Further improvements on a global nuclear mass model

The semi-empirical macroscopic-microscopic mass formula is further improved by considering some residual corrections. The rms deviation from 2149 known nuclear masses is significantly reduced to 336 keV, even lower than that achieved with the best of the Duflo-Zuker models. The $\alpha$-decay energies of super-heavy nuclei, the Garvey-Kelson relations, and the isobaric multiplet mass equation (IMME) can be reproduced remarkably well with the model, and the predictive power of the mass model is good. With a systematic study of 17 global nuclear mass models, we find that the quadratic form of the IMME is closely related to the accuracy of nuclear mass calculations when the Garvey-Kelson relations are reproduced reasonably well. Fulfilling both the IMME and the Garvey-Kelson relations seem to be two necessary conditions for improving the quality of the model prediction. Furthermore, the $\alpha$-decay energies of super-heavy nuclei should be used as an additional constraint on global nuclear mass models.

Figure 1

(a) Positions of some known doubly magic nuclei (squares). The stars denote the predicted tetrahedral doubly magic nuclei in Refs. [23, 24]. (b) Shell corrections of nuclei with WS [10]. The solid line shows the position of $N=1.37Z+13.5$.

Figure 2

(a) Deviations of calculated nuclear masses from the experimental data as a function of neutron number. The squares and the solid circles denote the results of FRDM and WS3, respectively. (b) The same as (a), but with the results of the DZ28 model for comparison.

Figure 3

$\alpha$-decay energies of some super-heavy nuclei calculated with WS3 (solid curve) and DZ28 (open circles). The squares denote the experimental data taken from [11] (and references therein).

Figure 4

Deviations of the calculated nuclear total energies at the ground state in this work from the results of (a) FRDM, (b) DZ28, (c) WS*, and (d) HFB-17, respectively. The calculated masses with FRDM, DZ28, WS*, and HFB-17 are taken from [8, 11, 12, 15], respectively. The stippling denote the region with deviations smaller than 2 MeV.

Figure 5

The rms deviation with respect to the masses as a function of average neutron-separation energy of nuclei. The lower striped area represents the average standard deviation errors of the measured masses [27].

Figure 6

A comparison of the predictive power of the various models. The vertical axis denotes the quantity $Y=\frac{\sigma \left(2003\right)-\sigma \left(1995\right)}{\sigma \left(2003\right)}$, as a measure of the predictive power of the mass formulas fitted to the 1995 data. Here, $\sigma \left(1995\right)$ and $\sigma \left(2003\right)$ denote the rms deviation to the masses of the atomic mass evaluation of 1995 (AME1995) [33] and AME2003 [27], respectively. See Table  for more information.

Figure 7

Comparison of rms deviation with respect to the masses from AME2003 with the various models. The dark (green) striped bars are for the 2149 measured masses and the gray bars denote the rms deviations to the evaluated masses (marked by $\#$) in AME2003. For the HFB-17 model, only the masses of nuclei with $Z⩽110$ are involved in the calculation.

Figure 8

(a) $b$ coefficients of nuclei in the IMME as a function of mass number. The solid squares and the solid curve denote the extracted results from mirror nuclei with $A⩽75$ according to Eq. (16) and those from the empirical formula [16] $b_{\mathrm{fit}}=0.710A^{2/3}-0.946$, respectively. The solid (open) circles denote the extracted results by fitting the measured binding energies with parabolas for a series of isobaric even-$A$ (odd-$A$) nuclei. See text for details. (b) The same as (a), but with the results from some mass models for comparison. The crosses, the open circles, and the filled circles denote the results for 179 neutron drip-line nuclei from ETF2, DZ10, and WS3 calculations, respectively.

Figure 9

(a) Deviations of the calculated $b$ coefficients with DZ10, ETF2, and WS3 models from $b_{\mathrm{fit}}=0.710A^{2/3}-0.946$ [16], as a function of isospin. (b) The Coulomb energy coefficient $a_c=E_C{A}^{1/3}{Z}^{-2}$ obtained with different models as a function of $(N-Z)/2$.

Figure 10

Values of $\sigma$(GK)/$\sigma \left(b\right)$ as a function of $\sigma$(GK)/$\sigma$($M$) from 17 different models (solid circles). Dashed lines are to guide the eyes.