Hyperspherical three-body model calculation for the bound and resonant states of the neutron dripline nuclei 42,44Mg using isospectral potential

Abstract

In this paper, an effective theoretical scheme is presented to investigate ground and resonant levels of weakly bound nuclei near the neutron-dripline. The hyperspherical harmonics expansion method is employed for the bound state while supersymmetric quantum mechanics (SSQM) is used for the resonant state. The three-body Schrödinger equation is solved for the lowest bound state with chosen set of two-body potentials to obtain the energy and normalized wavefunction. The three-body effective potential has a very shallow well following a low-wide barrier giving a broad resonance due to far extended wavefunction in the asymptotic region. Numerical computation of such broad resonance is very challenging due to large computational errors. Hence, a one-parameter family of isospectral potential is constructed with the ground state energy and wavefunction, by the use of the algebra of SSQM. This enhanced potential facilitates a more accurate computation of the resonance energy and width. Effectiveness of the scheme has been checked for the J=π0+ bound and resonant states of neutron-rich nuclei 42,44Mg in the coreNN three-body cluster model where core=40,42Mg. In the present calculation, two-neutron separation energies obtained with very large number of partial waves for the J=π0+ bound states of neutron-rich nuclei 42,44Mg are found to be 0.41433 MeV and 0.44975 MeV respectively. Results of the calculation have been compared with those found in the literature.