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.

在本文中，我们提出了一个优雅的理论方案来研究\(^{19}\) C 晕核中的束缚态和共振态。原子核\(^{19}\) C 是弱束缚的单中子晕，可以看作是由\(^{18}\)C核加一个外核价中子。通过将现象学的核子 - 核子势折叠到核心核的密度分布中，可以得出有效的核 - 核子势。求解有效核-核子势的二体薛定谔方程以找到束缚态的能量和波函数。通过应用超对称量子力学，如此获得的波函数被用来构建一个等谱势的单参数族。新构建的等谱电位用于薛定谔方程来计算共振态。计算结果与文献中相应的观察值非常吻合。