Microscopic formulation of interacting fermion-boson systems

Naotaka Yoshinaga, T. Mizusaki, A. Arima +1 more

The validity of the essential ingredients of the microscopic formulation of the interacting boson model: (i) truncation of the shell-model or fermion space and (ii) the procedures for mapping the truncated fermion space on to the boson space, is tested over various (spherical, deformed and transitional) regions both in the simplistic single j-shell, identical boson systems and the more realistic multi j-shell, proton-neutron systems depending on the feasibility of such calculations. In the situations where the truncation and mapping procedures fail to reproduce the exact shell-model results, it is demonstrated that renormalization and higher order mapping procedures cure the associated problems, respectively and provide excellent agreements. In addition, a Hamiltonian of the interacting boson-fermion model which is relevant for a study of odd mass nuclei is derived for a single j-shell case in the shell-model framework, which yields results identical to those in the shell-model for the monopole pairing interaction.

Olaf Scholten

Cheng-Li Wu, D.H. Feng, Jin-Quan Chen +1 more

An effective boson Hamiltonian is derived from the original Hamiltonian of a many-fermion system. The results show that when the intrinsic motion of bosons is collective and the excitation energies of the system are small, the effective boson-boson interaction can be reduced to a two-body interaction while for odd systems or systems with uncorrelated fermions, there is an additional two-body boson-fermion interaction. Both these interactions can be calculated from the original fermion-fermion ones. Thus, the microscopic foundation of the interacting boson model is established without recourse to mapping procedures.NUCLEAR STRUCTURE Interacting boson model, boson fermion hybrid representation, microscopic foundation.

Martin R. Zirnbauer, D.M. Brink

B. Sørensen

Yang Li-ming

For strongly pair-correlated systems, a new transformation is derived similar in form to the usual Bogoliubov-Valatin transformation, but with the transformation coefficients replaced by operators. The original fermion operators are now replaced by two sets of independent operators, the pair operators and the quasi-fermions . The transformation conserves the particle number. Among other applications, it is particularly suited for the construction of a microscopic theory of the type of the interacting boson model. The new transformation given here also serves to provide a connection between the usual ph picture of a phonon and the pp picture-of bosons in IBM. However, the boson picture that evolves from the present formulation differs from the ideal boson picture in IBM..