  In this communication, we present an efficient method for computation of
energy and wave function of weakly bound nuclei by the application of
supersymmetric quantum mechanics (SSQM) and bound states in continuum (BIC)
technique. As a case study the scheme is implemented to the two-body ($^{30}$Ne
+ n) cluster model calculation of neutron-rich nucleus $^{31}$Ne. Woods-Saxon
central potential with spin-orbit component is used as the core-nucleon
interaction. The two-body Schr\"{o}dinger equation in relative coordinate is
solved numerically to get the energy and wave function of the low-lying bound
states. A one-parameter family of isospectral potential (IP) is constructed
from the bound state solutions following algebra of SSQM to find energies and
wave functions of the resonance states. In addition to the 2p$_{3/2^-}$ (-0.33
MeV) ground state, two bound excited states: s$_{1/2}$ (-0.30 MeV), $p_{1/2}$
(-0.15 MeV) are also obtained. Few low-lying resonance states: f$_{7/2_1}$
(2.57 MeV), f$_{7/2_2}$ (4.59 MeV), f$_{5/2_1}$ (5.58 MeV), p$_{1/2_1}$(1.432
MeV), p$_{1/2_2}$ (4.165 MeV), p$_{3/2_1}$ (1.431 MeV), p$_{3/2_2}$ (4.205 MeV)
are predicted. Among the predicted resonance states, the f$_{7/2^{-}}$ state
having resonance energy $E_R \simeq 4.59$ MeV is in excellent agreement with
the one found in the literature.

Nuclear Theory