Geodesic
Wave-packet continuum discretization method for solving the~three-body
Teoretičeskaâ i matematičeskaâ fizika, Tome 150 (2007) no. 3, pp. 473-497

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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. 
@article{TMF_2007_150_3_a7,
     author = {V. I. Kukulin and V. N. Pomerantsev and O. A. Rubtsova},
     title = {Wave-packet continuum discretization method for solving the~three-body},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {473--497},
     publisher = {mathdoc},
     volume = {150},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_150_3_a7/}
}
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V. I. Kukulin; V. N. Pomerantsev; O. A. Rubtsova. Wave-packet continuum discretization method for solving the~three-body. Teoretičeskaâ i matematičeskaâ fizika, Tome 150 (2007) no. 3, pp. 473-497. http://geodesic.mathdoc.fr/item/TMF_2007_150_3_a7/