Abstract
We propose a novel mathematical approach for the calculation of resonances in weakly bound systems. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features can be generated. For systems having no bound ground state, an isospectral potential with a bound state in the continuum is possible. The quasi-bound state in the original shallow potential will be effectively trapped in the deep well of the isospectral family, facilitating more accurate calculation of resonance energy. Application to 6He, 6Li and 6Be yield excellent results. Another application is the calculation of Efimov states in weakly bound threebody system. We present the result of 4He trimer, where the first excited state is claimed to be an Efimov state.
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Chakrabarti, B. Use of supersymmetric isospectral formalism to realistic quantum many-body problems. Pramana - J Phys 73, 405–416 (2009). https://doi.org/10.1007/s12043-009-0132-6
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DOI: https://doi.org/10.1007/s12043-009-0132-6