Ginocchio model

Motivated by these considerations, we have recently proposed a multi-chain fermionic dynamical symmetry model (FDSM) which was developed to specifically address the above raised questions. Our starting point is the Ginocchio SO(8) model 10(since from now on only fermion groups will be mentioned, we shall drop the use of the F superscript to denote them). In our opinion, Ginocchio was the first person to seriously pursue the concept of multi-chain dynamical symmetries from a fermionic viewpoint. The main ingredients of the Ginocchio model can be summarized as follows. If one were to take the fermion pair (i.e. a+a+ type of operators) with =0 S) and 2(D) and certain multipole operators (i.e. a+a type of operators), both types are constructed from... 

It is also valuable to investigate on how our new form of BET would perform, when it is applied to simple models. During the past year or so we indeed did this, the models taken up being the single-j shell model (lj-SM) and the Ginocchio model [9]. 

Ginocchio model is a degenerate 4-j SM, the j values ranging from -3/2 to +3/2, for a given . In spite of this 4-j shell nature, the specific combination of the 4 shells makes this model very similar to lj-SM. Thus, again the seniority scheme can be constructed easily. In addition to this, the (S,D) space becomes a closed space. This makes the algerbra of the Ginocchio model even simpler than that of lj-SM. 

In the above, we have repeatedly mentioned the bound of applicability of the BCS theory. It means more specifically that the BCS theory is to be used only when the (effective) space size and the particle number n, are both sufficiently larger than is the quasi-particle number (which is the senioprity v in the Ginocchio model). 

Fig.l. Level spectra predicted by various boson theories in the S0(6) limit of the Ginocchio model. 

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