Some U(n1 + n2) ⊃U(n1) ⊗U(n2) isoscalar factors

Some of the U(n1 + n2) ⊃U(n1) ⊗U(n2) isoscalar factors (IFs), involving the U(n1 + n2) couplings of the type [N] × [p,−q] → [N′], are obtained using the building-up procedure. It is shown that such type of IFs are relevant to the quantum-mechanical treatment of the two-component many-body systems.

[1]  P. Isacker,et al.  Symmetries and deformations in the spherical shell model , 2016, 1601.02837.

[2]  V. Kota,et al.  Random Matrix Theory for Transition Strength Densities in Finite Quantum Systems: Results from Embedded Unitary Ensembles , 2015, 1504.00759.

[3]  S. Alǐsauskas.  Comment on ‘‘The matrix representation of U4 in the U2×U2 basis and isoscalar factors for Up+q⊇Up×Uq’’ [F. Pan, J. Math. Phys. 31, 1333 (1990)] , 1992 .

[4]  Chen.  Generalized quantization formalism. , 1991, Physical review. C, Nuclear physics.

[5]  G. Long,et al.  Coefficients of fractional parentage for a double-l boson system , 1990 .

[6]  F. Pan.  The matrix representation of U4 in the U2×U2 basis and some isoscalar factors for Up+q ⊇Up×Uq , 1990 .

[7]  D. Rowe,et al.  New perspective on the U(n) Wigner-Racah calculus. I. Vector coherent state theory and construction of Gel'fand bases , 1987 .

[8]  Jin-quan Chen,et al.  Coefficients of fractional parentage for U(m + p/n + q) ⊃ U(m/n) × U(p/q) and U(m/n) ⊃ U(m) × U(n) , 1984 .

[9]  B. G. Wybourne,et al.  Classical Groups for Physicists , 1974 .

[10]  J. Vergados.  SU(3) ⊃ R(3) Wigner coefficients in the 2s-1d shell , 1968 .

[11]  P. Kramer.  Recoupling coefficients of the symmetric group for shell and cluster model configurations , 1968 .

[12]  K. Hecht.  Five-dimensional quasi-spin the n , T dependence of shell-model matrix elements in the seniority scheme , 1967 .

[13]  K. Hecht.  SU3 recoupling and fractional parentage in the 2s-1d shell , 1965 .