论文标题
$ r $ -matrix理论中复杂波数的散射矩阵扩展
Scattering matrix pole expansions for complex wavenumbers in $R$-matrix theory
论文作者
论文摘要
在[R-Matrix理论的替代参数化中的阴影杆的后续文章中，我们在R-Matrix理论中为复杂的波数散射矩阵极扩展而建立了新的结果。过去，出现了两个理论形式主义的分支，以描述核物理学中的散射矩阵：R-矩阵理论和极点扩展。两者彼此之间非常孤立。最近，我们对Brune对R-Matrix理论的替代参数化的研究表明，有必要将散射矩阵（以及基础的R-Matrix操作员）扩展到复杂的波数。这两种相互竞争的方式从历史歧义中出现了$ \ boldsymbol {s} $和穿透性$ \ boldsymbol {p} $ functions的定义：传统泳道\＆thomas“力量封闭”方法，与分析延续（这是数学物理学的标准）。 R-Matrix社区尚未达成共识，即在诸如ENDF之类的标准核数据库中进行评估。 在本文中，我们主张R-Matrix运营商的分析延续。我们将R-Matrix理论桥接带有Humblet-Rosenfeld Pole的扩展，并揭示了Siegert-Humblet放射性杆和宽度的新属性，包括它们的不变性属性，以变化通道半径$ A_C $的变化。然后，我们表明R-Matrix运算符的分析延续保留了散射矩阵的重要物理和数学特性 - 取消伪造杆并保证概括性单位性 - 同时仍然能够关闭低于阈值的通道。
In this follow-up article to [Shadow poles in the alternative parametrization of R-matrix theory, Ducru (2020)], we establish new results on scattering matrix pole expansions for complex wavenumbers in R-matrix theory. In the past, two branches of theoretical formalisms emerged to describe the scattering matrix in nuclear physics: R-matrix theory, and pole expansions. The two have been quite isolated from one another. Recently, our study of Brune's alternative parametrization of R-matrix theory has shown the need to extend the scattering matrix (and the underlying R-matrix operators) to complex wavenumbers. Two competing ways of doing so have emerged from a historical ambiguity in the definitions of the shift $\boldsymbol{S}$ and penetration $\boldsymbol{P}$ functions: the legacy Lane \& Thomas "force closure" approach, versus analytic continuation (which is the standard in mathematical physics). The R-matrix community has not yet come to a consensus as to which to adopt for evaluations in standard nuclear data libraries, such as ENDF. In this article, we argue in favor of analytic continuation of R-matrix operators. We bridge R-matrix theory with the Humblet-Rosenfeld pole expansions, and unveil new properties of the Siegert-Humblet radioactive poles and widths, including their invariance properties to changes in channel radii $a_c$. We then show that analytic continuation of R-matrix operators preserves important physical and mathematical properties of the scattering matrix -- cancelling spurious poles and guaranteeing generalized unitarity -- while still being able to close channels below thresholds.
