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Application of Supersymmetric Quantum Mechanics to Calculate Resonance Energy and Wave Function of \(^{19}\)C Halo Nucleus

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Abstract

In this paper, we presented an elegant theoretical scheme to investigate the bound and resonance states in the \(^{19}\)C halo nucleus. The nucleus \(^{19}\)C being weakly bound one-neutron halo, can be treated as a two-body system consisting of the \(^{18}\)C core plus one outer core valence neutron. An effective core-nucleon potential is derived by folding a phenomenological nucleon-nucleon potential into the density distribution of the core nucleus. The two-body Schrödinger equation for the effective core-nucleon potential is solved to find the energies and wave functions of the bound states. The wave functions so obtained are used to construct a one-parameter family of isospectral potentials by the application of supersymmetric quantum mechanics. The newly constructed isospectral potentials are used in the Schrödinger equation to compute the resonant states. The calculated results are in excellent agreement with their corresponding observed values as found in the literature.

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Acknowledgements

This work has been supported by a computational facility at Aliah University, India.

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  1. Department of Physics, Aliah University, IIA/27, Newtown, Kolkata, 700160, India

    Md. A. Khan, M. Hasan, S. H. Mondal & M. Alam

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  1. Md. A. Khan
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  2. M. Hasan
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Khan, M.A., Hasan, M., Mondal, S.H. et al. Application of Supersymmetric Quantum Mechanics to Calculate Resonance Energy and Wave Function of \(^{19}\)C Halo Nucleus. Few-Body Syst 62, 54 (2021). https://doi.org/10.1007/s00601-021-01640-1

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