  We investigate a description of shape-mixing and shape-transitions using
collective coordinates. To that end we apply a theory of adiabatic
large-amplitude motion to a simplified nuclear shell-model, where the
approximate results can be contrasted with exact diagonalisations. We find
excellent agreement for different regimes, and contrast the results with those
from a more standard calculation using a quadrupole constraint. We show that
the method employed in this work selects diabatic (crossing) potential energy
curves where these are appropriate, and discuss the implications for a
microscopic study of shape coexistence.
