The Reflection Asymmetric Shell Model

In this thesis, the experimental and theoretic evidence for intrinsic reflection-asymmetric shapes in nuclei is reviewed. It is shown that the necessary condition forthe presence of low-energy octupole collectivity is the existence, near the Fermi level,of pairs of orbits strongly coupled by the octupole interaction. The descriptions ofnuclear surface shape including octupole deformation are discussed. Some usefultheoretic methods, experimental systematics and rotational properties related to theoctupole-deformation and the octupole-correlation are briefly introduced.The framework of the Reflection Asymmetric Shell Model (RASM) used todescribe the high-spin states of octupole-deformed nuclei has been formulated in thisthesis. Before doing this, we reviewed both the Cranking Shell Model (CSM) and thestandard Shell Model (SM), and introduced the Projected Shell Model (PSM). Thenapplied the Generator-Coordinate Method (GCM) to obtain the RASM, which is ageneralization of PSM. We constructed the RASM wave function of a nucleus as alinear combinaion of intrinsic states and their reflections with different orientations.This wave function can be determined by set the energy expectation value to a limit.After the variational procedure, we obtained the RASM eigenvalue equation.Simultaneously, the RASM wave function becomes as an eigenstate of angularmomentum and parity due to the invariance of the RASM Hamiltonian under rotationand reflection. In this thesis, the RASM Hamiltonian including quadrupole octupoleand hexadecapole interactions as well as monopole and quadrupole pairing.Correspondingly, the intrinsic Nilsson+BCS multi-quasiparticle states is quadruole,octupole and hexadecapole deformed. We get the RASM basis by projecting thesedeformed states onto good angular momentum and parity. The octupole rotationalbands can be calculated from the RASM eigenvalue equation.Three interesting characteristics of the octupole deformed Yrast bands in even-even nuclei can be reproduced in the framework of our model. i.e., (l) The sequenceof states with even-spin, positive parity and odd-spin negative parity due to theequivalence of the vacuum state and its time reversal. (2) The parity splitting at lowspins. The l～- and 3～- states remain energetically higher than the 2～+ and 4～+ states,respectively. According to the RASM, this is caused by the comparaively smalloctupole deformation rather than the octupole vibration. In fact, our calculations showthat small octupole deformation leads to large parity splitting, and large octupoledeformation leads to small or no parity splitting. (3) The parity splitting decreases tozero with increasing spin at a given octupole deformation. An analytic expression ofoctupole rotational band has been derived from the RASM with some approximation,which indicates this property of octupole bands..We accomplished the Fortran code of Reflection Asymmetric Shell Model, andapplied it to the even-even Radium isotopes with mass number from 222 to 230. Thecalculated Yrast bands are in a good agreement with the experimental data. It isshown tha these bands exhibit smooth behavior, showing no sharp band crossing upto very high spins. As a matter of fact, the mixing of the intruder unique parityorbits with the normal parity orbits can be induced by octupole deformaion, whichleads to the fragmentaion of angular momentUIn alignInent, and thus no sharp bandcrossing occurs. This effect of octuPole defbrmation remains included in the RASM,and the smooth behavior of the Yrast octuPole bands can be reproduced by the RASMcalculations. It also can be seen from our calculations that parity splitting can beconsidered as a sensitive measure of the eXtellt tO which the system possesses thereflection asymmetry Finally, we found the possibility of very large hexadecaPoledeformation exiSting in these calculatCd Ra isotopes.Some possible developments of the RefleCtion Asynunetric Shell Mode...