The Reduced Description framework associated with the Matrix Shell Model Formalism


Authors : Debopam Ghosh

Volume/Issue : Volume 6 - 2021, Issue 7 - July

Google Scholar : http://bitly.ws/9nMw

Scribd : https://bit.ly/2V7PXiM

The present research article formulates a Mathematical Framework that simplifies the computational requirements associated with the Matrix Shell Model Formalism [5],[25]. This is achieved by removal of the computations involving the Matrix Shell Interaction coefficients and setting them all to unity, additional simplification is achieved by introducing appropriate “ Averaging” at the level of Pathways which results in a single, Hermitian matrix ( The Reduced State-Interaction Matrix description) being associated with every constituent Matrix Shells. This ultimately results in a single, Hermitian matrix (The Reduced State-Interaction Matrix description of the Matrix Shell system) for the given numerical realization of the Fundamental matrix associated with the Matrix Shell System ‘N’. Numerical Illustrations are drawn from U(2) subset of Complex Matrix space of order ‘2’, The set of Analytical Expressions pertaining to the Overlap elements associated with N=2 Matrix Shell system in a U(2) Matrix numerical realization is also compiled and presented in this paper.

Keywords : The Matrix Shell Model Formalism, State-Interaction matrices associated with Matrix Shell System Configurations, Reduced State-Interaction Matrix description of a Matrix Shell, Directional states associated with a Pathway, State interaction Matrix description of the Matrix Shell System ‘N’, Reduced State-Interaction Matrix Description of the Matrix Shell system ‘N’

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