  I present an analytic model for the early post-collapse evolution of a
spherical density peak on the coherence scale of the initial fluctuations in a
universe filled with collisionless and pressure-free "dust". On a time-scale
which is short compared to the peak's collapse time $t_0$, its inner regions
settle into an equilibrium cusp with a power-law density profile, $\rho\propto
r^{-12/7}$. Within this cusp, the circular orbit period $P$ at each radius is
related to the enclosed mass $M$ by $P = t_0 (M/M_c)^{2/3}$ where $M_c$ is a
suitably defined characteristic mass for the initial peak. The relaxation
mechanism which produces this cusp gives insight into those which are active in
high-resolution simulations of first halo formation in Cold or Warm Dark Matter
universes, and, indeed, a simple argument suggests that the same power-law
index $\gamma=-12/7$ should describe the prompt cusps formed during the
collapse of generic peaks, independent of any symmetry assumption. Further work
is needed to investigate whether additional factors are required to explain the
slightly flatter exponent, $\gamma\approx -1.5$, found in high-resolution
numerical simulations of peak collapse.
