scholarly journals Degeneracies whenT=0two body interaction matrix elements are set equal to zero: Talmi’s method of calculating coefficients of fractional parentage to states forbidden by the Pauli principle

2001 ◽  
Vol 64 (5) ◽  
Author(s):  
Shadow J. Q. Robinson ◽  
Larry Zamick
Keyword(s):  
Pauli Principle ◽  
Interaction Matrix ◽  
Matrix Elements ◽  
Body Interaction ◽  
Fractional Parentage

Theoretical studies in nuclear structure. II. Nuclear d 2 , d 3 and d 4 configurations. Fractional parentage coefficients and central force matrix elements

1951 ◽  
Vol 205 (1081) ◽  
pp. 192-237 ◽  
Keyword(s):  
Group Theory ◽  
Nuclear Structure ◽  
Central Force ◽  
Irreducible Representations ◽  
Theoretical Studies ◽  
Matrix Elements ◽  
Energy Matrix ◽  
Body Interaction ◽  
Fractional Parentage

The orbital and charge-spin fractional parentage coefficients for the nuclear d 3 and d 4 con­figurations are derived using group theory. The orbital coefficients are given in a form appropriate to the new subclassification of the states according to irreducible representations of R 5 discussed in part I (Jahn 1950). Using these coefficients the complete energy matrices for the d 3 and d 4 configurations are derived, for a general charge-symmetric central two-body interaction, from the known energy matrix for the d 2 configuration.

Quasi-particles in atomic shell theory

1970 ◽  
Vol 315 (1520) ◽  
pp. 27-37 ◽  
Keyword(s):  
Shell Theory ◽  
Particle Creation ◽  
Rotation Group ◽  
Coupling Scheme ◽  
Matrix Elements ◽  
Spin Orientation ◽  
Quasi Particle ◽  
Quantum Numbers ◽  
Fractional Parentage ◽  
Electronic Configurations

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 Ɵ) corresponds to the irreducible representatio n (½ ½ ... ½ ) of the rotation group R Ɵ (2 l +1). The generators for this group are constructed from quasi-particle creation and annihilation operators. The angular momentum quantum numbers l Ɵ arising from the decomposition of (½ ½ ... ½) into representations of R Ɵ (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 state s of g N .

Weak interaction matrix elements with staggered fermions (I). Theory and a trial run

1987 ◽  
Vol 286 ◽  
pp. 253-292 ◽  
Author(s):  
Stephen R. Sharpe ◽  
Apoorva Patel ◽  
Rajan Gupta ◽  
Gerald Guralnik ◽  
Gregory W. Kilcup
Keyword(s):  
Weak Interaction ◽  
Interaction Matrix ◽  
Matrix Elements ◽  
Staggered Fermions
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