Fragmented metastable states exist in an attractive Bose-Einstein condensate for atom numbers well above the critical number of the Gross-Pitaevskii theory

It is well known that attractive condensates do not posses a stable ground state in three dimensions. The widely used Gross-Pitaevskii theory predicts the existence of metastable states up to some critical number N-cr(GP) of atoms. It is demonstrated here that fragmented metastable states exist for atom numbers well above N-cr(GP). The fragments are strongly overlapping in space. The results are obtained and analyzed analytically as well as numerically. The implications are discussed.