Gross-Pitaevski equation and resonances in Bose-Einstein condensates

PACS. 34.20.-b – Interatomic and intermolecular potentials and forces, potential energy sur-faces for collisions. PACS. 34.90.+q – Other topics in atomic and molecular collision processes and interactions. Abstract. – The investigation provides a criterion for the occurrence of resonances for the scattering by potentials. The Gross-Pitaevski equation, used in describing physical properties in Bose-Einstein condensates, is not compatible with the occurrence of the observed resonances. On the other hand, Geltman-Bambini and Krauss-Stevens potentials could fulfill this criterion. It has been customary to use the Gross-Pitaevski equation (GPE) [1,2] to investigate the physical properties of Bose-Einstein condensates (BEC) in trapped ultra-cold atoms having temperature, T, of about 100 nK. The GPE is basically a mean-field Hartree equation, where the two-particle potential is a replaced by a repulsive Dirac δ-function, the strength of which is then related to positive scattering length a used in describing very low-energy scattering cross-section in earlier experiments. Subsequent measurements, however, have determined a to be positive in some cases [3–6] and negative in other cases [7–9]. Geltman and Bambini [10] have already questioned the use of the GPE for the negative scattering length and raised question