  Assemblies of interacting quantum particles often surprise us with properties
that are difficult to predict. One of the simplest quantum many-body systems is
the spin 1/2 Heisenberg antiferromagnetic chain, a linear array of interacting
magnetic moments. Its exact ground state is a macroscopic singlet entangling
all spins in the chain. Its elementary excitations, called spinons, are
fractional spin 1/2 quasiparticles; they are created and detected in pairs by
neutron scattering. Theoretical predictions show that two-spinon states exhaust
only 71% of the spectral weight while higher-order spinon states, yet to be
experimentally located, are predicted to participate in the remaining. Here, by
accurate absolute normalization of our inelastic neutron scattering data on a
compound realizing the model, we account for the full spectral weight to within
99(8)%. Our data thus establish and quantify the existence of higher-order
spinon states. The observation that within error bars, the entire weight is
confined within the boundaries of the two-spinon continuum, and that the
lineshape resembles a rescaled two-spinon one, allow us to develop a simple
physical picture for understanding multi-spinon excitations.
