Abstract: The SU(3) flavour symmetry for quarks and antiquarks has been demonstrated via the complexified octonion space, where the six complex octonion operators are essentially identical to the SL(3,C) group generators. It has been developed an extensive analysis of the quark flavour theory in the context of complex-octonion space by analyzing the connection between octonions and the SU(3) group. Therefore, it is argued that the extended theory of quark flavors, which preserves the property of non-commutativity, is the complexified variant of octonions. This theoretical model may be further extended to the SU(3) color symmetry, which is regarded as an exact symmetry. In this work, to gain a complete understanding of quark color theory in the framework of complex octonionic space, we have derived the relationship between octonions and the SU(3)c color group. It has been studied that only eight possibilities of paired gluons are available to provide colorless states of hadrons in order to represent theoretically the octonion glueballs. With the help of Feynman diagrams, we examined the octonionic interaction of color quarks (such as quark-quark, quark anti-quark, and anti-quarks anti-quarks interactions). For the interactions, we have obtained the complex octonion algebraic form of the interaction term, propagator, vertex factor, and color factor. Most importantly, we have examined the conditions for valid and invalid interactions for the complex-octonion formalism.Abstract: The SU(3) flavour symmetry for quarks and antiquarks has been demonstrated via the complexified octonion space, where the six complex octonion operators are essentially identical to the SL(3,C) group generators. It has been developed an extensive analysis of the quark flavour theory in the context of complex-octonion space by analyzing the connecti...Show More
Abstract: Doubly excited systems, particularly in heliumoid configurations, represent a complex area of research due to the strong interactions between the electrons. The diagonalization method is a powerful technique for studying these systems, simplifying the problem to a system of linear algebraic equations. This method makes it possible to obtain resonance parameters, such as energies E and partial widths Γ, with great precision. In the literature, there are no experimental measurements of the energies of doubly excited states in heliumoid systems, nor of the associated partial widths. The theoretical results available are few and often show inconsistencies. Moreover, even states have not yet been treated exhaustively using diagonalization or other theoretical methods. In this work, we focus on doubly excited resonances of 1,3Ge symmetry sublevels. Using a diagonalization method, we have performed robust numerical calculations to determine the resonance parameters (energies E and widths Γ) of the (3l1kl2) 1,3Ge states of the ion. The numerical advantages of the diagonalization method make it possible to obtain these resonance parameters simply and accurately. We report for the first time the resonance parameters of the 1,3Ge states, including E energies and Γ partial widths. The calculations have shown high accuracy, with results consistent with the few existing theoretical data. This study makes a significant contribution to our understanding of doubly excited states in heliumoid systems. These results fill a gap in the literature and provide a solid basis for future theoretical and experimental studies. The numerical advantages of the diagonalization method make it a technique of choice for the study of complex quantum systems. The results obtained pave the way for further investigations into other configurations and symmetries of doubly excited states. They also encourage the development of experimental measurements to validate theoretical predictions and improve our understanding of self-ionization processes in multi-electron ions.Abstract: Doubly excited systems, particularly in heliumoid configurations, represent a complex area of research due to the strong interactions between the electrons. The diagonalization method is a powerful technique for studying these systems, simplifying the problem to a system of linear algebraic equations. This method makes it possible to obtain resonan...Show More