Method of analytic continuation in the coupling constant in the theory of systems of several particles. Resonance state as analytic continuation of a bound state
We propose a new approach to the dynamics of systems of several particles, based on analytic continuation in the coupling constant by the use of Pade approximants of the second kind. In the present paper this approach is used to construct a theory of resonant states in nuclei by means of analytic continuation in the coupling constant of the attractive part of the interaction. A technique for finding the parameters of resonances is described; these include the energies, widths, and wave functions of Gamow states and the corresponding quantities for antibound (virtual) states of real and complex Hamiltonians. The same technique of analytic extrapolation is used to calculate matrix elements involving resonance wave functions. It is shown that this theory leads to a procedure for regularizing resonance matrix elements which is exactly equivalent in its result to the well known Zel'dovich regularization but is much simpler than that method in practice. The possibility is discussed of applying this formalism to a shell model with two particles in the continuum and to the theory of many-particle resonances.
- Research Organization:
- Institute of Nuclear Physics, Moscow State University
- OSTI ID:
- 5786214
- Journal Information:
- Sov. J. Nucl. Phys. (Engl. Transl.); (United States), Vol. 29:3
- Country of Publication:
- United States
- Language:
- English
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RESONANCE
SHELL MODELS
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MANY-BODY PROBLEM
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