Formal Aspects of Nuclear Moment-of-Inertia Theory

Projected Hartree-Fock states are used as a representation in calculating nuclear wave functions. The rotational energy is determined consistently through $\frac{J(J+1\mathrm{})\mathrm{}}{〈J^2〉}$, and the moment of inertia thus obtained is compared with the expressions of other authors. The formulas of Peierls and Yoccoz and Thouless and Valatin yield approximately the same results as ours, but all of these formulas exhibit discrepancies with the Inglis independent-particle cranking-model formula. We find that the spurious state $J_x|\phi 〉$ plays a dominant role, in agreement with Banerjee, D'Oliveira, and Stephenson. Interesting observations are made for the case of the soluble $\mathrm{SU}\left(3\right)\mathrm{}$ model of Elliott.