By F. Iachello
This publication describes the mathematical framework on which the interacting boson-fermion version is outfitted and provides functions to quite a few events encountered in nuclei. It addresses either the analytical and the numerical elements of the matter. The analytical point calls for the creation of really advanced workforce theoretic equipment, together with using graded (or great) Lie algebras. the 1st (and to date in simple terms) instance of supersymmetry happening in nature is additionally mentioned.
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9 of this volume. 16) where E01 = eo + e1N + e2N(N + 5) + e3 + 4e4 + e5N. 5 7/2 ( 2 11 1 )- 5/2 I/2 BF 0 ( 2, z )- 3/2 (6) Spin m Fig. 3-1 A typical spectrum with SpinBF(6) (III) symmetry for NB = 2, NF = 1. The Spin BF(6) quantum numbers are shown on top, the SpinBF(5) quantum numbers to the left and the angular momentum J to the right of each level. The quantity E01 does not contribute to the excitation energies but only to the binding energies. 16) is shown in Fig. 1. 15). 2) as follows: C2(SpinBF6) = 2G(2) G(2) + 4G(1) G(1) + 4G(3) G(3), C2(SpinBF5) = 4G(1) G(1) + 4G(3) G(3) C2(SpinBF3) = 20G(1) G(1).
The expansion is IN+Z;r1;J) _ N+2 ''jIN, T',L';1,1,3/2;J). 19). The s are the expansion coefficients and the sum goes over r' = T1 ± 2, L' = J±3/2, J±1/2. The expansion coefficients can also be interpreted as isoscalar factors for the group chain SU(4) Spin(6) D Sp(4) Spin(5) D SU(2) Spin(3). A technique which has been found useful for obtaining the isoscalar factors is that of considering matrix elements of operators which can be evaluated in a straightforward way. In the present case it is sufficient to consider the operator G(2) G(2).
Following the order of presentation. 1 Lattice of algebras This symmetry was the first to be investigated in detail (Iachello, 1980; Iachello and Kuyucak, 1981; 3 Bose-Fermi symmetries 40 Kuyucak, 1982). It corresponds to bosons with 0(6) symmetry and fermions occupying a state with j = 3/2. ^s Spin(3). l I Spin BF (5) l SUF (2) SpinBF (3) I Spin BF (2) We consider here in detail the route a. 2) Deleting Gµ2> gives the generators of SpinBF(5) and further deleting Gµ3) gives those of Spin BF(3).