标题： Khuri-Jones阈值因子作为自守函数 显示英文标题

标题： The Khuri-Jones Threshold Factor as an Automorphic Function

摘要： 阈值处Khuri-Jones对部分波散射振幅的修正是一个二面体的自守函数。 在上半平面映射到半无限条带内部的极点处得到了部分波振幅的表达式。 对于束缚态，Lehmann椭圆存在于阈值以下。 当系统从阈值以下变为阈值以上时，类型1的离散二面体（椭圆）群转变为类型3的群，其双曲元素保持固定点0和$\infty$不变。 中性固定点从-1和+1转变为源-汇固定点0和$\infty$是角动量虚部有限共振宽度的结果。 群的对称性变化及其镶嵌结构可以用来区分束缚态和共振态。 显示英文摘要

摘要： The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-plane maps on to the interior of semi-infinite strip. The Lehmann ellipse exists below threshold for bound states. As the system goes from below to above threshold, the discrete dihedral (elliptic) group of Type 1 transforms into a Type 3 group, whose loxodromic elements leave the fixed points 0 and $\infty$ invariant. The transformation of the indifferent fixed points from -1 and +1 to the source-sink fixed points 0 and $\infty$ is the result of a finite resonance width in the imaginary component of the angular momentum. The change in symmetry of the groups, and consequently their tessellations, can be used to distinguish bound states from resonances.