We develop a fully self-consistent subtracted second random-phase approximation for charge-exchange processes with Skyrme energy-density functionals. As a first application, we study Gamow-Teller excitations in the doubly magic nucleus ${}^{48}\mathrm{Ca}$, the lightest double-$\beta$ emitter that could be used in an experiment, and in ${}^{78}\mathrm{Ni}$, the single-beta-decay rate of which is known. The amount of Gamow-Teller strength below 20 or 30 MeV is considerably smaller than in other energy-density-functional calculations and agrees better with experiment in ${}^{48}\mathrm{Ca}$, as does the beta-decay rate in ${}^{78}\mathrm{Ni}$. These important results, obtained without ad hoc quenching factors, are due to the presence of two-particle–two-hole configurations. Their density progressively increases with excitation energy, leading to a long high-energy tail in the spectrum, a fact that may have implications for the computation of nuclear matrix elements for neutrinoless double-$\beta$ decay in the same framework.

中文翻译：

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电荷交换减去第二随机相逼近Ca48和Ni78中的Gamow-Teller强度

我们使用Skyrme能量密度函数为电荷交换过程开发了完全自洽相减的第二随机相近似。作为第一个应用，我们研究双魔核中的Gamow-Teller激发${}^{48}钙$，最轻的双$\beta$ 可以在实验中使用的发射器 ${}^{78}你$，其单β衰减率是已知的。低于20 MeV或30 MeV的Gamow-Teller强度量要比其他能量密度函数计算中的要小得多，并且与实验结果更好地吻合${}^{48}钙$，以及中的beta衰减率 ${}^{78}你$。这些重要的结果是在没有特殊淬灭因子的情况下获得的，这是由于存在两粒子两孔结构。它们的密度随着激发能的增加而逐渐增加，从而导致光谱中长的高能尾巴，这一事实可能对无中微子双核的核基质元素的计算有影响。$\beta$ 在同一框架中衰减。