描述虚态的有效值域扩展
Effective Range Expansion for Describing a Virtual State
摘要：
本文通过求解薛定谔方程的二阶微分方程，对几种类型的中心势（如中心势）的弹性散射进行了数值研究。square well，Yukawa，and Woods-Saxon）来寻找势内的波函数，并将解扩展到势范围外的区域。势范围外的波函数可按球贝塞尔函数和黎曼函数展开。在边界处求出了对数导数，为计算相移提供了依据。一旦我们有了相移，散射振幅就可以用多项式展开，并且可以推导出微分截面。此外，在低能量的散射进行了研究，并讨论了连接到有效范围扩展，以确定散射长度和有效半径。从$1$中子从$11$核子散射的虚态的签名被发现为每个潜在的和最好的能量描述的列入$\mathcal{O}(k^{10})$的有效范围扩展。
英文摘要：
I present numerical study of an elastic scattering by solving second order differential equations of Schroedinger Equation for some types of central potential (eg. square well, Yukawa, and Woods-Saxon) to find the wave function inside the potential, and extending the solution with the region outside the range of potential. The wave function outside the range of potential can be expanded in terms of spherical bessel and neumann function. At the boundary, logarithmic derivative is found which becomes a base to compute the phase shift. Once we have a phase shift, the scattering amplitude can then be expanded in terms of polynomial legendre, and the differential cross section can be deduced. Furthermore, the scattering at low energies is studied and the connection to the effective range expansion is discussed to determine the scattering length and effective radius. The signature of the virtual state from the scattering of $1$ neutron from $11$ nucleons are found for each potential and the energies are best described by the inclusion of the $\mathcal{O}(k^{10})$ in the effective range expansion.
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