  Momentum distributions of particles from nuclear break-up of fast three-body
halos are calculated consistently, and applied to $^{11}$Li. The same two-body
interactions between the three particles are used to calculate the ground state
structure and the final state of the reaction processes. We reproduce the
available momentum distributions from $^{11}$Li fragmentation, together with
the size and energy of $^{11}$Li, with a neutron-core relative state containing
a $p$-state admixture of 20\%-30\%. The available fragmentation data strongly
suggest an $s$-state in $^{10}$Li at about 50 keV, and indicate a $p$-state
around 500 keV.
