicate regular motion for the isoscalar mode, and chaotic dynamics for the isovector oscillations. Information-theoretic functionals identify and quantify the nonlinear dynamics of giant resonances in quantum syst…
The evolution of the pairing correlations from closed shell to middle shell nuclei is analyzed with a Finite Range Density Dependent interaction in the Sn isotopes. As theoretical approaches we use the Hartree-Fock-Bogoliubov, the Lipkin-Nogami, their particle number projected counterparts and the full variation after particle number projection method. We find that whereas all approaches succeed rather well in the description of the total energy they differ significantly in the pairing correlation content of the wave functions. The description of the evolution from the weak to the strong pairi…
Experimental studies of one nucleon knockout from magic nuclei suggest that their nucleon orbits are not fully occupied. This conflicts a commonly accepted view of the shell closure associated with such nuclei. The conflict can be reconciled if the overlap between initial and final nuclear states in a knockout reaction are calculated by a non-standard method. The method employs an inhomogeneous equation based on correlation-dependent effective nucleon-nucleon (NN) interactions and allows the simplest wave functions, in which all nucleons occupy only the lowest nuclear orbits, to be used. The m…
Microscopic investigation of magnetic and antimagnetic rotational motion in atomic nuclei
University of Kashmir（克什米尔大学）；Govt. Degree College Kulgam（库尔加姆政府学位学院）；Indian Institute of Technology Bombay（孟买印度理工学院）；University of Engineering and Management（工程与管理大学）；GDC Shopian（肖皮安政府学位学院）；Islamic University of Science and Technology（伊斯兰科学技术大学）
Monograph includes the results of the scientific work of the author for approximately 10 years and it is dedicated to theoretical studies of the structure of light atomic nuclei on the basis of potential cluster model with the forbidden states. Are examined questions of the single-valued construction of the intercluster potentials, which contain the forbidden states and simultaneously applied in the continuous and discrete spectra for the light nuclear systems with a mass of from 2 to 16. Is presented the mathematical apparatus and some calculation methods, utilized in the cluster model. Many …
A system of equations is obtained for the Cooper gap in nuclei. The system takes two mechanisms of superfluidity into account in an approximation quadratic in the phonon- production amplitude : a Bardeen- Cooper- Schrieffer (BCS) type mechanism and a quasiparticle- phonon mechanism. These equations are solved for 120 Sn in a realistic approximation. If the simple procedures proposed are used to determine the new particle- particle interaction and to estimate the average effect, then the contribution of the quasiparticle- phonon mechanism to the observed width of the pairing gap is 26% and the …
Based on the leading-order covariant pionless effective field theory, a relativistic nuclear Hamiltonian is derived and solved using the variational Monte Carlo approach for $A\le 4$ nuclei by representing the nuclear many-body wave functions with a symmetry-based artificial neural network. It is found that the relativistic effects rescue the renormalizability of the theory, and overcome the energy collapse problem for $^3$H and $^4$He without promoting a repulsive three-nucleon interaction to leading order as in nonrelativistic calculations. Nevertheless, to exactly reproduce the experimental…
Using a classical analytical criterion (that of curvature) and numerical results (Poincarè sections and spectral statistics), a transition order--chaos--order in the roto--vibrational model of atomic nuclei has been shown. Numerical calculations were performed for some deformed nuclei.
Toward $\textit{Ab Initio}$ Quantum Simulations of Atomic Nuclei Using Noisy Qubits
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University（北京大学物理学院核物理与技术国家重点实验室）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
The possible existence of stable axial octupole and tetrahedral deformations is investigated in $^{80}$Zr and $^{98}$Zr. HFBCS calculations with parity projection have been performed for various parametrizations of the Skyrme energy functional. The correlation and excitation energies of negative parity states associated with shape fluctuations have been obtained using the generator coordinate method (GCM). The results indicate that in these nuclei both the axial octupole and tetrahedral deformations are of dynamic character and possess similar characteristics. Various Skyrme forces give consis…
Collisions of actinide nuclei form, during very short times of few $10^{-21}$ s, the heaviest ensembles of interacting nucleons available on Earth. Such very heavy ions collisions have been proposed as an alternative way to produce heavy and superheavy elements. These collisions are also used to produce super-strong electric fields by the huge number of interacting protons to test spontaneous positron-electron ($e^+e^-$) pair emission predicted by the quantum electrodynamics theory. The time-dependent Hartree-Fock theory which is a fully microscopic quantum approach is used to study collision …
The Lagrangian density of standard relativistic mean-field (RMF) models with density-dependent meson-nucleon coupling vertices is modified by introducing couplings of the meson fields to derivative nucleon densities. As a consequence, the nucleon self energies, that describe the effective in-medium interaction, become momentum dependent. In this approach it is possible to increase the effective (Landau) mass of the nucleons, that is related to the density of states at the Fermi energy, as compared to conventional relativistic models. At the same time the relativistic effective (Dirac) mass is …
Instituto de Física Corpuscular (IFIC), Consejo Superior de Investigaciones Científicas (CSIC) and Universidad de Valencia（粒子物理研究所（IFIC），西班牙国家研究委员会（CSIC）和瓦伦西亚大学）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；Argonne National Laboratory（阿贡国家实验室）；INFN-TIFPA Trento Institute for Fundamental Physics and Applications（意大利核物理研究所-特伦托基础物理与应用研究所）
A simple, empirical signature of a first order phase transition in atomic nuclei is presented, the ratio of the energy of the 6+ level of the ground state band to the energy of the first excited 0+ state. This ratio provides an effective order parameter which is not only easy to measure, but also distinguishes between first and second order phase transitions and takes on a special value in the critical region. Data in the Nd-Dy region show these characteristics. In addition, a repeating degeneracy between alternate yrast states and successive excited 0+ states is found to correspond closely to…
A new symplectic-based shell-model approach to clustering in atomic nuclei is proposed by considering the simple system $^{20}$Ne. Its relation to the collective excitations of this system is mentioned as well. The construction of the Pauli allowed Hilbert space of the cluster states with maximal permutational symmetry is given for the $^{16}$O+$^{4}$He $\rightarrow$ $^{20}$Ne channel in the case of one-component many-particle nuclear system. The equivalence of the obtained cluster model space to that of the semi-microscopic algebraic cluster model is demonstrated.
We study time-dependent coupled-cluster theory in the framework of nuclear physics. Based on Kvaal's bi-variational formulation of this method [S. Kvaal, arXiv:1201.5548], we explicitly demonstrate that observables that commute with the Hamiltonian are conserved under time evolution. We explore the role of the energy and of the similarity-transformed Hamiltonian under real and imaginary time evolution and relate the latter to similarity renormalization group transformations. Proof-of-principle computations of He-4 and O-16 in small model spaces, and computations of the Lipkin model illustrate …
Shell model calculations reveal that the ground and low-lying yrast states of the $N=Z$ nuclei $^{92}_{46}$Pd and $^{96}$Cd are mainly built upon isoscalar spin-aligned neutron-proton pairs each carrying the maximum angular momentum J=9 allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region. This mode of excitation is unique in nuclei and indicates that the spin-aligned pair has to be considered as an essential building block in nuclear structure calculations. In this contribution we will discuss this neutron-proton pair coupling scheme in detail. In particular, we will explo…
We consider the development of Cooper pairs in a self-consistent Hartree Fock mean field for the even Sm isotopes. Results are presented at the level of a BCS treatment, a number-projected BCS treatment and an exact treatment using the Richardson ansatz. While projected BCS captures much of the pairing correlation energy that is absent from BCS, it still misses a sizable correlation energy, typically of order $1 MeV$. Furthermore, because it does not average over the properties of the fermion pairs, the exact Richardson solution permits a more meaningful definition of the Cooper wave function …
The three moments of inertia associated with the wobbling mode built on the superdeformed states in 163Lu are investigated by means of the cranked shell model plus random phase approximation to the configuration with an aligned quasiparticle. The result indicates that it is crucial to take into account the direct contribution to the moments of inertia from the aligned quasiparticle so as to realize J_x > J_y in positive-gamma shapes. Quenching of the pairing gap cooperates with the alignment effect. The peculiarity of the recently observed 163Lu data is discussed by calculating not only the el…
