Analysis of g₂ for the cold-collision frequency shift in the hydrogen condensate experiments

We compute an approximate set of longitudinal quasiparticle modes for a hydrogen condensate as produced in the MIT experiments. An expansion in quasiparticles using a simple one-dimensional Bogoliubov picture shows however that at the high temperatures (\approx 44muK) and in the very shallow trap employed (omega_z = 2\pi\times 10.2Hz) the contribution to the density from the quasiparticles is about 20% of that from the condensate mode, leading to an effective $ g_2(x,x) which varies between 1 and 3 depending on the position in the condensate.