An approximation for rotation-projected expectation values of the energy for deformed nuclei and a derivation of the cranking variational equation

An approximation is given for the expectation value of the Hamiltonian with functions: where ¦?〉 is a HFB wave function of a deformed nucleus. This is achieved by expanding the overlap function of the energy 〈?¦ HD(Ω)¦?〉 in derivatives of the overlap function of the norm 〈? D(Ω)¦?〉. The cranking equations for even nuclei are yielded by varying the approximate energy.