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arXiv 1012.0512nucl-thhep-ph
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再论$0νββ$和$2νββ$核基质元素之间的关系

Relation between the $0νββ$ and $2νββ$ nuclear matrix elements revisited

Fedor Šimkovic, Rastislav Hodák, Amand Faessler, Petr Vogel

摘要:

我们表明,占主导地位的Gamow-Teller部分,$M^{0ν}_{GT}$,控制的无中微子$ββ$衰变的核矩阵元有关的矩阵元$M^{2ν}_{cl}$管理允许的双中微子$ββ$衰变。当这些矩阵元被表示为在$ββ$衰变中转化为一对质子的中子对之间的相对距离$r$的函数时,这种关系被揭示出来。分析这种关系使我们能够理解当$A$和$Z$改变时这些矩阵元素的对比行为;当$M^{0ν}_{GT}$缓慢而平稳地改变时,$M^{2ν}$具有明显的壳效应。我们还讨论了从$β^{\pm}$强度函数的实验研究中确定$M^{2ν}_{cl}$和$M^{0ν}_{GT}$值的可能性。

英文摘要:

We show that the dominant Gamow-Teller part, $M^{0ν}_{GT}$, of the nuclear matrix element governing the neutrinoless $ββ$ decay is related to the matrix element $M^{2ν}_{cl}$ governing the allowed two-neutrino $ββ$ decay. That relation is revealed when these matrix elements are expressed as functions of the relative distance $r$ between the pair of neutrons that are transformed into a pair of protons in the $ββ$ decay. Analyzing this relation allows us to understand the contrasting behavior of these matrix elements when $A$ and $Z$ is changed; while $M^{0ν}_{GT}$ changes slowly and smoothly, $M^{2ν}$ has pronounced shell effects. We also discuss the possibility of phenomenological determination of the $M^{2ν}_{cl}$ and from them of the $M^{0ν}_{GT}$ values from the experimental study of the $β^{\pm}$ strength functions.

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