Computation of 2⁺ resonance in ⁶He: bound state in the continuum

Calculation of the 2⁺ resonance state of ⁶He in a three-body model (⁴He + n + n) is done by adopting a novel theoretical technique. The effective three-body potential for the 2⁺ state of ⁶He is obtained using hyperspherical harmonics and it presents a shallow well followed by a low and wide barrier. Numerical diffculties present in the calculation of the resonance energy of such a shallow well–barrier combination are overcome by the construction of a one-parameter (λ) isospectral potential having a bound state in the continuum. This potential develops a deep well followed by a high barrier for small positive values of λ. This effectively traps the system in a sharp resonant state and facilitates calculation of the resonance energy accurately. We obtain the first 2⁺ resonance at 1.814 MeV with a width of 135 keV. We also get a second 2⁺ resonance at 4.9 MeV.