Authors :
Debopam Ghosh
Volume/Issue :
Volume 6 - 2021, Issue 7 - July
Google Scholar :
http://bitly.ws/9nMw
Scribd :
https://bit.ly/2V7PXiM
Abstract :
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’
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’
