R-矩阵理论Brune参数化中的影极
Shadow poles in Brune parametrization of R-matrix theory
摘要：
我们对核截面的集体知识作为共振参数记录在核数据库中。为了评估这些参数，运动的测量与参数模型的核截面称为R-矩阵理论。为了消除Wigner-Eisenbud R矩阵参数化中的任意边界参数，该社区正在考虑将所有核数据库转换为Brune参数。在这篇文章中，我们展示了比以前认为的更多的Brune参数。低于通道阈值，我们证明存在两种类型的额外的“影子极点”-分支影子极点和解析影子极点-这取决于我们如何继续R-矩阵算子复波数（这样做，我们建立R-矩阵算子的Mittag-Leffler展开）。这意味着有更多的布伦共振能量比水平。然而，我们也证明了，选择任何子集的Brune极点将产生相同的截面比使用整个集的Brune极点，只要它至少有水平的数量。在实践中，这意味着影子布伦极点可以从新的核数据库中丢弃。许多同位素都是用Reich-Moore近似来计算的，引入了复杂的共振能来消除某些通道。我们推广布鲁恩的参数化，包括Reich-Moore近似和额外的影极，并表明，所有的布鲁恩参数取决于我们选择什么样的公约，继续复杂的波数的R-矩阵算子。为了将核数据库转换为Brune参数，核科学家社区必须首先决定这样一个约定。作者主张解析延拓。在布鲁内的R矩阵理论的替代参数化中，第一个影子极的证据是在同位素氙-134中观察到的，自旋宇称群为1/2（-）。
英文摘要：
Our collective knowledge of nuclear cross sections is recorded as resonance parameters in nuclear data libraries. To evaluate these parameters, campaigns of measurements are fitted with a parametric model of nuclear cross sections called R-matrix theory. In order to remove the arbitrary boundary parameters in the Wigner-Eisenbud R-matrix parametrization, the community is considering converting all nuclear data libraries to Brune parameters. In this article, we show there are more Brune parameters than previously thought. Below the channel threshold, we prove there exists two types of additional 'shadow poles' - branch shadow poles and analytic shadow poles - depending on how we continue R-matrix operators to complex wavenumbers (to do so we establish Mittag-Leffler expansions of R-matrix operators). This entails there are more Brune resonance energies than levels. Yet, we also prove that choosing any subset of Brune poles will yield the same cross sections than using the entire set of Brune poles, as long as it has at least the number of levels. In practice, this means that shadow Brune poles can be discarded from the new nuclear data libraries. Many isotopes are evaluated with the Reich-Moore approximation, introducing complex resonance energies to eliminate certain channels. We generalize Brune's parameterization to encompass the Reich-Moore approximation and the additional shadow poles, and show that all Brune parameters depend on what convention we choose to continue the R-matrix operators to complex wavenumbers. To convert nuclear data libraries to Brune parameters, the nuclear scientists community must thus first decide on such a convention. The authors argue in favor of analytic continuation. The first evidence of shadow poles in Brune's alternative parametrization of R-matrix theory is observed in isotope xenon-134, spin-parity group 1/2(-).
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