Radial basis function approach in nuclear mass predictions

Abstract

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 figure

Toward precision mass measurements of neutron-rich nuclei relevant to r-process nucleosynthesis

“…For very neutron-rich nuclei, the predictions of various mass models can differ by more than a few mega-electron volts. Hybrid models including the use of the radial basis function approach [125,126], the residual proton-neutron interactions [127], and the systematics of the alpha decay energies [128] can provide highly precise predictions for nuclei near the known mass surface; however, the growth of the intrinsic error for nuclei far from the known region remains a serious problem. In this sense, any reliable experimental data can serve as a critical test of existing mass models and guide their further development.…”

Improved radial basis function approach with odd-even corrections

“…More details can be found in Ref. [39,40]. In this approach, the solution at point x is represented as a sum of m radial basis functions φ( x − x i ) weighted by an appropriate coefficient ω i , i.e.,…”

“…In addition, as in Refs. [38][39][40], the Euclidean norm is defined to be the distance between nuclei (Z i , N i ) and (Z j , N j ) on the nuclear chart:…”

“…An alternative simple and effective approach to improve the accuracy of mass models is the radial basis function (RBF). Recent works [38][39][40] already demonstrated its ability to improve the description of nuclear masses and the two-neutron severation energies.…”

Influence of binding energies of electrons on nuclear mass predictions

“…The model standard deviation of the HFB-27 mass model has been reduced to 0.5 MeV [25]. In the relativistic framework, the first microscopic mass model was developed in 2005 [26] with the TMA effective interaction [27], and its rms deviation to the known masses in AME12 is about 2.2 MeV for nuclei with Z, N 8 [28,29]. By fitting to the properties of 60 spherical nuclei, the effective interaction PC-PK1 [7] remarkably improves the mass predictions comparing with the TMA effective interaction [30][31][32][33], and also successfully describes many other nuclear properties, such as nuclear β decay [34], low-lying excited states [35][36][37][38][39], pairing transition at finite temperature [40], exotic shape [41], and the fission barrier [42,43].…”