  We present a resonant inelastic x-ray scattering (RIXS) study of spin and
charge excitations in overdoped La1.77Sr0.23CuO4 along two high-symmetry
directions. The line shape of these excitations is analyzed and they are shown
to be highly overdamped. Their spectral weight and damping are found to be
strongly momentum dependent. Qualitative agreement between these observations
and a calculated RPA susceptibility is obtained for this overdoped compound,
implying that a significant contribution to the RIXS signal stems from a
continuum of charge excitations. Furthermore, this suggests that the
spin-excitations in the overdoped regime can be captured qualitatively by an
itinerant picture. Our calculations also predict a new low-energy spin
excitation branch to exist along the nodal direction near the zone center. With
the energy resolution of the present experiment, this branch is not resolvable
but we show that next generation of high-resolution spectrometers will be able
to test this prediction.
