Maximal-Decoupling Variational Principle and Optimal Auxiliary Hamiltonians for Nuclear Collective Motions
An important task in studying nuclear collective motion is to determine the relevant collective degrees of freedom, such as the collective monopole and quadrupole degrees of freedom related to the SD-truncation (by retaining only the most correlated J = 0 and J = 2 pairs) of the shell-model space. A viable method particularly useful for this purpose is the recently developed maximal-decoupling principle1,2, which allows one to unambiguously pin down the collective subspace in an optimal way. On the other hand, in order to take into account effectively the various correlations of the nuclear system under study, one often relies on calculation schemes based on quasi-particle methods or truncated boson mapping methods which violate the symmetry properties possessed by the system. One way to restore these broken symmetries approximately in an indirect fashion is to use an appropriate auxiliary Hamiltonian in place of the given Hamiltonian. This maximal-decoupling principle turns out to be also very useful in determining the optimal auxiliary Hamiltonians to be used for these symmetry-violating calculation schemes. In the following the viability of this maximal-decoupling variational principle for nuclear collective motions are demonstrated through its application to a simplified shell model.
KeywordsBoson Operator Boson State Collective Degree Quasiparticle State Boson Condensate
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