Details

Autor(en) / Beteiligte

• CARVALHO, MARIA JULIANA S. TEMES DE OLIVEIRA

Titel

ALGEBRAIC STUDY OF ROTATIONAL FEATURES IN NUCLEI

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

1984

Link zum Volltext

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• Rotational features of nuclei are analysed, from the algebraic point of view, using models which admit a microscopic expression of states and observables. Several models have been successful in predicting rotational states of which the most familiar is the Bohr-Mottelson collective model. Also, it is known that for large dimensional su(3) representations the low-lying states have properties indistinguishable from those of the collective rotational model. Naturally one asks: is su(3) equivalent to the rotational model? One main objective of this thesis is to examine su(3) to see how it relates to the rotational model, algebraically designated R('5) so(3). We conclude that equivalence of both models at the algebraic level, i.e. L(L+1) dependence of energy spectrum and B(E2) ratios following the Alaga rule, doesn't imply equivalence of their physical contents. This is an important result since there is a widespread claim that, in the large (lamda) limit, the IBM su(3) model is equivalent to the BM model which we prove to be false. Next, from shell model considerations one is lead to an sl(3,R) model as containing the complementary aspects of the rotational model. It is shown that one possible limit (contraction) of the union u(3) u gl(3,R) is the u(3)-boson model previously presented as the hydrodynamic limit of the fully miscroscopic sp(3,R) model. Thus sp(3,R) emerges as being a complete model for the microscopic description of collective states. An application to heavy deformed nuclei namely ('126)Ba, ('154)Sm, ('164)Yb and ('166)Er, leaves no doubt of the importance and success of this algebraic model. Finally, considering the fact that models based on contracted algebras (e.g. u (3)-boson) have the advantage of allowing a quick prediction of results and a better understanding of them, we propose a new model, the rotator-vibrator model, based on a double contraction of sp(3,R). However, the merit of this new limit is not only that it gives physical insight into sp(3,R) results but also that it allows the introduction of pairing and spin-orbit forces. For, due to its simple structure it is computationally possible to mix sp(3,R) irreducible representations in the contraction limit. Consequently, the proposed rotator-vibrator model has the potentiality of allowing for more realistic intrinsic shapes without loosing its shell-model foundation.