This article is cited in 20 papers

Wave-packet continuum discretization method for solving the three-body scattering problem

V. I. Kukulin, V. N. Pomerantsev, O. A. Rubtsova

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

Abstract: We generalize the wave-packet continuum discretization method previously developed for the scattering problem to the three-body system. For each asymptotic channel, we construct a basis of three-body wave packets given by square-integrable functions. We show that the projections of the channel resolvents on the subspace of three-body wave packets are determined by diagonal matrices, whose eigenvalues we find explicitly. We express the amplitudes of $2\to 2$ processes explicitly in terms of "wave-packet" finite-dimensional projections of the full resolvent. To illustrate our formalism, we calculate the differential cross section of elastic deuteron scattering on a heavy nucleus above the three-body breakup threshold and the $s$-wave quartet $(n-d)$-scattering amplitude. The results of the calculations agree well with the results obtained by other methods. In terms of complexity, the proposed scheme for solving the three-body scattering problem is comparable to solving a similar problem for bound states.

Keywords: quantum scattering theory, few-body system, discretization of the continuum.

Received: 22.04.2005
Revised: 19.05.2006

DOI: 10.4213/tmf5991

 English version: Theoretical and Mathematical Physics, 2007, 150:3, 403–424

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