Microscopically derived interacting boson model

The microscopic basis of the Interacting Boson Model is discussed. The IBM Hamiltonian is constructed microscopically in the following two steps. In the first step, the collective nucleon pairs of J=0+ (S), 2+ (D), etc. are mapped onto the corresponding bosons. Nucleon‐nucleon interactions are also mapped onto boson‐boson interactions. The mapping method for spherical nuclei is reviewed, and the mapping method for deformed nuclei, which was recently developed, is discussed in some detail. Low‐lying collective states primarily consist of S and D pairs. Consequently, the corresponding boson states mainly consist of s and d bosons, while there are some admixture of g‐bosons. In the second step of the derivation of the IBM Hamiltonian, effects of these g‐bosons are included within the s‐d boson space by a unitary transformation which transforms a combination of d and g bosons into a new d‐boson. It is demonstrated that the s‐d Hamiltonian thus derived indeed reproduces spectra of the original s‐d‐g Hamiltonian.