The interacting boson approximation

The equivalence between the bosons and collective fermions pair states is discussed. The microscopic approach to the interacting boson model and the S and D pairs, are considered. The general structure of the Hamiltonian in the interacting boson fermion approach is obtained. It is shown that the Hamiltonian can account for most of the observed features in the spectra of odd-mass nuclei. Parameters extracted from calculations for isotopic chains show that the extracted mass dependence of the parameters is in agreement with the predictions, but in some cases violations are observed. The validity limits of the approach are analyzed. A variety of other mapping procedures are developed but a satisfactory answer is not yet found.