Chaotic Motion Of Single Particle In The Potential With Nonaxial Symmetric Octupole Deformation Y₃₂+Y_3-2

In this thesis, the single particle motion in the potential of non-axial symmetric octupoleY₃₂+Y_3-2 is analyzed systematically from classical and quantum mechanics points of view. It isshowed that the broken symmetry in the potential will enhance the non-linearity in the system andpush the system to tend to chaos easilier.The stability analysis of the classical trajectory suggests that the main reason for the singleparticle chaotic motion is the negative parameters existing on the potential surface. It is foundfrom the maximum Lyapunov exponent calculated in the present thesis that the chaotic motion canhappen under small strength of deformation for prolate and oblate harmonic oscillator potential ifan extra non-axial symmetric octupole deformation potential of Y₃₂+Y_3-2 is added and the chaoticdegree of the motion is much more stronger than that of adding a axial symmetric octupoledeformation.The quantum mechanic calculation tells us that the avoided level crossing between the twoenergy levels, an important indication of the chaotic motion, is commonly accompanied with thestrength of non-axial symmetric Y₃₂+Y_3-2 deformation increasing. In order to analyze the dynamiccharacteristics of the chaotic motion, the time evolution of an initial state of a three dimensionalcoherent harmonic oscillator is investigated. The expectation values of dynamic variables, theuncertainties of them and the heterogeneity in the quantum phase space are calculated and a goodclassical –quantum correspondence is obtained. The dynamics differences between the systemsof the non-axial symmetric Y₃₂+Y_3-2 and the axial symmetric octupole deformations are comparedunder the weakly integrable condition.The previous study of a nucleon's chaotic motion in the mean field is generalized in thepresent thesis from axial symmetric deformation to a non-axial symmetric deformation potential.This enriches people's understanding about chaotic motion in high dimensional Hamiltoniansystem and provides a possible simple mechanism for a nucleon, which is not easy to get into thechaotic motion in an axial symmetry potential, to tend to chaos by adding a non-axial symmetricpotential.