Abstract
We consider a system of three one-dimensional particles with one of pair potentials V α(x α) decaying at infinity as |xα|−ρ, 0 <ρ < 1/2. It is shown that such a system can possess channels of scattering not included in the usual list of channels called the asymptotic completeness.
A similar result holds for the two-particle Schrödinger operator with a long-range potential if the usual condition on its derivatives is relaxed.
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Yafaev, D. (1997). New Channels of Scattering for Two-and Three-Body Quantum Systems with Long-Range Potentials. In: Truhlar, D.G., Simon, B. (eds) Multiparticle Quantum Scattering With Applications to Nuclear, Atomic and Molecular Physics. The IMA Volumes in Mathematics and its Applications, vol 89. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1870-8_7
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DOI: https://doi.org/10.1007/978-1-4612-1870-8_7
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