The authors consider the two-electron Hamiltonian H=- Delta 1 - Delta 2 -r 1 -1 -r 2 -1 +Ar 12 -1 at precisely that critical value of A where the ground state energy has just hit the continuum. For that A, it is proven that H has a square integrable eigenfunction at the bottom of the continuum.
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Hoffmann-Ostenhof et al. (1983) studied this question.
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