Nuclear structure theory has recently gone through a major renewal with the development of ab initio techniques that can be applied to a large number of atomic nuclei, well beyond the light sector that had been traditionally targeted in the past. Self-consistent Green's function theory is one among these techniques. The present work aims to give an overview of the self-consistent Green's function approach for atomic nuclei, including examples of recent applications and a discussion on the perspectives for extending the method to nuclear reactions, doubly open-shell systems and heavy nuclei.
Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - II. Numerical implementation at second order with a two-nucleon interaction
We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact approach. We consider the limitations of the laboratory frame formulation of the Green's function theory and discuss why the body-fixed frame formulation is needed in order to go beyond the Born-Oppenheimer theory. We give exact forms of the electronic and nuclear Green's functions written in terms of the exact factorized states, providing a systematic approach b…
We discuss recent \emph{ab initio} calculations based on self-consistent Green's function theory. It is found that a simple extension of the formalism to account for two-nucleon scattering outside the model space allows to calculate non-soft interactions. With this, it is possible to make predictions for Lattice QCD potentials, obtained so far at pion masses of $m_π= 0.47$GeV/c$^2$. More traditional calculations that use saturating chiral EFT forces yield a good description of nuclear responses and nucleon knockout spectroscopy.
Ab initio calculations of bulk nuclear properties (ground-state energies, root mean square charge radii and charge density distributions) are presented for seven complete isotopic chains around calcium, from argon to chromium. Calculations are performed within the Gorkov self-consistent Green's function approach at second order and make use of two state-of-the-art two- plus three-nucleon Hamiltonians, $NN$+$3N\text{(lnl)}$ and NNLO$_{\text{sat}}$. An overall good agreement with available experimental data is found, in particular for differential energies (charge radii) when the former (latter)…
The present paper is a comment regarding the robustness of the chirality in presence of the space-reflection asymmetry, which leads to pairs of interleaved positive- and negative-parity bands. The recent results reported in Ref. \cite{2006.12062} which introduced the $chiture$ and $chiplex$ quantum numbers to describe an ideal nuclear system with simultaneous chiral and reflection symmetry breaking, are commented.
To study the exotic odd nuclear systems, the self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with Green's function technique is extended to include blocking effects with the equal filling approximation. Detailed formula are presented.To perform the integrals of the Green's function properly, the contour paths $C_{\rm b}^{-}$ and $C_{\rm b}^{+}$ introduced for the blocking effects should include the blocked quasi-particle state but can not intrude into the continuum area. By comparing with the box-discretized calculations, the great advantages of the Green's function …
Long-lived opposite-parity states and the onset of octupole collectivity in atomic nuclei
San Diego State University（圣地亚哥州立大学）；Ho Chi Minh City University of Education（胡志明市教育大学）；Institute for Basic Science（基础科学研究院）；Tel Aviv University（特拉维夫大学）
We test the Coulomb exchange and correlation energy density functionals of electron systems for atomic nuclei in the local density approximation (LDA) and the generalized gradient approximation (GGA). For the exchange Coulomb energies, it is found that the deviation between the LDA and GGA ranges from around $ 11 \, \% $ in $ {}^{4} \mathrm{He} $ to around $ 2.2 \, \% $ in $ {}^{208} \mathrm{Pb} $, by taking the Perdew-Burke-Ernzerhof (PBE) functional as an example of the GGA\@. For the correlation Coulomb energies, it is shown that those functionals of electron systems are not suitable for at…
It is shown that the collinear tripartition in the case of spontaneous fission of 252Cf generically follows the principles of the collective Bohr's model. Qualitative consideration is supported by the numerical trajectory calculations.
A systematic study of $γ$-bands observed in atomic nuclei is performed using the triaxial projected shell model (TPSM) approach. The staggering phase between the even and odd spin members of the $γ$-band for most the nuclei investigated in the present work is found to have even-I-below-odd-I, which in the framework of the collective model is considered as a signature of $γ$-softness. It is observed that out of twenty-three systems studied, only four nuclei, namely, $^{76}$Ge, $^{112}$Ru, $^{170}$Er and $^{232}$Th depict staggering phase with odd-I-below-even-I, which is regarded as an indicati…
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.
We propose a phenomenological approach to examine the role of short- and long-range nucleon-nucleon correlations in the quenching of single-particle strength in atomic nuclei and their evolution in asymmetric nuclei and neutron matter. These correlations are thought to be the reason for the quenching of spectroscopic factors observed in $\rm (e,e'p)$, $\rm (p,2p)$ and transfer reactions. We show that the recently observed increase of the high-momentum component of the protons in neutron-rich nuclei is consistent with the reduced proton spectroscopic factors. Our approach connects recent result…
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 microscopic origin of the $γ$-softness (fluctuations in the triaxiality parameter $γ$ of the nuclear shape) observed in atomic nuclei is studied in the framework of the triaxial projected shell model approach, which is based on the deformed mean-field picture with multi-quasiparticle configuration space. It is demonstrated that the coupling to quasiparticle excitations drives the system from a $γ$-rigid to a $γ$-soft pattern. As an illustrative example for a $γ$-soft nucleus, a detailed study has been performed for the $^{104}$Ru nucleus. The experimental energies and a large sample of mea…
We predict the limits of existence of atomic nuclei, the proton and neutron drip lines, from the light through medium-mass regions. Starting from a chiral two- and three-nucleon interaction with good saturation properties, we use the valence-space in-medium similarity renormalization group to calculate ground-state and separation energies from helium to iron, nearly 700 isotopes in total. We use the available experimental data to quantify the theoretical uncertainties for our ab initio calculations towards the drip lines. Where the drip lines are known experimentally, our predictions are consi…
A very good linear correlation is found between the four-point charge radius relation $δR_{2p-2n}(Z,N)$ with that of quadrupole deformation data in even-even nuclei. This results in a further improved charge radius relation that holds in a precision of about 5$\times 10^{-3}$ fm. Such correlations are also seen in global nuclear models, their precisions, however, are not enough to be consistent with the experimental data. The new relation between charge radii and deformation of even-even nuclei can be generalized to the reduced electric quadrupole transition probability $B(E2)$ between the fir…
While the main features of atomic nuclei are well described by nuclear mean-field models, there is a large and growing body of evidence which indicates an important additional role played by spatially-correlated nucleon-nucleon structures. The role of nucleonic structures was first suggested by Heidmann in 1950 to explain pick-up reactions of energetic nucleons. Since then a steady flux of new experimental evidence has confirmed the presence of similar structures inside atomic nuclei, dominated by correlations between pairs of nucleons. The role of these internal nucleon-nucleon correlations h…
A chronicle describing the historical context and the development of ideas and experiments leading to the discovery of the back-bending phenomenon in rapidly rotating atomic nuclei some 50 years ago is presented. The moment of inertia of some atomic nuclei increases anomalously at a certain rotational frequency, revealing important clues to our understanding of nuclear structure. I highlight the decisive interactions and contacts between experimentalists and theorists, which created the right environment, allowing for the revelation of an undetected phenomenon in Nature. Finally, I reflect on …
The nuclear Chirality-Parity (ChP) violation, a simultaneous breaking of chiral and reflection symmetries in the intrinsic frame, is investigated with a reflection-asymmetric triaxial particle rotor model. A new symmetry for an ideal ChP violation system is found and the corresponding selection rules of the electromagnetic transitions are derived. The fingerprints for the ChP violation including the nearly degenerate quartet bands and the selection rules of the electromagnetic transitions are provided. These fingerprints are examined for ChP quartet bands by taking a two-$j$ shell $h_{11/2}$ a…
Nuclides sharing the same mass number (isobars) are observed ubiquitously along the stability line. While having nearly identical radii, stable isobars can differ in shape, and present in particular different quadrupole deformations. We show that even small differences in these deformations can be probed by relativistic nuclear collisions experiments, where they manifest as deviations from unity in the ratios of elliptic flow coefficients taken between isobaric systems. Collider experiments with isobars represent, thus, a unique means to obtain quantitative information about the geometric shap…
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）
From closed shells to open shells: Coupled-cluster calculations of atomic nuclei
Johannes Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学）；Facility for Rare Isotope Beams, Michigan State University（密歇根州立大学稀有同位素束设施）；Oak Ridge National Laboratory（橡树岭国家实验室）；Université Libre de Bruxelles（布鲁塞尔自由大学）；KU Leuven（荷语鲁汶大学）；Helmholtz-Institut Mainz（美因茨亥姆霍兹研究所）；CEA, Université Paris-Saclay（法国原子能和替代能源委员会，巴黎萨克雷大学）；University of Tennessee（田纳西大学）
Facility for Rare Isotope Beams, Michigan State University（密歇根州立大学稀有同位素束设施）；Physics Division, Oak Ridge National Laboratory（橡树岭国家实验室物理部）；Department of Physics and Astronomy, University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校物理与天文学系）
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.
Using the one-dimensional potential well with realistic parameters for atomic nuclei, we illustrate the movement of the poles of the S-matrix, and the transmission coefficient when the well supports an anti-bound state. We calculate the phase shift of the atomic nuclei 5He using the three-dimensional potential well, and compare it with the experimental one. The paper gives a glance of some of the properties found in realistic loosely and resonant nuclear systems, using equations at the level of undergraduate students.
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…
