高度奇异位势S矩阵元在角动量变数λ的虚部趋于无穷大时的渐近行为

对于满足文献的条件的高度奇异位势,证明了当角动量变数λ的虚部趋于无穷大时,其分波S矩阵元具有渐近行为s(λ,k)～Ce~(-xImλ),从而对于高度奇异位势我们有下列结论:(1)散射幅的Watson-Sommerfeld变换是不成立的。(2)结合文献的结果,进而知道在虚轴的小角邻域内存在着实部趋于无穷大的Regge极点。

THE ASYMPTOTIC BEHAVIOUR OF THE S-MATRIX ELEMENT IN HIGHLY SINGULAR POTENTIAL SCATTERING FOR LARGE IMAGINARY VALUES OF ANGULAR MOMENTUM

For the highly singular potential satisfying the conditions of ref. (Ⅰ), it is proved that the partial wave S-matrix element posseses the asymptotic behaviour S(λ,k)～Ce^-nImλ as the imaginary values of angular momentum tending to infinity. From this we obtained the following conclusions:(1) The WATSON-SOMMERFELD transformation of the scattering amplitude does not hold.(2) Using the result of ref. (I) and above equation, we get existance of REGGE poles with real part tending to infinity in the little angle neighbourhood of the imaginary axis.