Improved Jänecke mass formula

In this paper we improve an empirical mass formula constructed by Jänecke and collaborators. This formula is enlightened by the Garvey-Kelson mass relations. The new version of the Jänecke formula reproduces 2275 atomic masses with neutron number $N\ge 10$ and proton number $Z\ge 6$, at an average accuracy of 128 keV, by employing 576 parameters. The predictive power of our formula is exemplified by comparison with predicted results of other mass models.

Figure 1

Values of $g_1\left(N\right)$, $g_2\left(Z\right)$, $g_3\left(A\right),$ and $g_4\left(E\right)$ with $g_5(N,Z)=0$ and $g_6(N,Z)=E_{\mathrm{p}}$. One sees that $g_1\left(N\right)$ and $g_2\left(Z\right)$ are smooth and that $g_3\left(A\right)$ and $g_4\left(E\right)$ exhibit odd-even staggerings.

Figure 2

Deviations $D(N,Z)=M^{\mathrm{th}}(N,Z)-M^{\mathrm{expt}}(N,Z)$ (in keV) of calculated masses from experimental data. Panels (a), (b), (c) correspond to results obtained by using Eqs. (6), (14), (15), respectively.

Figure 3

Correlation between deviations $D(N,Z)=M^{\mathrm{th}}(N,Z)-M^{\mathrm{expt}}(N,Z)$ and $\overline{D}$ [see Eq. (15)] for different parity of $(N,Z)$. $r$ represents the linear correlation coefficients and is around $-0.8$ here. This means a strong correlation between $D(N,Z)$ and $\overline{D}$.

Figure 4

Deviations $D(N,Z)$ (in MeV) for Eqs. (6), (14), and (15) versus mass number $A$. The results in panel (a) correspond to the 2275 nuclei considered in this paper, and those in panel (b) correspond to deviations of theoretical masses based on the AME2003 database [10] with respect to the AME2012 database (without those known nuclei in the AME2003 database).

Figure 5

Contours of differences (in keV) between the extrapolated and experimental values of the excluding nuclei satisfying $|N-126|\le d$ and $|Z-82|\le d$, where panels (a), (b), and (c) correspond to $d=4,5,$ and 6, respectively.