  Analytic models based on spherical and ellipsoidal gravitational collapse
have been used to derive the mass functions of dark matter halos and their
progenitors (the conditional mass function). The ellipsoidal model generally
provides a better match to simulation results, but there has been no simple
analytic expression in this model for the conditional mass function that is
accurate for small time steps, a limit that is important for generating halo
merger trees and computing halo merger rates. We remedy the situation by
deriving accurate analytic formulae for the first-crossing distribution, the
conditional mass function, and the halo merger rate in the ellipsoidal collapse
model in the limit of small look-back times. We show that our formulae provide
a closer match to the Millennium simulation results than those in the spherical
collapse model and the ellipsoidal model of Sheth & Tormen (2002).
