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Nuclear masses are predicted with the Bayesian neural networks by learning the mass surface of even-even nuclei and the correlation energies to their neighbouring nuclei. By keeping the known physics in various sophisticated mass models and performing the delicate design of neural networks, the proposed Bayesian machine learning (BML) mass model achieves an accuracy of $84$~keV, which crosses the accuracy threshold of the $100$~keV in the experimentally known region. It is also demonstrated the corresponding uncertainties of mass predictions are properly evaluated, while the uncertainties increase by about $50$~keV each step along the isotopic chains towards the unknown region. The shell structures in the known region are well described and several important features in the unknown region are predicted, such as the new magic numbers around $N = 40$, the robustness of $N = 82$ shell, the quenching of $N = 126$ shell, and the smooth separation energies around $N = 104$., Comment: 14 pages, 5 figures

For radioactive nuclear data, $\beta$ decay is one of the most important information and is applied to various fields. However, some of the $\beta$-decay data are not available due to experimental difficulties. From this respect, theoretically calculated results have been embedded in the $\beta$-decay data to compensate the missing information. To calculate the $\beta$-decay half-lives, a proton-neutron quasi-particle random phase approximation on top of a Skryme energy density functional is applied with an assumption of spherical symmetry. The isoscalar pairing strength is estimated by a Bayesian neutral network (BNN). We verify the predicted isoscalar pairing strengths by preparing the training data and test data. It was confirmed that the finite-range isovector pairing ensures the $\beta$-decay half-lives insensitive to the model space, while the zero-range one was largely dependent on it. The half-lives calculated with the BNN isoscalar pairing strengths reproduced most of experimental data, although those of highly deformed nuclei were underestimated. We also studied that the predictive performance on new experimental data that were not used for the BNN training and found that they were reproduced well. Our study demonstrates that the isoscalar pairing strengths determined by the BNN can reproduce experimental data in the same accuracy as other theoretical works., Comment: 13 page, 15 figures

Giant dipole resonance (GDR) is one of the fundamental collective excitation modes in nucleus. Continuous efforts have been made to the evaluation of GDR key parameters in different nuclear data libraries. We introduced multitask learning (MTL) approach to learn and reproduce the evaluated experimental data of GDR key parameters, including both GDR energies and widths. Compared to the theoretical GDR parameters in RIPL-3 library, the accuracies of MTL approach are almost doubled for 129 nuclei with experimental data. The significant improvement is largely due to the right classification of unimodal nuclei and bimodal nuclei by the classification neural network. Based on the good performance of the neural network approach, an extrapolation to 79 nuclei around the $\beta$-stability line without experimental data is made, which provides an important reference to future experiments and data evaluations. The successful application of MTL approach in this work further proofs the feasibility of studying multi-output physical problems with multitask neural network in nuclear physics domain., Comment: 9 pages, 6 figures

Nuclear $\beta$ decay is a key process to understand the origin of heavy elements in the universe, while the accuracy is far from satisfactory for the predictions of $\beta$-decay half-lives by nuclear models up to date. In this letter, we pave a novel way to accurately predict $\beta$-decay half-lives with the machine-learning based on the Bayesian neural network, in which the known physics has been explicitly embedded, including the ones described by the Fermi theory of $\beta$ decay, and the dependence of half-lives on pairing correlations and decay energies. The other potential physics, which is not clear or even missing in nuclear models nowadays, will be learned by the Bayesian neural network. The results well reproduce the experimental data with a very high accuracy and further provide reasonable uncertainty evaluations in half-life predictions. These accurate predictions for half-lives with uncertainties are essential for the $r$-process simulations., Comment: 6 pages, 6 figures

Bayesian neural network (BNN) approach is employed to improve the nuclear mass predictions of various models. It is found that the noise error in the likelihood function plays an important role in the predictive performance of the BNN approach. By including a distribution for the noise error, an appropriate value can be found automatically in the sampling process, which optimizes the nuclear mass predictions. Furthermore, two quantities related to nuclear pairing and shell effects are added to the input layer in addition to the proton and mass numbers. As a result, the theoretical accuracies are significantly improved not only for nuclear masses but also for single-nucleon separation energies. Due to the inclusion of the shell effect, in the unknown region, the BNN approach predicts a similar shell-correction structure to that in the known region, e.g., the predictions of underestimation of nuclear mass around the magic numbers in the relativistic mean-field model. This manifests that better predictive performance can be achieved if more physical features are included in the BNN approach., Comment: 15 pages, 4 figures, and 3 tables

The radial basis function (RBF) approach has been used to improve the mass predictions of nuclear models. However, systematic deviations exist between the improved masses and the experimental data for nuclei with different odd-even parities of ($Z$, $N$), i.e., the (even $Z$, even $N$), (even $Z$, odd $N$), (odd $Z$, even $N$), and (odd $Z$, odd $N$). By separately training the RBF for these four different groups, it is found that the systematic odd-even deviations can be cured in a large extend and the predictive power of nuclear mass models can thus be further improved. Moreover, this new approach can better reproduce the single-nucleon separation energies. Based on the latest version of Weizs\"acker-Skyrme model WS4, the root-mean-square deviation of the improved masses with respect to known data falls to $135$ keV, approaching the chaos-related unpredictability limit ($\sim 100$ keV)., Comment: 7 pages, 5 figures

The self-consistent quasiparticle random-phase approximation (QRPA) approach is formulated in the canonical single-nucleon basis of the relativistic Hatree-Fock-Bogoliubov (RHFB) theory. This approach is applied to study the isobaric analog states (IAS) and Gamov-Teller resonances (GTR) by taking Sn isotopes as examples. It is found that self-consistent treatment of the particle-particle residual interaction is essential to concentrate the IAS in a single peak for open-shell nuclei and the Coulomb exchange term is very important to predict the IAS energies. For the GTR, the isovector pairing can increase the calculated GTR energy, while the isoscalar pairing has an important influence on the low-lying tail of the GT transition. Furthermore, the QRPA approach is employed to predict nuclear $\beta$-decay half-lives. With an isospin-dependent pairing interaction in the isoscalar channel, the RHFB+QRPA approach almost completely reproduces the experimental $\beta$-decay half-lives for nuclei up to the Sn isotopes with half-lives smaller than one second. Large discrepancies are found for the Ni, Zn, and Ge isotopes with neutron number smaller than $50$, as well as the Sn isotopes with neutron number smaller than $82$. The potential reasons for these discrepancies are discussed in detail., Comment: 34 pages, 14 figures

Based on the recent data in NUBASE2012, an improved empirical formula for evaluating the $\alpha$-decay half-lives is presented, in which the hindrance effect resulted from the change of the ground state spins and parities of parent and daughter nuclei is included, together with a new correction factor for nuclei near the shell closures. The calculated $\alpha$-decay half-lives are found to be in better agreements with the experimental data, and the corresponding root-mean-square (rms) deviation is reduced to $0.433$ when the experimental $Q$-values are employed. Furthermore, the $Q$-values derived from different nuclear mass models are used to predict $\alpha$-decay half-lives with this improved formula. It is found that the calculated half-lives are very sensitive to the $Q$-values. Remarkably, when mass predictions are improved with the radial basis function (RBF), the resulting rms deviations can be significantly reduced. With the mass prediction from the latest version of Weizs\"{a}cker-Skyrme (WS4) model, the rms deviation of $\alpha$-decay half-lives with respect to the known data falls to $0.697$., Comment: 7 pages, 3 figures and 3 tables, submitted to Journal of Physics G: Nuclear and Particle

The self-consistent proton-neutron quasiparticle random phase approximation approach is employed to calculate $\beta$-decay half-lives of neutron-rich even-even nuclei with $8\leqslant Z \leqslant 30$. A newly proposed nonlinear point-coupling effective interaction PC-PK1 is used in the calculations. It is found that the isoscalar proton-neutron pairing interaction can significantly reduce $\beta$-decay half-lives. With an isospin-dependent isoscalar proton-neutron pairing strength, our results well reproduce the experimental $\beta$-decay half-lives, although the pairing strength is not adjusted using the half-lives calculated in this study., Comment: 5 pages, 4 figures

The recent progress in the studies of nuclear charge-exchange excitations with localized covariant density functional theory is briefly presented, by taking the fine structure of spin-dipole excitations in 16O as an example. It is shown that the constraints introduced by the Fock terms of the relativistic Hartree-Fock scheme into the particle-hole residual interactions are straightforward and robust., Comment: 4 pages, 1 figure, Proceedings of INPC2013, Florence, Italy, 2-7 June 2013

The radial basis function (RBF) approach is applied in predicting nuclear masses for 8 widely used nuclear mass models, ranging from macroscopic-microscopic to microscopic types. A significantly improved accuracy in computing nuclear masses is obtained, and the corresponding rms deviations with respect to the known masses is reduced by up to 78%. Moreover, strong correlations are found between a target nucleus and the reference nuclei within about three unit in distance, which play critical roles in improving nuclear mass predictions. Based on the latest Weizs\"{a}cker-Skyrme mass model, the RBF approach can achieve an accuracy comparable with the extrapolation method used in atomic mass evaluation. In addition, the necessity of new high-precision experimental data to improve the mass predictions with the RBF approach is emphasized as well., Comment: 18 pages, 8 figures

We formulate the finite-temperature relativistic Hartree-Bogoliubov theory for spherical nuclei based on a point-coupling functional, with the Gogny or separable pairing force. Using the functional PC-PK1, the framework is applied to the study of pairing transitions in Ca, Ni, Sn, and Pb isotopic chains. The separable pairing force reproduces the gaps calculated with the Gogny force not only at zero temperature, but also at finite temperatures. By performing a systematic calculation of the even-even Ca, Ni, Sn, and Pb isotopes, it is found that the critical temperature for a pairing transition generally follows the rule $T_c =0.6 \Delta_n(0)$, where $\Delta_n(0)$ is the neutron pairing gap at zero temperature. This rule is further verified by adjusting the pairing gap at zero temperature with a strength parameter., Comment: 19 pages, 7 figures

Guiding by the relativistic local density approximation, we explore a phenomenological formula for the coupling strength of Coulomb field to take into account the Coulomb exchange term effectively in the relativistic Hartree approximation. Its validity in finite nuclei is examined by comparing with the exact treatment of the Coulomb exchange energies in the relativistic Hartree-Fock-Bogoliubov approach. It is found that the exact Coulomb exchange energies can be reproduced by employing the phenomenological formula with the relative deviations less than 1% for semi-magic Ca, Ni, Sn, and Pb isotopes. Furthermore, we check the applicability of the phenomenological formula for the effective interactions in the relativistic Hartree approach by investigating the binding energy differences of mirror nuclei., Comment: 10 pages, 4 figures

Self-consistent proton-neutron quasiparticle random phase approximation based on the spherical nonlinear point-coupling relativistic Hartree-Bogoliubov theory is established and used to investigate the $\beta^+$/EC-decay half-lives of neutron-deficient Ar, Ca, Ti, Fe, Ni, Zn, Cd, and Sn isotopes. The isoscalar proton-neutron pairing is found to play an important role in reducing the decay half-lives, which is consistent with the same mechanism in the $\beta$ decays of neutron-rich nuclei. The experimental $\beta^+$/EC-decay half-lives can be well reproduced by a universal isoscalar proton-neutron pairing strength., Comment: 12 pages, 4 figures

The global dynamical correlation energies for 575 even-even nuclei with proton numbers ranging from Z=8 to Z=108 calculated with the covariant density functional theory using the PC-PK1 parametrization are presented. The dynamical correlation energies include the rotational correction energies obtained with the cranking approximation and the quadrupole vibrational correction energies. The systematic behavior of the present correlation energies is in good agreement with that obtained from the projected generator coordinate method using the SLy4 Skyrme force although our values are systematically smaller. After including the dynamical correlation energies, the root-mean-square deviation predicted by the PC-PK1 for the 575 even-even nuclei masses is reduced from 2.58 MeV to 1.24 MeV., Comment: 14 pages and 3 figures, version to be published in the Frontiers of Physics

The $\beta$-decay half-lives of neutron-rich nuclei with $20 \leqslant Z \leqslant 50$ are systematically investigated using the newly developed fully self-consistent proton-neutron quasiparticle random phase approximation (QRPA), based on the spherical relativistic Hartree-Fock-Bogoliubov (RHFB) framework. Available data are reproduced by including an isospin-dependent proton-neutron pairing interaction in the isoscalar channel of the RHFB+QRPA model. With the calculated $\beta$-decay half-lives of neutron-rich nuclei a remarkable speeding up of $r$-matter flow is predicted. This leads to enhanced $r$-process abundances of elements with $A \gtrsim 140$, an important result for the understanding of the origin of heavy elements in the universe., Comment: 14 pages, 4 figures

We explore the effects of nuclear masses on the temperature and neutron density conditions required for r-process nucleosynthesis using four nuclear mass models augmented by the latest atomic mass evaluation. For each model we derive the conditions for producing the observed abundance peaks at mass numbers A ~ 80, 130, and 195 under the waiting-point approximation and further determine the sets of conditions that can best reproduce the r-process abundance patterns (r-patterns) inferred for the solar system and observed in metal-poor stars of the Milky Way halo. In broad agreement with previous studies, we find that (1) the conditions for producing abundance peaks at A ~ 80 and 195 tend to be very different, which suggests that, at least for some nuclear mass models, these two peaks are not produced simultaneously; (2) the typical conditions required by the critical waiting-point (CWP) nuclei with the N = 126 closed neutron shell overlap significantly with those required by the N=82 CWP nuclei, which enables coproduction of abundance peaks at A ~ 130 and 195 in accordance with observations of many metal-poor stars; and (3) the typical conditions required by the N = 82 CWP nuclei can reproduce the r-pattern observed in the metal-poor star HD 122563, which differs greatly from the solar r-pattern. We also examine how nuclear mass uncertainties affect the conditions required for the r-process and identify some key nuclei including76Ni to 78Ni, 82Zn, 131Cd, and 132Cd for precise mass measurements at rare-isotope beam facilities., Comment: 28 pages,9 figures,1 table