Momentum Distributions of Particles from Three--Body Halo Fragmentation: Final State Interactions

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.