位势在原点有高于二阶的极点时散射振幅的Regge行为

当位势V(z)在原点有高于二阶的极点时(在右半平面V(z)解析,当z→∞时z²V→0),证明了(1)S矩阵元为λ(λ=ι+1/2,ι是角动量)的半纯函数;(2)当λ在右半平面|argλ|<π/2内趋于无穷大时,|S-1|≤C((log|λ|)/|λ|)。

REGGE BEHAVIOUR FOR THE SCATTERING UNDER A POTENTIAL WITH A SINGULARITY AT ORIGIN HIGHER THAN z~(-2)

Assuming that: (l), the potential V(z)→z^-n(n>2) as z→0; (2), V is regular in Re z>0; (3), V(z)z²→0 as z→∞ in |arg z|<π/2, the following assertions are proved: (l), the scattering matrix element S is meromorphic in the whole λ plane (λ=l+1/2,l—angular momentum);(2)S-1→O((log|λ|)/|λ|) as λ→∞ in |arg λ|<π/2.