Quantum Mechanics of the Two Mass-Point Model for the Rotational Spectra of Deformed Even–Even Nuclei

Abstract

The representation of a deformed nucleus by a two mass-point system is treated quantum mechanically to obtain absolute values of energies of the ground state rotational band and the first excited 0+ vibrational state of even–even nuclei in the rare-earth region. Calculations are made using both harmonic and anharmonic restoring potentials. Although the model is not applicable to spherical nuclei, it is found that for the deformed nuclei in the rare-earth region it correlates the quadrupole moment and the moment inertia data more satisfactorily than the rigid-body and hydrodynamic models. The values of energies, quadrupole moments, and the ratio B(E2; 4+ → 2+)/B(E2; 2+ → 0+), predicted on the basis of the model, are in agreement with the corresponding experimental values for the nuclei around the middle of the region [Formula: see text]. The variation of the stiffness of the potential with neutron and proton numbers is studied.