By F. Iachello

This ebook describes the mathematical framework on which the interacting boson-fermion version is outfitted and provides functions to various events encountered in nuclei. It addresses either the analytical and the numerical features of the matter. The analytical element calls for the creation of really complicated crew theoretic equipment, together with using graded (or tremendous) Lie algebras. the 1st (and up to now basically) instance of supersymmetry happening in nature can also be mentioned.

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**The Interacting Boson-Fermion Model**

This booklet describes the mathematical framework on which the interacting boson-fermion version is outfitted and provides purposes to a number of events encountered in nuclei. It addresses either the analytical and the numerical facets of the matter. The analytical point calls for the creation of quite advanced team theoretic equipment, together with using graded (or large) Lie algebras.

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**Extra info for The Interacting Boson-Fermion Model**

**Example text**

However, the representations (nl, n2) of Sp(4) are restricted and can actually be labelled by one quantum number, namely the number of is in the Young tableau, VF. This number is given by NF, NF - 2, ... ,1 or 0. 19). 34) Mi Also here the representations (n1, n2, n3) of Sp(6) are restricted and there is only one quantum number, vF. The four quantum numbers NF, VF, J, Mj are sufficient to determine the states uniquely. This situation persists up to and including j = 7/2. For larger js further quantum numbers are needed.

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).

For example, in the isoscalar factor for 0(6) D 0(5), All A2 and A are 0(6) labels, while A1, A2 and \ are 0(5) labels. This notation will become clearer later when applied to the explicit computation of isoscalar factors. 58) which is again a generalization of the familiar Clebsch-Gordan relation for the rotation group. The knowledge of isoscalar factors allows one to compute the matrix elements of transition operators T and transfer operators P of Sect. 53). Examples of such calculations will be given later.