Single-particle degrees of freedom and the generator-coordinate method

The generator-coordinate method which is usually used to describe collective degrees of freedom is extended to include two quasiparticle excitations and the coupling between these two different modes. As generating wave functions angular momentum and particle number projected Hartree-Fock-Bogoliubov states and quasiparticle excitations built on them are used. The Hartree-Fock-Bogoliubov functions are constrained to a given quadrupole moment, which serves as the generator coordinate. This method is applied to the $\mathrm{pf}$- shell nuclei ${}_{}{}^{46,50}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$.