The chart of the nuclides is limited by particle drip lines beyond which nuclear stability to proton or neutron emission is lost. Predicting the range of particle-bound isotopes poses an appreciable challenge for nuclear theory as it involves extreme extrapolations of nuclear masses beyond the regions where experimental information is available. Still, quantified extrapolations are crucial for a variety of applications, including the modeling of stellar nucleosynthesis. We use microscopic nuclear mass models and Bayesian methodology to provide quantified predictions of proton and neutron separation energies as well as Bayesian probabilities of existence throughout the nuclear landscape all the way to the particle drip lines. We apply nuclear density functional theory with several energy density functionals. To account for uncertainties, Bayesian Gaussian processes are trained on the separation-energy residuals for each individual model, and the resulting predictions are combined via Bayesian model averaging. This framework allows to account for systematic and statistical uncertainties and propagate them to extrapolative predictions. We characterize the drip-line regions where the probability that the nucleus is particle-bound decreases from $1$ to $0$. In these regions, we provide quantified predictions for one- and two-nucleon separation energies. According to our Bayesian model averaging analysis, 7759 nuclei with $Z\leq 119$ have a probability of existence $\geq 0.5$. The extrapolations obtained in this study will be put through stringent tests when new experimental information on exotic nuclei becomes available. In this respect, the quantified landscape of nuclear existence obtained in this study should be viewed as a dynamical prediction that will be fine-tuned when new experimental information and improved global mass models become available.
The limits of the nuclear landscape are determined by nuclear binding energies. Beyond the proton drip lines, where the separation energy becomes negative, there is not enough binding energy to prevent protons from escaping the nucleus. Predicting properties of unstable nuclear states in the vast territory of proton emitters poses an appreciable challenge for nuclear theory as it often involves far extrapolations. In addition, significant discrepancies between nuclear models in the proton-rich territory call for quantified predictions. With the help of Bayesian methodology, we mix a family of …
We develop an effective field theory (EFT) for nuclear vibrations. The key ingredients - quadrupole degrees of freedom, rotational invariance, and a breakdown scale around the three-phonon level - are taken from data. The EFT is developed for spectra and electromagnetic moments and transitions. We employ tools from Bayesian statistics for the quantification of theoretical uncertainties. The EFT consistently describes spectra and electromagnetic transitions for $^{62}$Ni, $^{98,100}$Ru, $^{106,108}$Pd, $^{110,112,114}$Cd, and $^{118,120,122}$Te within the theoretical uncertainties. This suggest…
Motivated by the newly observed $^{39}$Na in experiments, systematic calculations of global nuclear binding energies with seven Skyrme forces are performed. We demonstrate the strong correlation between the two-neutron separation energies ($S_{2n}$) of $^{39}$Na and the total number of bound nuclei of the whole nuclear landscape. Furthermore, with calculated nuclear masses, we perform astrophysical rapid-neutron capture process ($r$-process) simulations by using nuclear reaction code TALYS and nuclear reaction network code SkyNet. $r$-process abundances from ejecta of neutron star mergers and …
A first-principles description of nuclear systems along the drip lines presents a substantial theoretical and computational challenge. In this paper, we discuss the nuclear theory roadmap, some of the key theoretical approaches, and present selected results with a focus on long isotopic chains. An important conclusion, which consistently emerges from these theoretical analyses, is that three-nucleon forces are crucial for both global nuclear properties and detailed nuclear structure, and that many-body correlations due to the coupling to the particle continuum are essential as one approaches p…
Mesoscopic chemical potentials across the (hyper)nuclear landscape
The Grainger College of Engineering, Illinois Center for Advanced Studies of the Universe, Department of Physics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格兰杰工程学院，宇宙高级研究中心，物理系）
The nuclear landscape has been investigated within the triaxial relativistic Hartree-Bogoliubov theory with the PC-PK1 density functional, and the beyond-mean-field dynamical correlation energies are taken into account by a microscopically mapped five-dimensional collective Hamiltonian without additional free parameters. The effects of triaxial deformation and dynamical correlations on the nuclear landscape are analyzed. The present results provide the best description of the experimental binding energies, in particular for medium and heavy mass regions, in comparison with the results obtained…
Exploring nucleon drip lines and astrophysical rapid neutron capture process (r-process) paths in the nuclear landscape is extremely challenging in nuclear physics and astrophysics. While various models predict similar proton drip line, their predictions for neutron drip line and the r-process paths involving heavy neutron-rich nuclei exhibit a significant variation which hampers our accurate understanding of the r-process nucleosynthesis mechanism. Using microscopic density functional theory with a representative set of non-relativistic and relativistic interactions, we demonstrate for the fi…
We exhibit a wide variety of the nuclear shape phases over the nuclear chart along with a shell model scheme. Various nuclear shapes are demonstrated within the framework of proton-neutron spin-orbital interactions; ferro-deformed, sub-ferro-deformed, and spherical shapes. The spherical shape is classified into the three magic-number categories in view of a large shell gap mechanism; double-magic nuclei I, double magic nuclei II, and double magic nuclei III. We discuss nuclear shape coexistence in the space Z = 76 to 84 as providing a new way to understanding the dynamical shape phases.
The assessment of the global performance of the state-of-the-art covariant energy density functionals and related theoretical uncertainties in the description of ground state observables has recently been performed. Based on these results, the correlations between global description of binding energies and nuclear matter properties of covariant energy density functionals have been studied in this contribution.
The ground-state properties of nuclei with 8 $\le$ Z $\le$ 120 from the proton drip line to the neutron drip line have been investigated using the relativistic continuum Hartree-Bogoliubov (RCHB) theory with the relativistic density functional PC-PK1. With the effects of the continuum included, there are totally 9035 nuclei predicted to be bound, which largely extends the existing nuclear landscapes predicted with other methods. The calculated binding energies, separation energies, neutron and proton Fermi surfaces, root-mean-square (rms) radii of neutron, proton, matter, and charge distributi…
Landscape of nuclear deformation softness with spherical quasi-particle random phase approximation
Ho Chi Minh City University of Education（胡志明市教育大学）；Institute for Basic Science (IBS)（韩国基础科学研究院）；San Diego State University（圣地亚哥州立大学）；Tel Aviv University（特拉维夫大学）
The study of nuclear limits has been performed and new physical mechanisms and exotic shapes allowing the extension of nuclear landscape beyond the commonly accepted boundaries have been established. The transition from ellipsoidal to toroidal shapes plays a critical role in potential extension of nuclear landscape to hyperheavy nuclei. Rotational excitations leading to the birth of particle (proton or neutron) bound rotational bands provide a mechanism for an extension of nuclear landscape beyond spin zero proton and neutron drip lines.
Nuclear landscape based on point-coupling density functional with localized exchange terms
Lanzhou University（兰州大学）；Frontier Science Center for Rare isotope, Lanzhou University（兰州大学稀有同位素前沿科学中心）；China Institute of Atomic Energy（中国原子能科学研究院）；Institute for Basic Science（韩国基础科学研究院）；Shanghai Jiao Tong University（上海交通大学）
Two new mechanisms active in rotating nuclei located in the vicinity of neutron drip line have been discovered. Strong Coriolis interaction acting on high-$j$ orbitals transforms particle-unbound (resonance) nucleonic configurations into particle-bound ones with increasing angular momentum. The point of the transition manifests the birth of particle-bound rotational bands. Alternative possibility of the transition from particle-bound to resonance rotational band (the death of particle-bound rotational bands) with increasing spin also exists but it is less frequent in the calculations. The birt…
We discuss up-to-date constraints on the Majorana neutrino mass $m_{ββ}$ from neutrinoless double beta decay ($0νββ$) searches in experiments using different isotopes: KamLAND-Zen and EXO ($^{136}$Xe), GERDA and MAJORANA ($^{76}$Ge) and CUORE ($^{130}$Te). Best fits and upper bounds on $m_{ββ}$ are explored in the general landscape of nuclear matrix elements (NME), as well as for specific NME values obtained in representative nuclear models. By approximating the likelihood of $0νββ$ signals through quadratic forms, the analysis of separate and combined isotope data becomes exceedingly simple, …
Nucleosynthesis is a complex process in astro-nuclear evolution. In this work, we construct a directed multi-layer nuclear reaction network using the substrate-product method from a thermonuclear reaction database, JINA REACLIB. The network contains four layers, namely $n$-, $p$-, $h$- and $r$, corresponding to the reaction types involved in neutrons, protons, $^4$He and the remainder, respectively. The degree values (i.e. numbers of reactions) for three layers of n-, p- and h- have a significant correlation with one another, and their topological structures exhibit a similar regularity. Howev…
A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $γ-$decay, together with one- and two-particle transfer reactions. In this way it is possible to probe the single-particle and collective components of the nuclear many-body wavefunction resulting from their mutual coupling and diagonalising the low-energy Hamiltonian. We address the question of how accurately such a description can account for experimental observations. It is concluded that renormalizing empirically and on equal footing bare…
The neutron and proton drip lines represent the limits of the nuclear landscape. While the proton drip line is measured experimentally up to rather high $Z$-values, the location of the neutron drip line for absolute majority of elements is based on theoretical predictions which involve extreme extrapolations. The first ever systematic investigation of the location of the proton and neutron drip lines in the covariant density functional theory has been performed by employing a set of the state-of-the-art parametrizations. Calculated theoretical uncertainties in the position of two-neutron drip …
Heavy hadron molecules were first theorized from a crude analogy with the deuteron and the nuclear forces binding it, a conjecture which was proven to be on the right track after the discovery of the $X(3872)$. However, this analogy with nuclear physics has not been seriously exploited beyond a few calculations in the two- and three-body sectors, leaving a great number of possible theoretical consequences unexplored. Here we show that nuclear and heavy hadron effective field theories are formally identical: using a suitable notation, there is no formal difference between these two effective fi…
The properties of hyperheavy nuclei and the extension of nuclear landscape to hyperheavy nuclei are extensively studied within covariant density functional theory. Axial reflection symmetric and reflection asymmetric relativistic Hartree-Bogoliubov (RHB) calculations are carried out. The role of triaxiality is studied within triaxial RHB and triaxial relativistic mean field + BCS frameworks. With increasing proton number beyond Z~130 the transition from ellipsoidal-like nuclear shapes to toroidal ones takes place. The description of latter shapes requires the basis which is typically significa…
We develop for the first time a microscopic global nucleon-nucleus optical potential with quantified uncertainties suitable for analyzing nuclear reaction experiments at next-generation rare-isotope beam facilities. Within the improved local density approximation and without any adjustable parameters, we begin by computing proton-nucleus and neutron-nucleus optical potentials from a set of five nuclear forces from chiral effective field theory for 1800 target nuclei in the mass range 12 $\leq$ A $\leq$ 242 for energies between 0 MeV $<$ E $\lesssim$ 150 MeV. We then parameterize a global optic…
In this review, we describe the experimental facilities and methods which make it possible to produce and measure the properties of the extreme neutron rich nuclei. We then develop the theoretical framework that will accompany us along the review; the shell-model approach with large scale configuration interaction (mixing) SM-CI, with special emphasis in the competition between the spherical mean field and the nuclear correlations (mainly pairing and quadrupole-quadrupole). The symmetry properties of the latter are treated in detail as they will show to be of great heuristic value. We explore …
The phenomenon of reflection-asymmetric nuclear shapes is relevant to nuclear stability, nuclear spectroscopy, nuclear decays and fission, and the search for new physics beyond the standard model. Global surveys of ground-state octupole deformation, performed with a limited number of models, suggest that the number of pear-shaped isotopes is fairly limited across the nuclear landscape. We carry out global analysis of ground-state octupole deformations for particle-bound even-even nuclei with $Z \leq 110$ and $N \leq 210$ using nuclear density functional theory (DFT) with several non-relativist…
The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interactions approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow Shell Model (GSM) provides such a framework as it is capable of describing resonant and non-resonant many-body states on equal footing. To make reliable predictions, quality input is needed that allows for t…
Bayesian calibration of a regional optical potential and uncertainty-quantified predictions for compound nucleus reactions
University of Surrey（萨里大学）；Facility for Rare Isotope Beams, Michigan State University（密歇根州立大学稀有同位素束设施）；Department of Physics and Astronomy, Michigan State University（密歇根州立大学物理与天文学系）；AWE Nuclear Security Technologies（阿韦核安全技术有限公司）
The dependence on the structure functions and Z, N numbers of the nuclear binding energy is investigated within the inverse problem(IP) approach. This approach allows us to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. The IP was formulated for the numerical generalization of the semi-empirical mass formula of BW. It was solved in step by step way based on the AME2012 nuclear database. The established parametrization describes the measured nuclear masses of 2564 isotopes with a maximum deviation less than…
Theoretical predictions need quantified uncertainties for a meaningful comparison to experimental results. This is an idea which presently permeates the field of theoretical nuclear physics. In light of the recent progress in estimating theoretical uncertainties in ab initio nuclear physics, we here present and compare methods for evaluating the statistical part of the uncertainties. A special focus is put on the (for the field) novel method of Lagrange multipliers (LM). Uncertainties from the fit of the nuclear interaction to experimental data are propagated to a few observables in light-mass…
Theoretical predictions of physical observables often involve extrapolations to regions that are poorly constrained by laboratory experiments and astrophysical observations. Without properly quantified theoretical errors, such model predictions are of very limited utility. In this contribution we use maximum-likelihood estimation to compute theoretical errors and assess correlations between physical observables. We illustrate the power and elegance of these methods using examples of both pedagogical and realistic interest. In particular, we implement a gaussian approximation to the likelihood …
The nuclear physics landscape has been redesigned as a sequence of effective field theories (EFTs) connected to the Standard Model through symmetries and lattice simulations of Quantum Chromodynamics (QCD). EFTs in this sequence are expansions around different low-energy limits of QCD, each with its own characteristics, scales, and ranges of applicability regarding energy and number of nucleons. We review each of the three main nuclear EFTs -- Chiral, Pionless, Halo/Cluster -- highlighting their similarities, differences, and connections. In doing so, we survey the structural properties and re…
Background: Charge-exchange reactions are a powerful tool for exploring nuclear structure and nuclear astrophysics, however, a robust charge-exchange reaction theory with quantified uncertainties is essential to extracting reliable physics. Purpose: The goal of this work is to determine the uncertainties due to optical potentials used in the theory for charge-exchange reactions to isobaric analogue states. Method: We implement a two-body reaction model to study (p,n) charge-exchange transitions and perform a Bayesian analysis. We study the (p,n) reaction to the isobaric analog states of $^{14}…
The evolution of the nuclear shapes along the triaxial landscape is studied in the Pt isotopic chain using the selfconsistent Hartree-Fock-Bogoliubov approximation based on the Gogny interaction. In addition to the parametrization D1S, the new incarnations D1N and D1M of this force are also included in our analysis to asses to which extent the predictions are independent of details of the effective interaction. The considered range of neutron numbers 88<N<26 includes prolate, triaxial, oblate and spherical ground state shapes and serves for a detailed comparison of the predictions obtained wit…
We use the recently developed Differential Equation Model for the reduced electric quadrupole transition probability B(E2) for predicting its values for a wide range of even-even nuclides almost throughout the nuclear landscape from Neon to Californium. This is made possible as the principal equation in the model, namely, the differential equation connecting the B(E2) value of a given nucleus with its derivatives with respect to neutron and proton numbers provides two different recursion relations, each connecting three different neighboring even-even nuclei from lower to higher mass numbers a…
We present an efficient method for calculating strength functions using the finite amplitude method (FAM) for deformed superfluid heavy nuclei within the framework of the nuclear density functional theory. We demonstrate that FAM reproduces strength functions obtained with the fully self-consistent quasi-particle random-phase approximation (QRPA) at a fraction of computational cost. As a demonstration, we compute the isoscalar and isovector monopole strength for strongly deformed configurations in $^{240}$Pu by considering huge quasi-particle QRPA spaces. Our approach to FAM, based on Broyden'…
