论文标题
$^{151} {\ rm \ bf sm} $和$^{171} {\ rm \ bf tm} $的经验捕获横截面{151} {\ rm \ bf sm} $
Empirical capture cross sections for cosmic neutrino detection with $^{151}{\rm \bf Sm}$ and $^{171}{\rm \bf Tm}$
论文作者
论文摘要
核$^{151} $ sm和$^{171} $ tm已被确定为检测宇宙中微子背景的有吸引力的候选者。两种同位素都经历了第一个非唯一的β衰减，仅使用对称性抑制其光谱形状的预测，到目前为止，这已经阻碍了对其中微子捕获横截面的明确预测。在这项工作中，我们指出，对于这两个要素，所谓的“ $ξ$ -Approximation”都是适用的，这有效地将光谱形状从最多偏离$ 1 \％$的光谱与如果Beta衰减为允许的类型，则会出现。使用测量的半衰期，我们提取相关的核基质元件，并预测两个同位素均为$ 1 \％$级别的中微子捕获横截面，这构成了许多相关效果，包括辐射校正和核的有限尺寸。我们获得了$（1.12 \ pm 0.01）\ times 10^{ - 46} {\ rm cm}^2 $ for $^{171} $ tm和$（4.77 \ pm 0.01）\ times 10^{ - 48} { - 48} {\ rm cm cm}^2 $ for $ cm}^2 $ for $^$^$^{151} $ sms。此方法是可靠的，因为它不依赖于β光谱端点附近的数据点，这可能会受到原子物理效应的污染，即移动和摇动。最后，我们计算宇宙中微子发现所必需的目标质量，并讨论与实验程序相关的几种瓶颈和各自的解决方案。我们得出的结论是，在$^{151} $ sm和$^{171} $ tm上对宇宙中微子背景的检测是可以实现的，并且没有理论上的局限性，但仍应遵守实验者在拟议的托勒密项目的上下文中应进一步调查的技术问题。
The nuclei $^{151}$Sm and $^{171}$Tm have been identified as attractive candidates for the detection of the cosmic neutrino background. Both isotopes undergo first-forbidden non-unique beta decays which inhibits a prediction of their spectral shape using symmetries alone and this has, so far, obstructed a definitive prediction of their neutrino capture cross sections. In this work we point out that for both elements the so-called "$ξ$-approximation" is applicable and this effectively reduces the spectral shape to deviate by at most $1\%$ from the one that would arise if beta decays were of the allowed type. Using measured half-lives we extract the relevant nuclear matrix element and predict the neutrino capture cross sections for both isotopes at $1\%$ level, accounting for a number of relevant effects including radiative corrections and the finite size of the nuclei. We obtained $(1.12\pm 0.01)\times 10^{-46}{\rm cm}^2$ for $^{171}$Tm and $(4.77\pm 0.01)\times 10^{-48}{\rm cm}^2$ for $^{151}$Sm. This method is robust as it does not rely on the data points near the end-point of the beta spectrum which may be contaminated by atomic physics effects, namely shake-up and shake-off. Finally, we calculate the target mass which is necessary for cosmic neutrino discovery and discuss several bottlenecks and respective solutions associated to the experimental program. We conclude that the detection of cosmic neutrino background by neutrino capture on $^{151}$Sm and $^{171}$Tm is achievable and free from theoretical limitations but still subject to technical issues that should be further investigated by the experimentalists in the context of the proposed PTOLEMY project.
