Moment of Inertia in Hartree-Fock Theory

The conditions under which a Hartree-Fock wave function may be a good description of the intrinsic state of a rotational nucleus are discussed from two points of view; first by studying the fluctuations of the modified Hamiltonian H-αJ² as a function of α, and second by studying the response of the wave function to a small external perturbation -ωJₓ. Following Thouless and Valatin, this response is given in terms of an anti-Hermitian cranking operator S. We demonstrate that, when the Hartree-Fock wave function is adequate, S, is of the form [Jₓ, ρ]ε, where ρ is the single-particle density operator and ε is twice the rotational energy content of the intrinsic state. These considerations lead to simple tests of the adequacy of the Hartree-Fock wave function as a rotational intrinsic wave function. A comparative study of various formulas for the moment of inertia, utilizing the aforementioned result for S, is presented.