Structural factor for Bose-Einstein double-component condensate

The structural factors for the single-and double-component Bose-Einstein condensates of neutral atoms in a spherically symmetric harmonic trap are derived. The approach adopted in this paper is applicable in the low excitation energy limit, where the well-known Stringari dispersion relation is valid. Our expression is compared with the quasi-classical one, which is shown to overestimate the structural factor. It is argued that the second component first splits the frequency of collective condensate oscillations, which corresponds to the energy transferred by scattering, into two branches and then multiplies the single-component structural factor by some coefficient that can be greater than unity. The analysis is used to estimate the properties of an experimentally implemented double-component condensate of ⁸⁷Rb atoms.