## Abstract

A new scheme is described for defining and classifying the states of the electronic configurations l$^{N}$. The spaces for which the spin orientation is either up or down are both factored into two parts. Each of these parts (distinguished by a symbol $\theta $) corresponds to the irreducible representation ($\frac{1}{2}$ $\frac{1}{2}\ldots \frac{1}{2}$) of the rotation group R$_{\theta}$(2l+1). The generators for this group are constructed from quasi-particle creation and annihilation operators. The angular momentum quantum numbers l$_{\theta}$ arising from the decomposition of ($\frac{1}{2}$ $\frac{1}{2}\ldots \frac{1}{2}$) into representations of R$_{\theta}$(3) can be used to couple the four parts together. No ambiguities arise when l < 9, thereby giving a very satisfactory coupling scheme. No coefficients of fractional parentage (c.f.p.) are required in the calculation of matrix elements. Simple explanations are given for some null c.f.p. and for some repeated eigenvalues of an operator that had previously been used to classify the states of g$^{N}$.

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