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

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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→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.

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Authors and Affiliations

  1. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia

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

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  1. V. I. Kukulin
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  2. V. N. Pomerantsev
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  3. O. A. Rubtsova
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 3, pp. 473–497, March, 2007.

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Kukulin, V.I., Pomerantsev, V.N. & Rubtsova, O.A. Wave-packet continuum discretization method for solving the three-body scattering problem. Theor Math Phys 150, 403–424 (2007). https://doi.org/10.1007/s11232-007-0030-3

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  • DOI: https://doi.org/10.1007/s11232-007-0030-3

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