Rotational Spectra of the Ground-State Bands of Even Nuclei by the Generator-Coordinate Method

The generator-coordinate method is applied to the rotational spectra of the ground state of even nuclei. The trial functions are generated from the Nilsson well, taking into account pairing correlations for fixed values of the deformation parameter $\delta$. This wave function is projected onto eigenstates of angular momentum and is used to evaluate the expectation value of the Hamiltonian, which consists of the kinetic energy and the interactions between nucleons. A Gaussian form with Rosenfeld mixture is assumed for the nucleon-nucleon potential. Numerical calculations are performed for isotopes of Hf. Without changing the values of parameters, characteristic features of the energy spectra are reproduced and agreement with experiment is good. The quadrupole moments of various rotational states, as well as $E2\mathrm{}$ transition matrix elements, are also calculated. To make more extensive comparisons, the kernels used in the above calculations are expressed in terms of parameters, which are selected to give agreement with experimental spectra up to the second excited states for each isotope. Then energy spectra are calculated using these adjusted parameters for all rotational nuclei with mass number greater than 100. Good agreement with experimental data is obtained.