Extended phonon projection model for nuclear collective motion

Abstract

The subject of this work is the formulation and application of a geometrical collective model with comparison to experiment and with other models dealing with low energy nuclear structure. This model, called the EPM(= Extended Phonon-Projection Model) avoids the use of an extensive diagonalization basis in the deformednucleus region by cleverly choosing a three dimensional model space with capability of producing the gross features encountered in moving from spherical vibrator nuclei to almost rigid rotors of deformed shapes. The use of deformed oriented states calls for angular momentum projection to restore the broken angular momentum conservation in the oriented wavefunctions. After having achieved, in this way, a suitable set of basis states, one obtains the excitation energies by diagonalizing a phenomenological effective boson expansion Hamiltonian in this basis. The diagonalization reproduces the basic feature of the earlier projection model of Lipas et al., namely the Sakai-Sheline scheme concerning the development of a harmonic vibrator spectrum to a band structure characterized rotor spectrum, The energy spectrum obtained in this way is, however, quite different from the earlier PM (=Projection Model of Lipas et al.). The E2 transition probabilities have U(S)-characterized selection rules in the limit of small deformations and the Alaga behaviour for large oriented deformations, A distinct feature of the EPM is the violent behaviour of many branching ratios at certain deformations. Application of the EPM is carried out in the Sm, Gd, Er, and Yb regions where also a comparison with the earlier PM and IBA-1 results is performed. The comparis shows that the 4- and 5-parameter EPM fits are comparable to or better than the 6-parameter IBA-1 fits and produce a systematic parameter behaviour, In contrast to other geometrical models, the low energy transitions are characterized by weak β -to -ground transitions and quite strong γ -to-ground transitions like the IBA. Also a comparison with the CSM (=Coherent State Model of Răduţă et al,) is performed showing a strong similarity between these models 1n both spectroscopic energies and B(E2) behaviour.