ANALYTIC PROPERTIES OF THE SCATTERING AMPLITUDE OF TWO INTERACTIVE CHARGED PARTICLES IN A YUKAWA TYPE POTENTIAL (in French)
Journal Article
·
· Nuovo Cimento (Italy) Divided into Nuovo Cimento A and Nuovo Cimento B
OSTI ID:4740360
A rigorous derivation is presented of the analytic properties of the S- wave scattering amplitude when, in addition to a superposition of Yukawa potentials, a Coulomb interaction is present. The method of proof starts from the usual effective range function which as well known is free of Coulomb singularities. It is shown that this effective range function is analytic in a strip in the k complex plane. Then, making use of the analytic properties of superpositions of exponential potentials with respect to the distance r we can solve the Schrodinger equation along a ray in the r-plane and rotate the initial strip of analyticity in k. Eventually we find that the effective range function is meromorphic in the whole k plane except for two cuts. As in the noncoulombic case the S-matrix can be written as the ratio of two functions, one with the lower cut, another one with the upper cut. The zeros of the denominator of S in the upper half k-plane can still be interpreted as bound states located on the imaginary k-axis. The connection between the successive Born approximations and the discontinuity of S in the upper half-plane is rigorously established and, from the integral representation of S we easily obtain the integral equation connecting the discontinuity in the upper half-plane and S itself. Finally the asymptotic behavior of S is studied. (auth)
- Research Organization:
- Laboratoire Joliot-Curie de Physique Nucleaire, Orsay, France
- NSA Number:
- NSA-17-005227
- OSTI ID:
- 4740360
- Journal Information:
- Nuovo Cimento (Italy) Divided into Nuovo Cimento A and Nuovo Cimento B, Journal Name: Nuovo Cimento (Italy) Divided into Nuovo Cimento A and Nuovo Cimento B Vol. Vol: (10), 26; ISSN NUCIA
- Country of Publication:
- Country unknown/Code not available
- Language:
- French
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