  The longitudinal (e,e') response function of 4He is calculated precisely with
full final state interaction. The explicit calculation of the four-body
continuum states is avoided by the method of integral transforms. Precision
tests of the response show the high level of accuracy. Non-relativistic nuclear
dynamics are used. The agreement with experimental data is very good over a
large energy range for all considered momentum transfers (q=300, 400, 500
MeV/c). Only at higher q the theoretical response overestimates the
experimental one beyond the quasi-elastic peak.
