  We analyze a proposed experiment [Boixo et al., Phys. Rev. Lett. 101, 040403
(2008)] for achieving sensitivity scaling better than $1/N$ in a nonlinear
Ramsey interferometer that uses a two-mode Bose-Einstein condensate (BEC) of
$N$ atoms. We present numerical simulations that confirm the analytical
predictions for the effect of the spreading of the BEC ground-state wave
function on the ideal $1/N^{3/2}$ scaling. Numerical integration of the
coupled, time-dependent, two-mode Gross-Pitaevskii equations allows us to study
the several simplifying assumptions made in the initial analytic study of the
proposal and to explore when they can be justified. In particular, we find that
the two modes share the same spatial wave function for a length of time that is
sufficient to run the metrology scheme.
