固定能量Cox-Thompson逆散射方法特殊情况下的半解析方程
Semi-analytic equations to the Cox-Thompson inverse scattering method at fixed energy for special cases
摘要：
在固定能量下Cox-Thompson逆散射问题的解[1，2，3]被重新表述为半解析方程。新的方程组的归一化常数和非物理（移位）角动量是免费的矩阵求逆运算。这种简化是只处理给定奇偶性的部分波的输入相移的结果。因此，所提出的方法可以应用于玻色子类型的相同粒子散射（或相同的费米子散射的某些情况下）。新的公式预计将在数值上更有效的比以前的。基于半解析方程组，提出了一种求解一般逆散射问题的近似方法。
英文摘要：
Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are free of matrix inversion operations. This simplification is a result of treating only the input phase shifts of partial waves of a given parity. Therefore, the proposed method can be applied for identical particle scattering of the bosonic type (or for certain cases of identical fermionic scattering). The new formulae are expected to be numerically more efficient than the previous ones. Based on the semi-analytic equations an approximate method is proposed for the generic inverse scattering problem, when partial waves of arbitrary parity are considered.
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