Algebraic and geometric description of the collectivity evolution in the even-even Yb nuclei

We have studied the 160-174 Yb isotopes in the frame of the Interacting Boson Model (IBA-1) and the Geometric Collective Model (GCM). The existing experimental information in these nuclei refers mainly to the ground state and gamma bands. The information is not so rich on the excited K=0 bands. Our aim was to describe the structure of the low-lying states. The energy of the first excited state of the ground-state band (21+) decreases continuously from E=243 KeV in 160 Yb to E=77 KeV in 174 Yb. The energy of the band-head of the gamma band increases from E=820 KeV in 160 Yb to E=1634 KeV in 174 Yb while the energy of the K=0 band-head (the 02+ level) is almost constant. IBA and GCM are two different approaches to the nuclear structure. IBA represents the algebraic approach while GCM the geometrical one. It has been shown that they describe the same physical structure. We used this study also to find out how far the similitude between the two models can go. The IBA computer codes 'PHINT' and 'FBEM' have been employed with the CQF parametrisation. It has been shown by Zhang et al that the GCM can also reproduce the three known symmetries (symmetric rotor, vibrator and gamma-unstable rotor) using only the first three terms in the potential part of the Hamiltonian. Therefore, in the GCM code we retained only four parameters - C2, C3 and C4 for potential, and the mass parameter B2. The first nucleus where the calculations have been performed was 172 Yb, which is situated very close to the rotor limit. We obtained good fits, both in IBA and GCM. The procedure was extended as follows: for each nucleus we first employed the parameters from the neighbour isotope. Then, slowly varying the parameters we looked for the best agreement with the experimental level scheme and the B(E2) values. The main problem of this procedure appears between the isotope with A=170 and the isotope with A=168. Here, the relative position of the gamma band and of the K=0 band changes. Therefore we had to accept a leap of the parameters in this point in order to reproduce this effect. In conclusion, we obtained acceptable agreement with the experimental values, both in IBA and GCM. The model parameters were kept in a narrow range. As we expected, the most difficult problem is the description of the K=0 bands. Their nature seems more complex than the simple assumptions of the pure collective models and we can observe a disagreement both for B(E2) values and the parameter of inertia of K=0 bands of some isotopes. Although the calculations in the two models have been developed independently, the results are similar. Differences appear in details such as the moments of inertia of the excited K=0 bands. Under the guidance of these calculations, we are planning our future experiments. (authors)