  Phase fluctuations in the superconducting order parameter, which are
responsible for the melting of the Abrikosov vortex lattice below the mean
field $H_{c2}$, are shown to dramatically enhance the scattering of
quasi-particles by the fluctuating pair potential, thus leading to enhanced
damping of the dHvA oscillations in the liquid mixed state. This effect is
shown to quantitatively account for the detailed field dependence of the dHvA
amplitude observed recently in the mixed state of a Quasi 2D organic SC.
