  Following a sudden change of interactions in an integrable system of
one-dimensional fermions, we analyze the dependence of the static structure
factor on the observation time after the quantum quench. At small waiting times
after the quench, we map the system to non-interacting bosons such that we are
able to extract their occupation numbers from the Fourier transform of the
density-density correlation function, and use these to compute a bosonic
entropy from a diagonal ensemble. By comparing this bosonic entropy with the
asymptotic steady state entanglement entropy per fermion computed with exact
diagonalization we find excellent agreement.
