Investigation of phase - equivalent potentials by a halo transfer reaction

Using the supersymmetric quantum mechanics we investigate the wave function-sensitive properties of the supersymmetric potentials which have received a lot of attention in the literature recently. We show that a su-perdeep potential and its phase-equivalent shallow-partner potential give very similar rms values for the weakly bound systems such as the deuteron and 11 Be nuclei. Although the corresponding eigenstates differ in the node-number, our investigation on the 11 Be(p, d) 10 Be single nucleon halo transfer reaction at 35 MeV show that also other physical quantities such as the cross section angular distributions calculated using these wave functions reflect the nodal structure rather weakly. This lends support to two nearly equivalent treatments of the Pauli principle.