Momentum Distribution for Bosons with Positive Scattering Length in a Trap

Abstract

The coordinate-momentum double distribution function $ρ({\bf r}, {\bf p}) d^{3}rd^{3}p$ is calculated in the local density approximation for bosons with positive scattering length $a$ in a trap. The calculation is valid to the first order of $a$. To clarify the meaning of the result, it is compared for a special case with the double distribution function $ρ_{w}d^{3} rd^{3}p$ of Wigner.