Group theory of the collective model of the nucleus
- 1 May 1977
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 18 (5) , 870-880
- https://doi.org/10.1063/1.523352
Abstract
In the present paper we extend the group theoretical analysis of a previous publication to obtain explicitly, as a polynomical in sinγ, cosγ, the function φλμlk(γ) required in the discussion of the quadrupole vibrations of the nucleus. The states appearing in the collective model 〈νλμLV〉=F1λ(β) ΣKφλμLK(γ) DL*MK(φi), l= (ν−λ)/2, are then defined, as Fλl(β), DL*MK(φi) are well known. All matrix elements required in the collective model of the nucleus are related then with the expression (λμL;λ′μ′L′;λ″μ″L″= ∂π0ΣKK′K″ (LL′L″KK′K″) φλμLK(γ) φλ′μ′L′K′ (γ) φλ″μ″L″K″ (γ)sin 3γdγ, which is a reduced 3j-symbol in the O(5) O(3) chain of groups.This publication has 13 references indexed in Scilit:
- Lie algebras in the Schrödinger picture and radial matrix elementsJournal of Mathematical Physics, 1976
- U(5) ⊃ O(5) ⊃ O(3) and the exact solution for the problem of quadrupole vibrations of the nucleusJournal of Mathematical Physics, 1976
- Elementary excitations in vibrational nucleiPhysics Letters B, 1975
- Coherent states and the Jahn-Teller effectPhysical Review B, 1975
- Boson symmetries in vibrational nucleiPhysics Letters B, 1974
- Canonical Transformations and Matrix ElementsJournal of Mathematical Physics, 1971
- O(2, 1) and the Harmonic Oscillator Radial FunctionJournal of Mathematical Physics, 1971
- Solution of bohr's collective hamiltonianNuclear Physics A, 1970
- Some simple R5 Wigner coefficients and their applicationNuclear Physics, 1965
- The γ-dependent part of the wave functions representing γ-unstable surface vibrationsNuclear Physics, 1959