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Some questions about the scattering amplitude for a complex nonlocal potential superposition of Yukawa potentials with a complex weight functionσ(t; q′)2, q2are studied. Under reasonable conditions onσ(t; q′)2, q2it is shown that the kernel of the Lippmann-Schwinger equation forT(z) is of the Hilbert-Schmidt class and that the von Neumann series converges for |z| large enough. The analyticity properties and asymptotic behaviours of the Born termsT(n)(q′, q) are studied. The properties thus established forT(n)(q′, q) are used for the study of the analyticity properties of the total amplitudeT(s, t) ending with a dispersion relation ins. |
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