Resonance Energy and Wavefunction of ³¹Ne: a Calculation Using Supersymmetric Quantum Mechanics

In this communication, we present an accurate and powerful method to compute the energy and wave function of weakly bound nuclei. As a case study, the scheme is implemented to the neutron-rich nucleus Ne-31 assuming a (Ne-30 + n) two-body cluster model. Spherically symmetric Woods-Saxon potential with a spin-orbit component is chosen for the core-nucleon interaction. The two-body Schrodinger equation in relative coordinate is solved numerically to get the energy and wavefunction of the low-lying bound states. A one-parameter family of isospectral potential is constructed using the bound state solutions following the algebra of supersymmetric quantum mechanics (SSQM) to find energies and wavefunctions of the low-lying resonances. In addition to the ground state 1(p3/2) (-0.33 MeV), two low-lying 2 bound excited states 1(s1/2) (-0.30 MeV) and 1(p1/2 )(0.15 MeV) are also obtained. Few low-lying resonances: 2(p1/2) (1.432MeV), 2(p3/2) (1.431 MeV), 1(f5/2)- (5.58 MeV) and 1(f7/2) (4.59 MeV) are also investigated. The calculated 1(f7/2) resonance at E-R similar or equal to 4.59 MeV is in excellent agreement with the one found in the literature.