a Microscopic Description of the Three Major Bands in Transitional Nuclei.
Abstract
We have extended the Coherent Phonon Model to the description of the three major bands in medium heavy transitional nuclei. The model assumes an axially symmetric deformed ground intrinsic state for the description of the low lying yrast levels of the ground band, while the excited bands are generated by intrinsic excitations of the ground band. Good angular momentum states are generated by the Peierls-Yoccoz angular momentum projection method. We started with a shell model plus Pairing and Quadrupole residual interaction Hamiltonian and transformed it into the quasi-particle representation by introducing the Bogolyubov-Valantin transformation. The BCS calculation is performed with particle conservation imposed at each angular momentum state J. The Quadrupole-Quadrupole interaction is mapped into a quadrupole boson space, the coefficients in the boson Hamiltonian being determined by imposing the condition that the matrix elements of the boson operators taken between normalized boson states be equal to the corresponding matrix elements of the quasifermion operators taken between analogous normalized states written in terms of quasiparticles. We obtained matrix elements of the boson Hamiltonian with respect to the angular momentum projected states and minimized them with respect to the boson structure constants. Employing only one free parameter (the quadrupole strength (chi)), a low order boson expansion, and a careful teatment of particle number conservation, we were able to reproduce fairly well the properties of the low spin states of even-Xenon, even-Barium and even-Cerium isotopes. It is found that for these nuclei backbending can be interpreted as a transition from a pair correlated state to a normal one. The transition occurs at a critical angular momentum which has a dependence on the number of valence nucleons. We found that for even-Xenon isotopes and for the lighter Barium isotopes the transition is from a proton correlated state to a normal state, while for the heavier Barium isotopes and for Cerium isotopes the transition is from a neutron correlated state to a normal one.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1986
- Bibcode:
- 1986PhDT........27P
- Keywords:
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- Physics: Nuclear