  Using a self consistent approximation for the spin distribution of Skyrmions
in the quantum Hall effect, we obtain an effective action for the Skyrmion
coordinates. The energy functional is minimised for a periodic distribution of
Skyrmions with an underlying hexagonal symetry. We calculate the phonon
spectrum of this lattice and find that near the classical minimum, breathing
modes of the Skyrmions are strongly suppressed. The resulting equal sized
Skyrmions interact via a residual Coulomb potential. Neglecting coupling
between phonons and spin waves due to dipole and higher order Coulomb
interactions, the Skyrmion crystal has a phonon spectrum identical to that of
an electronic Wigner crystal. The transition to a liquid of equal sized
Skyrmions is discussed using the theory of dislocation melting and a comparison
is made between the predictions of this theory and the results of a recent
experiment.
