A Possible Canonical Theory for Description of Pairing Correlation: Comparison with the BCS Plus RPA Approach

In order to go beyond the conventional BCS plus RPA approach for the description of pairing correlation, we have developed a possible canonical theory. In this theory, we can exactly get rid of the well· known difficulty of the particle·number non·conservation in the BCS approximation. We give, in this paper, its approximate form in order to clarify the relation with the conventional approach. We show that our theory in its approximate form can reproduce the same result as that obtained by the BCS plus RPA approach. The equivalence between the approach developed by Suzuki et a1. and the present one is also shown, within the RPA order at least. We give some perspective for the description of higher-order non-linear effect, such as the coupling between the pairing rotation and pairing vibration, in conclusion. In the conventional approach based on the BCS plus RP A method, the symmetry (the conservation of particle number) broken in the BCS approxima tion is restored in the RP A order and the system can be decomposed into the pairing rotation as the result of restoring the broken symmetry and the pairing vibration as the fluctuation of the pair field. As is well known, the investigation of various non-linear effects on the collective motion is unavoidable for deeper understanding of nuclear structure. Therefore, it is interesting to investigate how the pairing rotation and the vibration are separated from each other and coupled mutually, beyond the conventional RPA order. However, a generaliza tion of the BCS plus RPA method is not straightforward. In this sense, it is indispensable to construct, with a special device, a new microscopic theory. Recently the present authors proposed a new microscopic theory with the aim of giving a unified description of collective and independent-particle motions under a consistent manner. 1) A characteristic of this theory exists in a canonical form with constraints in Dirac's sense :2) The extra variables are introduced for the collective motion and, in compensation of the double counting of the degrees of freedom, certain constraints govern the variables. Further, the basic idea proposed in Ref. 1) was applied to the description of the pairing correlation in the preceding papers. 3),4) In the first paper,3) a classical theory was developed in