Angular-momentum cranking applied to multiphonon anharmonic collective vibrations: Cranked bifurcation theory

It is shown that the self-consistent angular-momentum cranking technique can be used to generate certain types of collective vibrational solutions of time-dependent mean-field equations. The method is suitable for systems having an equilibrium mean held with an axis of symmetry and is founded on a theorem (cranking bifurcation theorem) proposed in this paper, according to which cranking about an equilibrium axis of symmetry leads to new symmetry-breaking solutions that bifurcate from the axially symmetric solution at the critical cranking frequencies given by Omega=omega(mu)/K-mu, where omega(mu) is a random-phase-approximation (RPA) frequency for any mode carrying K(mu)not equal 0 units of angular momentum along the symmetry axis. The bifurcating solutions correspond to aligned multiphonon excitations including possible large-amplitude anharmonicities. A general heuristic proof of the method is provided, as well as a perturbative demonstration within the framework of the cranked Hartree-Fock (CHF) approximation, which includes a derivation of the RPA. The static CHF approach is then compared to a perturbative treatment of the time-dependent Hartree-Fock equations using the Lindstedt method. It is also shown that the cranking approach may be applied to phenomenological mean-field models to obtain anharmonic corrections to the vibrating potential model. Finally, the calculation of transition matrix elements is briefly discussed.