The modified Tamm-Dancoff approximation has been used to study the states of odd-mass Ni isotopes as the superposition of one- and three-quasiparticle states. The three-quasiparticle basic states are classified according to the well-known seniority scheme and are expressed in an equivalent second-quantized form. These three-quasiparticle states form an orthonormal and nonredundant set. The effect of the spurious $0^{+}$ two-quasiparticle state has also been removed from these basis wave functions. Several different kinds of two-body residual interaction have been used in the calculation. Fairly decent agreement is obtained in the energy spectra between our results and the exact shell-model results, using the effective interaction of Cohen et al. Various approximate methods, such as the perturbation theory and a phonon approximation, are discussed in the context of the present method. The effect of the ground-state correlation is also studied. The admixture of the three-quasiparticle states in the lowest few levels causes very little change in the magnetic moment, and the $M1\mathrm{}$ transition rates calculated on the basis of a single-quasiparticle structure of these states. The $E2\mathrm{}$ transition rate is fairly sensitive to the admixture and the type of interaction used.

• Received 29 May 1967

DOI:https://doi.org/10.1103/PhysRev.162.1139