We study the $a$, $b$, and $c$ coefficients of the isobaric-multiplet mass equation (IMME) using a macroscopic-microscopic approach developed by P. Möller and collaborators [At. Data Nucl. Data Tables 59, 185 (1995); At. Data Nucl. Data Tables 109-110, 1 (2016)]. We show that already the macroscopic part of the finite-range liquid-drop model (FRLDM) describes the general trend of the $a$ and $b$ coefficients relatively well, while the staggering behavior of $b$ coefficients for doublets and quartets can be understood in terms of the difference of average proton and neutron pairing energies. The sets of isobaric masses, predicted by the full macroscopic-microscopic approaches, are used to explore the general trends of IMME coefficients up to $A=100$. We conclude that while the agreement for $a$ coefficients is quite satisfactory, the full approaches have less sensitivity to predict the IMME $b$ and $c$ coefficients in detail. The best set of theoretical $b$ coefficients, as given by the modified macroscopic part of the FRLDM, is used to predict masses of proton-rich nuclei based on the known experimental masses of neutron-rich mirror partners, and subsequently to investigate their one- and two-proton separation energies in proton-rich nuclei up to the $A=100$ region. The estimated position of the proton drip line is in fair agreement with known experimental data. These masses are important for simulations of the astrophysical $rp$ process.

中文翻译：

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宏观-微观方法中的等压多重质量方程

我们研究 $\mathrm{一种}$， $b$， 和 $C$使用P.Möller和合作者[ At。数据核 数据表 59，185（1995）; 在。数据核 数据表 109-110，1（2016）]。我们已经表明，有限范围液滴模型（FRLDM）的宏观部分已经描述了流体的总体趋势。$\mathrm{一种}$ 和 $b$ 系数相对较好，而 $b$可以通过平均质子和中子对能量的差来理解双峰和四重峰的系数。通过完整的宏观-微观方法预测的等压质量集合用于探究IMME系数的一般趋势，直至$\mathrm{一种}=100$。我们得出结论，尽管$\mathrm{一种}$ 系数非常令人满意，完整的方法对IMME的预测灵敏度较低 $b$ 和 $C$详细系数。最好的理论集$b$ 由FRLDM的修改后的宏观部分给出的系数用于基于已知的富含中子的镜子配偶的实验质量来预测富含质子的原子核的质量，并随后研究它们在氢原子中的一质子和二质子分离能。富质子核 $\mathrm{一种}=100$地区。质子滴线的估计位置与已知实验数据完全吻合。这些质量对于天体物理模拟非常重要$\mathrm{[R}p$ 过程。