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arXiv quant-ph/0204112quant-phnucl-th
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散射理论中达布变换的相位等价链

Phase equivalent chains of Darboux transformations in scattering theory

Boris F. Samsonov, Fl. Stancu

备注：
22 pages, 4 figures, REVTeX
发表信息：
Phys.Rev. C66 (2002) 034001
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摘要：

我们提出了一个基于相位等价链的达布变换来产生满足径向薛定谔方程的局部势，并共享相同的散射数据。对于相关的潜力链的变换的解析表达式推导出的Jost功能。它示出了如何相同的系统的$S$矩阵极点可以不同地分布在极点和零点之间的Jost函数，对应于不同的电位与相等的相移。分析了浅相等效势和深相等效势的概念，并与不同的极点分布相联系。结果表明，相位等效链不违反列文森定理。应用该方法导出了描述核子-核子散射的$^1S_0$分波的浅相等效势和一族深相等效势。

英文摘要：

We propose a procedure based on phase equivalent chains of Darboux transformations to generate local potentials satisfying the radial Schrödinger equation and sharing the same scattering data. For potentials related by a chain of transformations an analytic expression is derived for the Jost function. It is shown how the same system of $S$-matrix poles can be differently distributed between poles and zeros of a Jost function which corresponds to different potentials with equal phase shifts. The concept of shallow and deep phase equivalent potentials is analyzed in connection with distinct distributions of poles. It is shown that phase equivalent chains do not violate the Levinson theorem. The method is applied to derive a shallow and a family of deep phase equivalent potentials describing the $^1S_0$ partial wave of the nucleon-nucleon scattering.

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