  The nuclei $^4$He, $^8$Be, $^{12}$C and $^{16}$O have been studied starting
from nucleon-nucleon interactions of $v_4$ type. The wave function is built as
the product of three terms, a Jastrow correlation factor, a linear correlation
factor and a model wave function. The correlation factors account for both the
short range repulsive and the spin and isospin dependence of the nuclear
potential. The model wave function is antisymmetric and has the values of the
angular momentum and parity of the state under description. For the model wave
function we have used two different schemes. The first one is based on a
Harmonic Oscillator shell model with and without deformation, and the second
one is based on the Margenau-Brink model of alpha clustering. Projection
operators of parity and total angular momentum are used. The performance of
these two models is studied and compared systematically. Wave functions for the
ground state and some members of its rotational band and some other bound
states of these nuclei have been obtained. Binding energies, root mean square
radius and the expectation value of the kinetic energy and the different
channels of the nuclear interactions and the one-- and two-- body densities are
reported. The two different model wave functions and the effects of the
different nucleon-nucleon correlations have been evaluated on those quantities.
All the results here presented have been obtained by using the Variational
Monte Carlo method.
