Forbidden states and the three-body bound state collapse - art. no. 044009

The appearance of bound states with large binding energies of several hundr ed MeV in the three-body system, known as bound state collapse, is investig ated. For this purpose three classes of two-body potentials are employed; l ocal potentials equivalent to nonlocal interactions possessing a continuum bound state, in addition to the usual negative-energy bound state; local po tentials with a strong attractive well sustaining a forbidden state; and su persymmetric transformation potentials. It is first shown that local potent ials equivalent to the above nonlocal ones have a strong attractive well in the interior region which supports, in addition to the physical deuteron s tate, a second bound state (usually called a pseudobound state) with a larg e binding energy, which is responsible for the bound state collapse in the three-body (and in general to the N-body) system. Second, it is shown that local potentials with a forbidden state also generate a three-body bound st ate collapse. implying that the role played by the forbidden state is simil ar to the one played by the pseudobound state. Finally, it is shown that th e removal of the forbidden state via supersymmetric transformations also re sults in the disappearance of the collapse. Thus one can safely argue that the presence of unphysical bound states with large binding energies in the two-body system is responsible for the bound state collapse in the three-bo dy system.