ABSTRACT
The considerations presented above lead to a model in which the determination of low lying eigenstates of the shell model Hamiltonian is replaced by diagonalization of a boson Hamiltonian. This boson Hamiltonian contains single boson terms and interactions between bosons. The boson space considered is that of Nπ proton bosons, Sπ, dπ , and Nv neutron bosons sv, dv . According to Section 37, the number Nπ (Nν ) is one half the number of valence protons (neutrons) in the first half of the major shell and one half of the number of holes between the middle and the end of the shell (Arima et al. 1977, Otsuka et al. 1978). The boson Hamiltonian which should have the same eigenvalues as the fermion Hamiltonian (38.4) with Vπν as in (38.7), also has the form (38.4). Since from now on only boson operators will appear, no different notation will be introduced. The boson Hamiltonians Hπ and Hv should have the same properties as the fermion ones. The latter have eigenstates with definite generalized seniority which implies, as explained in Section 37, that the boson Hamiltonians should have U(5) symmetry. The boson quadrupole interaction breaks this symmetry and the quadrupole boson operator is approximated 868by () Q μ = d μ + s + s + d ˜ μ + χ ( d + × d ˜ ) μ ( 2 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203739716/ff034a11-a369-4bc6-a470-f8cf1794dcb5/content/eq4341.tif"/>
