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• W1539556491 abstract "Algorithm, based on explicit representations for analytic continuation of the T-matrix Faddeev components on unphysical sheets, is worked out for calculations of resonances in the three-body quantum problem. According to the representations, poles of the T-matrix, scattering matrix and resolvent on unphysical sheets, inter- preted as resonances, coincide with those complex energy values where appropriate truncations of the scattering matrix have zero as eigenvalue. Scattering amplitudes on the physical sheet, necessary to construct scattering matrix, are calculated on the basis of the Faddeev differential equations. Effectiveness of the algorithm developed is demonstrated for example of searching for resonances in the system nnp and in a model three-boson system. We make a numerical test of the approach proposed in Ref. (1) to treat the three-body resonances in the case of pairwise interactions falling off in coordinate space not slower than exponentially. This approach is based on a construction of explicit representations for the Faddeev components M��(z), �,� = 1,2,3, of the three-body T-matrix T(z) as well as for the scattering matrices S(z) and resolvent R(z) continued on unphysical sheets of the energy z plane. For the sheets, the notationl is used with l, an enumerating multi- index (see (1)). The representations constructed demonstrate a structure of kernels of the above operators after continuation and give new capacities for analytical and numerical studies of three-body resonances. In particular the representations for analytic contin- uation M(z)| �l of the matrix M(z) = {M��(z)} on the sheetl with details omitted read M| �l = M| �0 Q † J † AS 1 l JQl The operator Ql(z) and the transposed one, Q † (z) are obviously constructed of the matrix M(z) taken on the physical sheet �0. A(z) is a number matrix, an entire function of z 2 C. By Sl(z) we understand a truncation (depending essentially on l) of the total three-body scattering matrix S(z). Operators J(z) and J † (z) realize a restriction of kernels of the operators Ql(z) and Q † (z) on the energy shells, respectively, in first and last momentum variables. So that the products Q † J † and JQl have half-on-shell kernels. Representations (1) for analytical continuation of the three-body scattering matrices and resolvent follow immediately from the representations above for M(z)| �l . As follows from the representations constructed, the nontrivial (i.e. differing from the poles at the discrete spectrum eigenvalues of the three-body Hamiltonian) singularities of the T-matrix, scattering matrices and resolvent situated on an unphysical sheetl, are singularities of the inverse truncated scattering matrix S 1" @default.
• W1539556491 created "2016-06-24" @default.
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• W1539556491 date "1997-02-14" @default.
• W1539556491 modified "2023-09-27" @default.
• W1539556491 title "THREE-BODY RESONANCES IN FRAMEWORK OF THE FADDEEV CONFIGURATION SPACE APPROACH 1" @default.
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• W1539556491 hasPublicationYear "1997" @default.
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