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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/λ3/2 exp[-λch-1(1+μ2/(2k2))]} for k > 0 and |argλ|≤π/2.
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