非定域位势e-μr/r·e-μr′/r′·e-αR/R及e-μr/r·e-μr′/r′·e(-(β(r+r′))1/2·R))/R的Regge渐近行为

本文证明了两个物理上有兴趣的非定域位势e^-μr/r·e^-μr′/r′·e^-αR/R及e^-μr/r·e^-μr′/r′·e^{(-(β(r+r′))1/2·R)})/R的分波S矩阵元对动量变数k在除沿虚轴的割线(-∞i,0),(μi,∞i)的全平面,对角动量变数λ在右半平面Reλ>-1/2的半纯性和当k,λ分别趋于无穷大时的渐近性质。最后得到了Regge渐近行为。

THE ASYMPTOTIC REGGE BEHAVIOUR FOR THE NONLOCAL POTENTIALS e-μr/r·e-μr′/r′·e-αR/R AND e-μr/r·e-μr′/r′·e(-(β(r+r′))1/2·R))/R

For the nonlocal potentials U(r,r′,R)=e^-μr/r·e^-μr′/r′·e^-αR/R and U(r,r′,R)=e^-μr/r·e^-μr′/r′·e^{(-(β(r+r′))1/2·R)})/R it is proved that the S matric element S(λ, k) is meromorphic in the topological product of the half λ -plane Reλ>-1/2 and the whole k plane cut along (-i∞, 0) and (iμ,+i∞) and that for large |λ|,S(λ, k)-1=O{1/λ^3/2 exp-λch^-1(1+μ²/(2k²))]} for k > 0 and |argλ|≤π/2.