On the boson mapping of fermion collective pairs

Jutta Meyer

Recently, the mathematical formalism of the Dyson boson mapping has been extended to a system of 3n fermions, leading to the boson–fermion and the baryon mapping. In the present paper, the case of a restriction to a subset of three-fermion quantum numbers, the collective indices, is discussed. A theory is developed for the representation of fermionic states and operators in a truncated ideal space where only collective boson–fermion pairs or collective ideal baryons are allowed. An exact reproduction of physical properties is proved to be possible provided that the original fermionic problem can be solved in a subspace where all three-fermion subsystems carry collective indices. Examples of simple applications are presented in the two subsequent papers of this series.

Joseph N. Ginocchio, Calvin W. Johnson

Akito Arima, N. Yoshida, Joseph N. Ginocchio

K. Taniguchi, Y. Miyanishi

By using a unitary operator which maps the fermion space to the boson-fermion space we give a new type of bosonization of the correlated pair modes exhibiting the nuclear collective oscillations approximately. The relation to the conventional boson expansion method is briefly discussed.

Asis Basu, Jayprokas Chakrabarti

Michelangelo Sambataro

The lowest seniority-zero eigenstates of an exactly solvable multilevel pairing Hamiltonian for a finite Fermi system are examined at different pairing regimes. After briefly reviewing the form of the eigenstates in the Richardson formalism, we discuss a different representation of these states in terms of the collective pairs resulting from the diagonalization of the Hamiltonian in a space of two degenerate time-reversed fermions. We perform a two-fold analysis by working both in the fermionic space of these collective pairs and in a space of corresponding elementary bosons. On the fermionic side, we monitor the variations which occur, with increasing the pairing strength, in the structure of both these collective pairs and the lowest eigenstates. On the bosonic side, after reviewing a fermion-boson mapping procedure, we construct exact images of the fermion eigenstates and study their wave function. The analysis allows a close examination of the phenomenon of pair condensation in a finite Fermi system and gives new insights into the evolution of the lowest (seniority-zero) excited states of a pairing Hamiltonian from the unperturbed regime up to a strongly interacting one.