A new approximate method for treating nn and pp pairing force in nuclei is presented. In this method the difficulties connected with the application of BCS-Bogolubov method to nuclei such as the non-conservation of the number of particles, the apperance of spurious states, and non-orthogonality between wave functions of different excited states are avoided. But the method can be conviently adopted only when the number of particles n and the number of levels Ω considered are small (n ≤10, Ω≤10 ). Also the approximation of this method is good onlv under such conditions. In this method the many-body nature of the excitation is displayed explicitly without introducing the conception of quasi-particles. The excitation of the system can be divided into two classes. The first class of excitation is a kind of single particle excitation embedded in a many-body system under the action of the pairing force. This would correspond to the excitation of a single quasi-particle av+a(v0) or to two quasi-particle excitation of the type αv+βv′+,αv+αv′+(v′≠v) etc. in the BCS-Bogolubov method. The second class of excitation is a pair excitation in which the distribution of the conjugated pairs of particles among the levels is altered. This type of excitation would correspond to superposition of quasi-particle excitations of the type αv+βv+,αv+βv+αμ+βμ+, Also examined is the effect of pairing force on the β- and γ-transition probability in the new formalism. In general, β-transition is retarded by the pairing force while in γ-transition the effect of pairing force varies according to the nature of the relative excitation between the initial and final states. When the relative excitation is of the first class, the transition is retarded to various extent, depending on the nature of the γ-transition. If the relative excitation is of the second class, the transition is forbidden when the pairing force is not in action, and is allowed only for electric transition arising from the charge-current distribution when the pairing force is present. Finally this method is applied to investigate the effect of pairing force on the intrinsic spectra and β-transition in 72Hf178 as an example.
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