More on Asymptotic behaviors of 9j Coefficients

International Journal of Mathematics and Mathematical Sciences, 1989

Noting that the expression [_n__] gives the number of terminating nines tl tO t which occur up to n but not including n, we will denote the above expression by t(n) and call t the "terminating nines function".

2006

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Nuclear Physics A, 2001

In β-decay experiments on 9C at CERN/ISOLDE the β-strength was determined to the ground state, the 12.2 MeV excited state and the Isobaric Analog State (IAS) at 14.655 MeV in 9B. A large β-strength asymmetry is deduced for the mirror transitions of 9C and 9Li to states around 12 MeV excitation energy. A satisfactory description of the three-body decay from a narrow energy

Journal of Mathematical Physics, 1995

We present derivations of su(2) and su(3)⊇so(3) Clebsch–Gordan coefficients in the limit of large quantum numbers. For su(3), we derive simple analytic expressions for the asymptotic coefficients needed for the decomposition of the product (λ1,0)⊗(λ2,0), in the limit of λ1→∞, in an so(3) basis.

Physical Review A, 2011

We derive a new asymptotic formula for the Wigner 9j-symbol, in the limit of one small and eight large angular momenta, using a novel gauge-invariant factorization for the asymptotic solution of a set of coupled wave equations. Our factorization eliminates the geometric phases completely, using gauge-invariant non-canonical coordinates, parallel transports of spinors, and quantum rotation matrices. Our derivation generalizes to higher 3nj-symbols. We display without proof some new asymptotic formulas for the 12j-symbol and the 15j-symbol in the appendices. This work contributes a new asymptotic formula of the Wigner 9j-symbol to the quantum theory of angular momentum, and serves as an example of a new general method for deriving asymptotic formulas for 3nj-symbols.

Journal of Mathematical Physics, 2006

Physics Letters B, 2003

Physics Letters B, 2003

A new measurement of the β-decay of 9 Li has clarified the feeding to the highest accessible states in 9 Be. It is found that the β-decay mainly populates the 11.8 MeV state, whose spin is determined as 5/2 − . The extracted B GT value of 5.3(0.9) is a factor 4.4(1.0) larger than that of the mirror transition from 9 C. A theoretical explanation of such a pronounced β-decay asymmetry is presently lacking.

Nuclear Physics A, 2001

2000

A new method for calculation of Clebsch-Gordan coefficients (CGCs) of the Lie algebra u(n) and its quantum analog Uq(u(n)) is developed. The method is based on the projection operator method in combination with the Wigner-Racah calculus for the subalgebra u(n-1) (Uq(n(n-l))). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form of the projection operator of u(n) and Uq(u(n)). It is shown that the Uq(u(n)) CGCs can be presented in terms of the Uq(u(n-1)) q-9j-symbols.