  Variational wave functions based on a Margenau-Brink cluster model with short
range and state dependent correlations, and angular momentum projection are
obtained for some nuclei with $12 \leq A \leq 16$. The calculations have been
carried out starting from the nucleon-nucleon interaction by using the
Variational Monte Carlo method. The configuration used consists of three alpha
clusters located at the apexes of an equilateral triangle, and an additional
cluster, not necessarily of alpha type, forming a tetrahedron. This cluster is
located at the top of its height. Short-range and state dependent correlations
are included by means of a central Jastrow factor and a linear operatorial
correlation factor respectively. Angular momentum projection is performed by
using the Peierls-Yoccoz operators. Optimal structures are obtained for all the
nuclei studied. Some aspects of our methodology have been tested by comparing
with previous calculations carried out without short range correlations. The
binding energy, the root mean square radius, and the one- and two-body
densities are reported. The effects of correlations on both the energy and the
nucleon distribution are analyzed systematically.
