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Intrinsic Pair Operators and the Number-conserved Treatment of Pairing Correlations in Nuclei

Ueno, M, Hayashi, D, Miyanishi, Y

Published Nov 7, 2001• 0 citations
OpenAlex

Abstract

By introducing the intrinsic pair operators which commute with number fluctuation operator, a new formalism is given for the number-conserving description of the pairing correlations. The difficulty in the conventional RPA treatment for pairing rotation is removed.

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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 al. 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.
Conservation of particle number in the number-operator approximation of Otsuka and Arima is shown to require a particular normalization for the pair-creation operator. Even with this normalization, two difficulties arise: (a) the average number of particles in a shell can easily violate the Pauli principle, and (b) the mean square fluctuation of the particle number can be negative. As a consequence of the tendency to Pauli violation, the approximate ground-state expectation of the single-particle energy per particle is too low and fails to increase with the number of particles.NUCLEAR STRUCTURE Number conservation and Pauli principle in number-operator approximation for pairing.