论文标题
来自能源独立的复杂单$ p $ -waves $ nn $来自马尔嫩科方程的潜力
Energy-independent complex single $P$-waves $NN$ potential from Marchenko equation
论文作者
论文摘要
我们扩展了解决量子散射理论的逆问题（Marchenko理论，固定 - $ L $倒置）的结果。特别是，我们以可分离的形式为Marchenko方程输入内核扩展应用了同步三角脉冲函数。可分离的形式允许将Marchenko方程降低到输出内核扩展系数的线性方程系统。我们表明，在单个部分波的一般情况下，输入内核的线性表达是根据$ q^{1-m}（1-m}（1-s（q））$在动量$ 0 \ leq q \ leq q \leqπ/h $ s（q）$ ang and and and ys $ s的有限范围内的fourier系列系数的函数，或者$ m = 0,1，\ dots，2l $]。因此，我们表明，有限间隔的部分$ s $ - 矩阵决定了$ h $ - 步骤准确性的潜在功能。计算出的部分电势描述了部分$ s $ - 矩阵，其精度为必要。部分$ s $ - 矩阵低于非弹性和非自动（吸收性）高于阈值的阈值。我们开发了一个程序，并将其应用于$ nn $弹性散射最多3 GEV的部分波分析（PWA）数据。我们表明，与能量无关的复杂部分电位描述了单个$ p $ - 波动的这些数据。
We extend our previous results of solving the inverse problem of quantum scattering theory (Marchenko theory, fixed-$l$ inversion). In particular, we apply an isosceles triangular-pulse function set for the Marchenko equation input kernel expansion in a separable form. The separable form allows a reduction of the Marchenko equation to a system of linear equations for the output kernel expansion coefficients. We show that in the general case of a single partial wave, a linear expression of the input kernel is obtained in terms of the Fourier series coefficients of $q^{1-m}(1-S(q))$ functions in the finite range of the momentum $0\leq q\leqπ/h$ [$S(q)$ is the scattering matrix, $l$ is the angular orbital momentum, $m=0,1,\dots,2l$]. Thus, we show that the partial $S$--matrix on the finite interval determines a potential function with $h$-step accuracy. The calculated partial potentials describe a partial $S$--matrix with the required accuracy. The partial $S$--matrix is unitary below the threshold of inelasticity and non--unitary (absorptive) above the threshold. We developed a procedure and applied it to partial-wave analysis (PWA) data of $NN$ elastic scattering up to 3 GeV. We show that energy-independent complex partial potentials describe these data for single $P$-waves.
