Assuming the universality of weak interactions, we have studied the weak processes such as β-decay and electron capture using the nuclear gross theory of beta decay (GTBD). We evaluate the β ± and electron capture decay rates and the neutrino–nucleus cross sections as a function of the energy of the incident neutrino, for E ν < 250 MeV. The evaluation performed some years ago for the electron neutrino–nucleus reactions in the mass region A < 70 is extended to the heavy one A < 220 for a set of 965 nuclear species of astrophysical interest. The nuclei are separated according to its parity in even–even, even–odd, odd–odd, and odd–even nuclei, both for β ± -decay and electron capture. The obtained cross sections are interpolated by means of a fourth-degree polynomial function in E ν . The coefficients in these polynomials are obtained and later fitted as a function of A and Z . The fitting procedure is described in detail paying special attention to the root mean square deviations in the adjustment. These polynomial functions provide a tool for the systematic evaluation of the cross sections needed in astrophysical processes like the r -process during the nucleosynthesis of supernovae.

中文翻译：

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可用于天体物理学应用的中微子-原子核横截面的系统计算

假设弱相互作用的普遍性，我们使用β衰变的核总理论（GTBD）研究了β衰变和电子捕获等弱过程。对于 E ν < 250 MeV，我们将 β ± 和电子俘获衰变率以及中微子-原子核截面作为入射中微子能量的函数进行评估。几年前对质量区域 A < 70 中的电子中微子 - 核反应进行的评估扩展到了质量区域 A < 220 的重核反应，用于一组 965 种具有天体物理学意义的核物种。原子核根据其在偶-偶核、偶-奇核、奇-奇核和奇-偶核中的奇偶性进行分离，用于 β ± 衰变和电子捕获。获得的横截面通过 E ν 中的四次多项式函数进行插值。获得这些多项式中的系数，然后将其拟合为 A 和 Z 的函数。详细描述了拟合过程，特别注意了调整中的均方根偏差。这些多项式函数为系统评估天体物理过程（如超新星核合成过程中的 r 过程）所需的横截面提供了一种工具。