The Cranking Nilsson model is applied to calculate the single-particle energy eigenvalues and eigenfunctions of nuclei in a strongly deformed potential. Accordingly, The L. D. Energy, the Strutinsky inertia, the L. D....The Cranking Nilsson model is applied to calculate the single-particle energy eigenvalues and eigenfunctions of nuclei in a strongly deformed potential. Accordingly, The L. D. Energy, the Strutinsky inertia, the L. D. inertia, the volume conservation factor , the smoothed energy, the BCS energy, the G-value and the electric quadrupole moment of the five uranium isotopes: 230U, 232U, 234U, 236U and 238U are calculated as functions of the deformation parameter. Furthermore, the single-particle Schrodinger fluid is applied to calculate the rigid-body model, the cranking-model and the equilibrium-model moments of inertia of the five uranium isotopes. Moreover, the collective model is applied to calculate the rotational energies of these isotopes. The best potential and deformation parameters are also given.展开更多
The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-parti...The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-particle potential which is deformed with time t, through its parametric dependence on a classical shape variable α(t). Also, the Nilsson model is designed for the calculations of the single-particle energy levels, the magnetic dipole moments, and the electric quadrupole moments of axially symmetric deformed nuclei by assuming that all the nucleons are moving in the field of an anisotropic oscillator potential. On the other hand, the nuclear superfluidity model is designed for the calculations of the nuclear moments of inertia and the electric quadrupole moments of deformed nuclei which have no axes of symmetry by assuming that the nucleons are moving in a quadruple deformed potential. Furthermore, the cranked Nilsson model is designed for the calculations of the total nuclear energy and the quadrupole moments of deformed nuclei which have no axes of symmetry by modifying the Nilsson potential to include second and fourth order oscillations. Accordingly, to investigate whether the six p-shell isotopes <sup>6</sup>Li, <sup>7</sup>Li, <sup>8</sup>Li, <sup>9</sup>Li, <sup>10</sup>Li, and <sup>11</sup>Li have axes of symmetry or not, we applied the four mentioned models to each nucleus by calculating their moments of inertia, their magnetic dipole moments, and their electric quadrupole moments by varying the deformation parameter β and the non-axiality parameter γ in wide ranges of values for this reason. Hence for the assumption that these isotopes are deformed and have axes of symmetry, we applied the single-particle Schrödinger fluid model and the Nilsson model. On the other hand, for the assumption that these isotopes are deformed and have no axes of symmetry, we applied the cranked Nilsson model and the nuclear super fluidity model. As a result of our calculations, we can conclude that the nucleus <sup>6</sup>Li may be assumed to be deformed and has an axis of symmetry.展开更多
Taking ^120Sn as an example, we discuss the pseudospin symmetry in the single proton resonant states by examining the energies, widths and the wavefunctions. The information of the single proton resonant states in sph...Taking ^120Sn as an example, we discuss the pseudospin symmetry in the single proton resonant states by examining the energies, widths and the wavefunctions. The information of the single proton resonant states in spherical nuclei are extracted from an analytic continuation in the coupling constant method within the framework of the self-consistent relativistic mean field theory under the relativistic boundary condition. We find small energy splitting in a pair of pseudospin partners in the resonant states. The lower components of the Dirac wavefunctions of a pseudospin doublet agree well in the region where nuclear potential dominates. It is concluded that the pseudospin symmetry is also well conserved for the resonant states in realistic nuclei.展开更多
The negative parity high spin states in 45Ti have been investigated with the interacting shell model including the full fp shell and the configuration dependent cranked Nilsson-Strutinsky approach. Generally, the shel...The negative parity high spin states in 45Ti have been investigated with the interacting shell model including the full fp shell and the configuration dependent cranked Nilsson-Strutinsky approach. Generally, the shell model has successfully reproduced the energy levels of negative parity bands, especially has a good description of the signature inversion at 17/2-. The reduced electric quadrupole transition probabilities of high spin states are calculated by the two models and compared with the experimental results. Reasonable agreement between theories and experiment are obtained, while the shell model can give more fine structures. The large differences of elctromagnetic moments between the shell model calculation and observation call for more elaborate effective interaction and more active shells.展开更多
文摘The Cranking Nilsson model is applied to calculate the single-particle energy eigenvalues and eigenfunctions of nuclei in a strongly deformed potential. Accordingly, The L. D. Energy, the Strutinsky inertia, the L. D. inertia, the volume conservation factor , the smoothed energy, the BCS energy, the G-value and the electric quadrupole moment of the five uranium isotopes: 230U, 232U, 234U, 236U and 238U are calculated as functions of the deformation parameter. Furthermore, the single-particle Schrodinger fluid is applied to calculate the rigid-body model, the cranking-model and the equilibrium-model moments of inertia of the five uranium isotopes. Moreover, the collective model is applied to calculate the rotational energies of these isotopes. The best potential and deformation parameters are also given.
文摘The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-particle potential which is deformed with time t, through its parametric dependence on a classical shape variable α(t). Also, the Nilsson model is designed for the calculations of the single-particle energy levels, the magnetic dipole moments, and the electric quadrupole moments of axially symmetric deformed nuclei by assuming that all the nucleons are moving in the field of an anisotropic oscillator potential. On the other hand, the nuclear superfluidity model is designed for the calculations of the nuclear moments of inertia and the electric quadrupole moments of deformed nuclei which have no axes of symmetry by assuming that the nucleons are moving in a quadruple deformed potential. Furthermore, the cranked Nilsson model is designed for the calculations of the total nuclear energy and the quadrupole moments of deformed nuclei which have no axes of symmetry by modifying the Nilsson potential to include second and fourth order oscillations. Accordingly, to investigate whether the six p-shell isotopes <sup>6</sup>Li, <sup>7</sup>Li, <sup>8</sup>Li, <sup>9</sup>Li, <sup>10</sup>Li, and <sup>11</sup>Li have axes of symmetry or not, we applied the four mentioned models to each nucleus by calculating their moments of inertia, their magnetic dipole moments, and their electric quadrupole moments by varying the deformation parameter β and the non-axiality parameter γ in wide ranges of values for this reason. Hence for the assumption that these isotopes are deformed and have axes of symmetry, we applied the single-particle Schrödinger fluid model and the Nilsson model. On the other hand, for the assumption that these isotopes are deformed and have no axes of symmetry, we applied the cranked Nilsson model and the nuclear super fluidity model. As a result of our calculations, we can conclude that the nucleus <sup>6</sup>Li may be assumed to be deformed and has an axis of symmetry.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10447102, 10475003, 10435010 and 10605004, and the Scientific Research Innovation Foundation of BUAA.
文摘Taking ^120Sn as an example, we discuss the pseudospin symmetry in the single proton resonant states by examining the energies, widths and the wavefunctions. The information of the single proton resonant states in spherical nuclei are extracted from an analytic continuation in the coupling constant method within the framework of the self-consistent relativistic mean field theory under the relativistic boundary condition. We find small energy splitting in a pair of pseudospin partners in the resonant states. The lower components of the Dirac wavefunctions of a pseudospin doublet agree well in the region where nuclear potential dominates. It is concluded that the pseudospin symmetry is also well conserved for the resonant states in realistic nuclei.
文摘The negative parity high spin states in 45Ti have been investigated with the interacting shell model including the full fp shell and the configuration dependent cranked Nilsson-Strutinsky approach. Generally, the shell model has successfully reproduced the energy levels of negative parity bands, especially has a good description of the signature inversion at 17/2-. The reduced electric quadrupole transition probabilities of high spin states are calculated by the two models and compared with the experimental results. Reasonable agreement between theories and experiment are obtained, while the shell model can give more fine structures. The large differences of elctromagnetic moments between the shell model calculation and observation call for more elaborate effective interaction and more active shells.
