Effective-range expansion for two coupled channels and properties of bound states |
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Authors: | L D Blokhintsev |
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Institution: | 1.Skobeltsyn Institute of Nuclear Physics,Moscow State University,Moscow,Russia |
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Abstract: | The S matrix and the scattering-amplitude matrix (F matrix) are considered for the case of two coupled elastic-scattering channels differing by the values of the orbital angular
momentum (l
1 and l
2 = l
1 + 2). The matrix elements of the S and F matrices in the absence of Coulomb interaction are expressed in terms of the matrix elements of the matrix K
−1 inverse to the reaction K matrix. The elements of the K
−1 matrix are written in the form of expansions that are generalizations of the single-channel effective-range expansion. If
there is a bound state in the system of colliding particles, then an analytic continuation of these expansions to the region
of negative energies makes it possible to obtain both the position of the pole corresponding to this bound state and the residues
of scattering amplitudes at this pole, the respective vertex constants and asymptotic normalization coefficients being expressed
in terms of these residues. By way of example, the developed formalism is applied to describing triplet neutron-proton scattering. |
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Keywords: | |
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