Quark Cluster Model Equations for $\beta \beta$ Decay

Abstract

In a separate paper we have discussed the possibility that six quark clusters can affect the rate of double-beta decay. In this article we develop the formalism needed in the evaluation of the energy of all six-quark cluster configurations, which can arise in a harmonic oscillator basis up to $2\hslash \omega$ excitations. The symmetries that were found useful for this purpose were the combined spin color symmetry $S{U}_{cs}(6)$, the orbital symmetry $S{U}_o(6)$ and the isospin symmetry $S{U}_I(2)$.

46 pages, 32 tables, no figures

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