Improved radial basis function approach with odd-even corrections

The radial basis function (RBF) approach has been used to improve the mass predictions of nuclear models. However, systematic deviations were found between the improved masses and the experimental data for nuclei with four different odd-even parities of $(Z,N)$, i.e., (even $Z$, even $N$), (even $Z$, odd $N$), (odd $Z$, even $N$), and (odd $Z$, odd $N$). In this work, we show that such deviations can be eliminated to a large extent by separately training the RBF for the groups of parities, resulting in a further improved predictive power of nuclear mass models and in particular single-nucleon separation energies. With this new RBF approach, the root-mean-square mass deviation for the latest version of the Weizsäcker-Skyrme model WS4, falls to 135 keV with respect to known data. This is approaching the chaos-related unpredictability limit ($\sim 100$ keV).

Figure 1

(a) Mass differences $\left(\mathrm{\Delta }M\right)$ between the experimental data and the predictions of the RMF+RBF model. (b) The reconstructed functions $S(Z,N)$ predicted by the RBFoe approach. The boundary of nuclei with known masses in AME2012 is shown by the black contours. (c) Mass differences ($\mathrm{\Delta }{M}^{\prime }$) between the experimental data and the predictions of the RMF+RBFoe model. The dotted lines denote the conventional magic numbers.

Figure 2

Mass differences between the experimental data and the predictions of RMF+RBF model for the (a) e-e, (b) e-o, (c) o-e, and (d) o-o nuclei.

Figure 3

Same as Fig. 2, but for the RMF+RBFoe model.

Figure 4

Single-neutron separation energies $S_n$ of the Ga and Ge isotopes predicted by (a) RMF, (b) RMF+RBF, and (c) RMF+RBFoe. The experimental data are shown with the filled squares. Note that $S_n$ of the Ge isotopes have been shifted up by 5 MeV.

Figure 5

Squared amplitudes $|F_k{|}^2$ of the Fourier transforms of the mass differences as a function of the frequency $\omega =k/N$. For comparison, the results obtained for the RMF and RMF+RBF approaches are shown together in (a), and those obtained for the RMF+RBF and RMF+RBFoe approaches are shown together in (b).