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Physics Letters B

“Independent-pair” property of condensed coherent fermion pairs and derivation of the IBM quadrupole operator

Takaharu Otsuka

Published Apr 1, 1984• 32 citations
Publisher
DOI
10.1016/0370-2693(84)91859-8

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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..
A derivation of the random phase approximation is given, which is based on the generalized Schwinger representation of the fermion-pairs. The method is made of two stages : First, the truncation of the boson space is done, and secondly comes the separation of boson operators into static and fluctuating parts. The pairing vibration in the super phase and the so-called quadrupole oscillation are treated by the method, which leads to the same results as those of RPA. Then the relations of these bosons to ones appearing in RPA are clarified.