Low-lying Resonance State of 15 C: Application of Supersymmetric Quantum Mechanics

Calculation of the low-lying resonance state of ¹⁵C is performed using a two-body model (¹⁴C+n) with the application of Supersymmetric Quantum Mechanics (SSQM). The effective two-body potential presents a shallow well followed by a low and wide barrier. Large spatial extension of the halo state causes loss of accuracy due to numerical difficulties in calculating low-lying resonances. Use of SSQM permits one to construct an isospectral potential with a deep well followed by a high barrier which can effectively trap the system and hence facilitates the numerical calculation of resonance states more accurately than the original shallow potential. This method gives quite accurate result for the resonance energy of the ${frac{3}{2}^{+}}$ state of ¹⁵C. Calculated width of this state also agrees fairly well within the experimental error bar.