Some Recent Developments in Nuclear Models
The shell model has been very effective in calculating states of simple configurations. For more complex cases it cannot be used unless a good truncation or coupling scheme is introduced. Such coupling scheme should give a fair description of low-lying levels and in particular of those of collective nature. For semi-magic nuclei a reasonable coupling scheme is that of generalized seniority. A certain set of valence proton states (and a similar one for valence neutrons) can be defined by considering the J=0 and J=2 identical nucleon pairs of generalized seniority. This set of proton states corresponds to states obtained by coupling Sp (with L=0) and dp (with L=2) proton bosons (and similarly for the neutrons). A quadrupole-quadrupole interaction between protons and neutrons can be diagonalized to a good approximation by truncation to the space defined by coupling those proton and neutron sets. Using the corresponding boson states and an equivalent boson Hamiltonian it is possible to reduce the complex shell model problem to a much simpler one. This way a shell model approach is obtained to the very exciting interacting boson model which has been recently introduced.
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