Fragmented many-body states of definite angular momentum and stability of attractive three-dimensional condensates

A three-dimensional attractive Bose-Einstein condensate is expected to collapse when the number of the particles N in the ground state or the interaction strength lambda(0) exceeds a critical value. We study systems of different particle numbers and interaction strength and find that even if the overall ground state is collapsed there is a plethora of fragmented excited states that are still in the metastable region. Utilizing the configuration interaction expansion we determine the spectrum of the ground (yrast) and excited many-body states with definite total angular-momentum quantum numbers 0 <= L <= N and -L <= M-L <= L, and we find and examine states that survive the collapse. This opens up the possibility of realizing a metastable system with overcritical numbers of bosons in a ground state with angular momentum L not equal 0. The multiorbital mean-field theory predictions about the existence of fragmented metastable states with overcritical numbers of bosons are verified and elucidated at the many-body level. The descriptions of the total angular momentum within the mean-field and the many-body approaches are compared.