We give a complete classification of basis with unitari (U(A-1), U(3)) and permutational (S)A)) symmetries. Thse are suitable as functions for (p-f)- nuclei (41<= A <= 80) with minimal configuration energy. We also give a brief survey of way in which are obtained.

A short summary of the theory of symmetric group and symmetric functions needed to follow the theory of Schur functions and plethysms is presented. One then defines plethysm, gives its properties and presents a procedure for its calculation. Finally, some aplications in atomic physics and nuclear structure are given.

The results of the evaluation of the Generalized Interacting Boson Model (GIBM) Hamiltonian in the framework of Restricted Dynamics Approach have been used in order to estimate the microscopical values for the parameters of two phenomenological collective models - the Bohr-Mottelson Model (BMM) and the standard Interacting Boson Model (IBM). The microscopically derived parameter values are calculated, using the effective NN-interaction potential parameter values obtained from the Strictly Restricted Dynamics Model (SRDM) energy calculations for light <FONT FACE="Symbol">a</font>-cluster type nuclei with 8 <FONT FACE="Symbol">£ </font>A <FONT FACE="Symbol">£ </font>60, and compared with the phenomenological model parameter values obtained from the direct fit to the experimental level energies of the same nuclei.