The cyclotron spin-flip excitations of a two-dimensional electron system in
the extreme quantum limit have been investigated by inelastic light scatte
ring. The electron interaction energy was directly determined from the gap
between the charge- and spin-density modes in a broad region of electron fi
lling factors. A comparison of the experimental results with the Hartree-Fo
ck and generalized single mode approximations indicates a strong correlatio
n between electrons at filling factors corresponding to both compressible a
nd incompressible states.