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Low-energy parameters in nonrelativistic scattering theory. (English) Zbl 0542.35056

The authors consider the low-energy behaviour of Schrödinger operators with short-range or Coulomb-type plus short-range potentials. Based on expansions of the short-range scattering amplitude with respect to low energy E in a Laurent series around \(E=0\) explicit expressions for low- energy parameter like scattering length and effective range parameter are obtained. To this end these concepts are generalized to the case of non- spherically symmetric potentials. Zero-energy resonances and zero-energy bound states are taken into account. In the last chapter the definitions are extended to the Coulomb case with short-range perturbation. Finally an explicit expression for the Coulomb-modified scattering length is given.
Reviewer: R.Picard

MSC:

35P25 Scattering theory for PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
81U05 \(2\)-body potential quantum scattering theory
35J10 Schrödinger operator, Schrödinger equation
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