General formalism of collective motion for any deformed system

Based on Bohr model, I have presented a general formalism describing the collective motion for any deformed system, in which the collective Hamiltonian is expressed as vibrations in the body-fixed frame, rotation of whole system around the laboratory frame, and coupling between vibrations and rotation. Under the condition of decoupling approximation, I have derived the quantized Hamiltonian operator. Based on the operator, I have calculated the rotational spectra for some special octupole and hexadecapole deformed systems and shown their dependencies on deformation. The result indicates that the contribution of octupole or hexadecapole deformations to the lowest band is regular, while that to higher bands is dramatic. These features reflecting octupole and hexadecapole deformations are helpful in recognizing the properties of real nuclei with octupole and/or hexadecapole deformations coexisting with quadrupole deformations.

Figure 1

Evolution of rotational spectra to ${\gamma }_3$ for an octupole deformed system. Here the solid, dashed, and dotted lines with the same color represent, respectively, the first, second, and third energy levels for these states with the same angular momentum and parity.

Figure 2

Evolution of rotational spectra to ${\gamma }_4$ for a hexadecapole deformed system $(\delta$ is fixed to $0^{\circ })$. Here, the solid, dash, and dot lines with the same color represent respectively the first, second, and third energy levels for these states with the same angular momentum and parity.

Figure 3

The same as Fig. 2, but ${\delta }_4$ is fixed to ${45}^{\circ }$.

Figure 4

The same as Fig. 2, but ${\delta }_4$ is fixed to ${90}^{\circ }$.