  We study the development of electron-electron correlations in circular
quantum dots as the density is decreased. We consider a wide range of both
electron number, N<=20, and electron gas parameter, r_s<18, using the diffusion
quantum Monte Carlo technique. Features associated with correlation appear to
develop very differently in quantum dots than in bulk. The main reason is that
translational symmetry is necessarily broken in a dot, leading to density
modulation and inhomogeneity. Electron-electron interactions act to enhance
this modulation ultimately leading to localization. This process appears to be
completely smooth and occurs over a wide range of density. Thus there is a
broad regime of ``incipient'' Wigner crystallization in these quantum dots. Our
specific conclusions are: (i) The density develops sharp rings while the pair
density shows both radial and angular inhomogeneity. (ii) The spin of the
ground state is consistent with Hund's (first) rule throughout our entire range
of r_s for all 4<N<20. (iii) The addition energy curve first becomes smoother
as interactions strengthen -- the mesoscopic fluctuations are damped by
correlation -- and then starts to show features characteristic of the classical
addition energy. (iv) Localization effects are stronger for a smaller number of
electrons. (v) Finally, the gap to certain spin excitations becomes small at
the strong interaction (large r_s) side of our regime.
