Matrix elements of operators in symmetrical U(6)containsU(3)containsU(2)containsU(1) and U(6)containsSU(3)containsSO(3)containsSO(2) basis

Journal Article · Wed Jul 01 04:00:00 EDT 1981 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.525060· OSTI ID:6189008

Quesne, C

In this paper we consider a basis for N boson states classified by the chain of groups U(6)containsU(3)containsU(2)containsU(1). We determine analytical expressions for the matrix elements of the boson creation and annihilation operators, as well as for the U(6) generators, with respect to that basis. For such purpose, we use the Wigner--Eckart theorem with respect to U(3) and calculate the reduced matrix elements of the appropriate irreducible tensors from their matrix elements between highest weight states. Then we apply the transformation brackets from the chain U(6)containsU(3)containsU(2)containsU(1) to the physical chain U(6)containsSU(3)containsSO(3)containsSO(2) to obtain the matrix elements of the above-mentioned operators in a basis corresponding to the latter. The matrix elements so determined can be used either in the nuclear interacting boson model of Arima and Iachello or in the microscopic nuclear collective model of Vanagas et al.

• Research Organization: Service de Physique Theorique et Mathematique CP 229, Universite Libre de Bruxelles, B-1050 Brussels, Belgium
• OSTI ID: 6189008
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 22:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

653007* -- Nuclear Theory-- Nuclear Models-- (-1987)
658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANGULAR MOMENTUM
ANNIHILATION OPERATORS
BOSONS
COLLECTIVE MODEL
CREATION OPERATORS
INTERACTING BOSON MODEL
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
NUCLEAR MODELS
QUANTUM OPERATORS
SHELL MODELS
SU GROUPS
SU-3 GROUPS
SYMMETRY GROUPS
U GROUPS
WIGNER COEFFICIENTS