Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects

Abstract

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 singlenucleon 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 meanfield model. This manifests that better predictive performance can be achieved if more physical features are included in the BNN approach.1 Mass is a fundamental property of atomic nuclei. It can be employed to extract various nuclear structure information, such as nuclear pairing correlation, shell effect, deformation transition, and so on [1]. Nowadays it has been also widely used to determine nuclear effective interactions [2]. Moreover, nuclear mass is essential to determine the nuclear reaction energy in astrophysics and hence plays a crucial role in understanding the origin of elements in Universe [3]. In addition, the accurate mass determination is very important to test the unitarity of Cabibbo-Kobayashi-Maskawa matrix [4,5].Measurements of nuclear mass have achieved great progress in recent years [6,7] and about 3000 nuclear masses have been measured up to now [8]. However, the accurate predictions of nuclear mass are still a great challenge for theoretical models, due to the difficulties in the exact theory of nuclear interaction and in the quantum many-body calculations. Nowadays three types of nuclear models are mainly used in global mass predictions: macroscopic, macroscopic-microscopic, and microscopic mass models. The Bethe-Weizsäcker (BW) mass formula is the first model used to estimate nuclear masses [9,10], which belongs to the macroscopic type. It assumes the nucleus is similar to a charged liquid drop, so the microscopic effects, such as shell effect, cannot be well described. By taking into account the important corrections related to the microscopic effects, the macroscopic-microscopic models are developed, such as the finite-range droplet model (FRDM) [11] and the Weizsäcker-Skyrme (WS) model [12]. The microscopic mass models are mainly rooted in the density functional theory, which are more complicated but potentially have a better ability of extrapolation. In the non-relativistic framework, a series of Hartree-Fock-Bogoliubov (HFB) mass models have been constructed with the Skyrme [13,14] or Gogny [15] effective interactions. In recent years,...

Impact of statistical uncertainties on the composition of the outer crust of a neutron star

“…This means that the NN has been able to grasp a signal in the residual and thus further improve the agreement with experimental data. Such a result is in agreement with previous findings [20,55]. Several architecture of the NN are possible, but from our analysis we did not obtain any significant improvement.…”

Neutron Drip Line in the Ca Region from Bayesian Model Averaging

“…Conclusions -In summary, in this Letter we quantified the neutron-stability of the nucleus in terms of its existence probability p ex , i.e., the Bayesian posterior probability that the neutron separation energy is positive. Our results are fairly consistent with recent experimental findings [1]: 60 Ca is expected to be well bound with S 2n ≈ 5 MeV while 49 S, 52 Cl, and 53 Ar are marginallybound threshold systems.…”

“…Indeed, with the exception of SV-min, UNEDF0, and FRDM-2012, other models calculate them to be either marginally bound or to lie outside the one-neutron drip line. Since 49 S, 52 Cl and 53 Ar do exist [1,7], this prior knowledge can inform the model averaging process [56][57][58] through posterior weights: 53 Ar, 49 S exist (1) (see additional discussion in SM). The weight w k reflects the ability of the model M k to predict the existence of nuclei in the Ca region.…”

“…New mass measurements on neutron-rich nuclei will help to develop increasingly more quantitative models of the atomic nucleus and also allow for a higher-fidelity statistical analysis. As illuminated by our Bayesian analysis of 49 S, 52 Cl, and 53 Ar, experimental discoveries of new nuclides will also be crucial for delineating the detailed behavior of the nuclear mass surface, including the placement of particle drip lines.…”

Impact of the nuclear mass uncertainties on the r process

“…Compared to the former mass relations, the accuracies of these global mass models are worse. Therefore, several methods have been introduced to improve their accuracies, such as the CLEAN image reconstruction technique [28], the radial basis function approach [29][30][31][32][33], and the neural network approach [34][35][36]. After Burbidge's systematic introduction to the r process for the first time [37], due to the lag of experimental and theoretical development, only the phenomenological nuclear droplet mass formula [38] could be considered for the r-process calculations in a long period.…”