Atomic mass relations of mirror nuclei

In this paper we study the mass relation of mirror nuclei with our focus on pairing and shell effects in the Coulomb energy. We present an accurate mass formula for neutron-deficient nuclei with mass number $A>20$ that achieves a root-mean square deviation (RMSD) of 70 keV when compared to experimental data from AME2020, and the RMSD further diminishes to 49 keV when excluding five nuclei with experimental uncertainties larger than 100 keV. Based on the mass formula, we predict 174 atomic masses near the proton drip line with $20<A<115$, and tabulate the results in the Supplemental Material of this paper.

Figure 1

Deviations of ${\mathrm{\Delta }}_k$ between the experimental data in AME2020 [29] and the theoretical values obtained using (a) Eq. (4), (b) Eq. (7), and (c) Eq. (9) (in units of keV). The circles in red, squares in blue, pentagons in green, and nablas in purple represent the mirror nuclei with $k=1,2,3,4$, respectively. The gray strip indicates the region of deviations below 100 keV. The RMSDs of Eqs. (4), (7), and (9) are 310 keV, 147 keV, and 70 keV, respectively. If we exclude five data values with experimental uncertainties larger than 100 keV, the RMSD of Eq. (9) is reduced to only 49 keV.

Figure 2

Comparison of atomic masses (in the unit of keV) of neutron-deficient nuclei from the experimental data in AME2020 [29], the extrapolations from AW2012 [33], the extrapolations using the local correlation approach (i.e., Ma2020) [28], and the extrapolations using Eq. (10) in this work based on the AME2012 database. Our prediction exhibit a good agreement with the experimental data.

Figure 3

Comparison of atomic masses (in the unit of keV) from the new experimental data in the references of Wang2023 [35] and Paul2021 [36], the experimental data in AME2020 [29], the results predicted in AW2020 [29], and the results predicted using Eq. (10) in this work based on the AME2020 database. Our results exhibit a remarkable agreement with the data in Wang2023 [35] and Paul2021 [36].

Figure 4

Deviation of ${\mathrm{\Delta }}_k$ derived using the experimental data in AME2020 [29], the new data in Wang2023 [35] and Paul2021 [36], and Eq. (9) from the function, $696A^{2/3}-1505$ keV. Here, we emphasize the odd-even staggering phenomenon.