Abstract:
A method is proposed for rearranging the Born series in scattering theory by means of
the recently proposed [1] orthogonally projecting pseudopotentials (OPP). It is proved
rigorously that even if the system contains bound states the rearranged Born series
will converge for all negative and small positive energies. It is shown how scattering
operators can be introduced accurately in the orthogonal subspaces. The OPP method
is compared with the projection technique developed by Feshbach. Physical applications
of the method are discussed.
Citation:
V. I. Kukulin, V. N. Pomerantsev, “Rearrangement and improvement of convergence of the born series in scattering theory on the basis of orthogonal projections”, TMF, 27:3 (1976), 373–385; Theoret. and Math. Phys., 27:3 (1976), 549–557
\Bibitem{KukPom76}
\by V.~I.~Kukulin, V.~N.~Pomerantsev
\paper Rearrangement and improvement of convergence of the born series in scattering theory on the basis of orthogonal projections
\jour TMF
\yr 1976
\vol 27
\issue 3
\pages 373--385
\mathnet{http://mi.mathnet.ru/tmf3340}
\transl
\jour Theoret. and Math. Phys.
\yr 1976
\vol 27
\issue 3
\pages 549--557
\crossref{https://doi.org/10.1007/BF01028623}
Linking options:
https://www.mathnet.ru/eng/tmf3340
https://www.mathnet.ru/eng/tmf/v27/i3/p373
This publication is cited in the following 5 articles:
V.S. Vasilevsky, Yu. A. Lashko, “How the antisymmetrization affects a cluster–cluster interaction: Two-cluster systems”, Annals of Physics, 415 (2020), 168114
R.A. Eramzhyan, B.S. Ishkhanov, I.M. Kapitonov, V.G. Neudatchin, “The giant dipole resonance in light nuclei and related phenomena”, Physics Reports, 136:4-6 (1986), 229
V. I. Kukulin, V. N. Pomerantsev, “Method of orthogonalized distorted waves in the theory of three-particle scattering”, Theoret. and Math. Phys., 47:2 (1981), 434–441
V.I Kukulin, V.N Pomerantsev, “The orthogonal projection method in scattering theory”, Annals of Physics, 111:2 (1978), 330
V. N. Pomerantsev, “Orthogonal projection in a system of three particles”, Theoret. and Math. Phys., 29:1 (1976), 951–957
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