  The Generalized Coherent State Model, proposed previously for a unified
description of magnetic and electric collective properties of nuclear systems,
is used to study the ground state band charge density as well as the E0
transitions from $0^+_{\beta}$ to $0^+_g$. The influence of the nuclear
deformation and of angular momentum projection on the charge density is
investigated. The monopole transition amplitude has been calculated for ten
nuclei. The results are compared with some previous theoretical studies and
with the available experimental data. Our results concerning angular momentum
projection are consistent with those of previous microscopic calculations for
the ground state density. The calculations for the E0 transitions agree quite
well with the experimental data. Issues like how the shape transitions or shape
coexistence are reflected in the $\rho(E0)$ behavior are also addressed.
