Abstract
In two key papers, Arima, Otsuka, Iachello and Talmi1 and Otsuka, Arima and Iachello2 (OAI) gave a microscopic foundation to the interacting boson model(IBM) by associating the s-boson with a J = 0 pair of like nucleons in a single j-shell and the d-boson with a J = 2 pair. The N-boson space was then mapped onto a subspace S in the n-nucleon shell-model, with n = 2N and with the number of d-bosons related to the shell-model seniority by 2N d = v. The quasi-spin group SU(2) provides general formulae in the shell-model for the matrix elements of an arbitrary interaction in the seniority basis, as functions of n. This allowed OAI to deduce a corresponding IBM hamiltonian which, for any n, would exactly reproduce the shell-model matrix elements in that part of the sub-space S with seniority not exceeding v = 4. The IBM hamiltonian contained only one and two-boson interactions but, since its parameters were functions of N,it included some many-body effects that may, for example, originate in the Pauli principle in the shell-model.
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