LAUSR

The matrix elements along the reduction chain Sp(12,R) \begin{document}$ \supset $\end{document} SU(1,1) \begin{document}$ \otimes $\end{document} SO(6) \begin{document}$ \supset $\end{document} U(1) \begin{document}$ \otimes $\end{document} SU \begin{document}$ _{pn} $\end{document} (3) \begin{document}$ \otimes $\end{document} SO(2) \begin{document}$ \supset $\end{document} SO(3) of the proton-neutron symplectic model (PNSM) are considered. Closed analytical expressions are obtained for the matrix elements of the basic building blocks of the PNSM and the Sp(12,R) symplectic generators, which in turn allows to compute the matrix elements of other physical operators of interest. The computational technique developed in the present paper generally provides us with the required algebraic tool for performing realistic symplectic-based shell-model calculations of nuclear collective excitations. Two simple examples are given which illustrate the application of the theory.