Neutrino properties such as the Majorana nature and the masses, which go beyond the standard model, are derived from the experimental double-beta decay (DBD) rate by using the DBD nuclear matrix element (NME). Theoretical evaluations for the NME, however, are very difficult. Single-charge exchange reactions (SCERs) and double-charge exchange reactions (DCERs) are used to study nuclear isospin ($\tau$) and spin ($\sigma$) correlations involved in the DBD NME and to theoretically calculate the DBD NME. Single and double $\tau \sigma$ NMEs for quasi-particle states are studied by SCERs and DCER. They are found to be reduced with respect to the quasi-particle model NMEs due to the $\tau \sigma$ correlations. The impact of the SCER- and DCER-NMEs on the DBD NME is discussed.

中文翻译：

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单电荷和双电荷交换反应和双β衰变的核基质元素

马约拉纳性质和质量等超出标准模型的中微子性质是通过使用 DBD 核基质元素 (NME) 从实验双β衰变 (DBD) 速率推导出来的。然而，对 NME 的理论评估非常困难。单电荷交换反应 (SCER) 和双电荷交换反应 (DCER) 用于研究核同位旋（$\tau$) 和旋转 ($\sigma$) DBD NME 中涉及的相关性和理论上计算 DBD NME。单双$\tau \sigma$SCER 和 DCER 研究了准粒子状态的 NME。发现它们相对于准粒子模型 NME 是减少的，因为$\tau \sigma$相关性。讨论了 SCER-和 DCER-NME 对 DBD NME 的影响。