PLETHYSM AND THE THEORY OF COMPLEX SPECTRA.

Notable progress in developing the theory of complex spectra has come from the exploitation of the symmetry properties of atomic wavefunctions using the theory of continuous groups. Many seemingly simple results have previously been obtained by what would appear to be unreasonably complex methods. Many of these complexities may be removed, and new results derived, using the algebra of plethysm first developed by Littlewood. Applications to three central problems in the theory of complex spectra are discussed: (1) the classification of the atomic states of n‐electron configurations; (2) the analysis and classification of the N‐particle operators that arise in the application of perturbation theory to atomic problems; (3) the derivation of selection rules for the matrix elements of operators.

[1]  B. Judd,et al.  A Class of Null Spectroscopic Coefficients , 1967 .

[2]  S. Feneuille.  Symétrie des opérateurs de l'interaction coulombienne pour les configurations (d + s)n , 1967 .

[3]  B. H. Flowers.  Studies in jj-coupling. I. Classification of nuclear and atomic states , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  D. E. Littlewood,et al.  Invariant theory, tensors and group characters , 1944, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[5]  G. Racah,et al.  Theory of Complex Spectra. IV , 1942 .

[6]  M. H. Macfarlane,et al.  The quasi-spin formalism and the dependence of nuclear matrix elements on particle number , 1965 .

[7]  S. Feneuille.  Application de la théorie des groupes de Lie aux configurations mélangées , 1967 .

[8]  H. Weyl.  The Classical Groups , 1939 .

[9]  H. Marvin.  Mutual Magnetic Interactions of Electrons , 1947 .

[10]  H. Mendlowitz,et al.  Second Quantization and Atomic Spectroscopy , 1967 .

[11]  B. Judd.  THREE-PARTICLE OPERATORS FOR EQUIVALENT ELECTRONS , 1966 .

[12]  J. P. Elliott,et al.  Collective motion in the nuclear shell model. I. Classification schemes for states of mixed configurations , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[13]  H. Weyl.  The Theory Of Groups And Quantum Mechanics , 1931 .

[14]  W. Scott,et al.  Group Theory. , 1964 .

[15]  D. E. Littlewood,et al.  Products and Plethysms of Characters with Orthogonal, Symplectic and Symmetric Groups , 1958, Canadian Journal of Mathematics.

[16]  H. Jahn.  Theoretical studies in nuclear structure I. Enumeration and classification of the states arising from the filling of the nuclear d-shell , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[17]  D. E. Littlewood.  Plethysm and the Inner Product of S‐Functions , 1957 .

[18]  B. Judd.  ZEEMAN EFFECT AS A PROTOTYPE FOR INTRA-ATOMIC INTERACTIONS , 1967 .

[19]  B. G. Wybourne,et al.  Selection Rules and the Decomposition of the Kronecker Square of Irreducible Representations , 1967 .

[20]  B. G. Wybourne,et al.  Configuration Interaction Effects in l N Configurations , 1963 .

[21]  G. B. Robinson,et al.  Representation theory of the symmetric group , 1961 .