The Calculations Of The Nuclear Electric Quadrupole Moments For Ground State

Nuclear electric quadrupole moment (NQM) is a physical quantity that can detect the deviation of nuclear charge distribution from spherical symmetry. It is one of the important parameters which describe the basic nature of the nuclides. And it is one of the important basic observable to understand the nuclear structure, nuclear models, nucleon-nucleon in-teractions, and so on. After several decades research, There are a variety of the calculation methods or theoretical models, but so far, theoretical calculation and experimental mea-surement are still not perfect. At present, most of the theoretical studies of the NQMs were mainly directed to certain isotope chains or a few nuclei. Furthermore, there were still serious differences between the theoretical values and the experimental values for many nuclei.The previous investigations of NQM show that the number of the measured NQM of ground state nuclei only accounts about 22% of the number of measured nuclear mass nu-clei. Therefore, the theoretical prediction for NQM is necessary. In this paper, several aspects of the NQM have been investigated as follows. (1) Based on the integral expres-sion of nuclear intrinsic electric quadrupole moment, after multiple and complex integral, a global formula of the NQM is given. This formula is closely dependent on the spin of the ground state I, nuclear charge number Z, mass number A, nuclear charge radius Rc and deformation parameters (β2, β4). In this expression, the latest nuclear charge radius Rc (its rms was 0.022fm) is employed to take into account the shell effect, isospin effects, etc. (2) In this paper, the global expression is applied to calculate the NQMs based on the deformation parameters derived from the macroscopic-microscopic nuclear mass models (WS3.2, WS*, WS3.6, WS4) and microscopic nuclear mass models (HFB21, HFB27*). This paper focuses on the differences between the experimental values and the calculation results, of which de-formation parameters obtained from WS4 mass model (rms deviation of nuclear mass was 0.298MeV) and HFB27* mass model (rms deviation of nuclear mass was 0.500MeV), re-spectively. For 527 nuclear ground state existing experimental NQM values, the root mean square deviations of WS4 and HFB27* are 0.552b and 0.657b, and the average deviation are 0.309b and 0.404b, respectively. Many nuclei of the theoretical calculation results can re-produce the experimental value well. The NQM rms deviation is small for the lighter mass nuclei, and is large relatively for the heavier mass nuclei. The results show that the rms deviation is maximum for odd-odd nuclei, and minimum for odd-even nuclei. Furthermore, the rms of 38 magic number nuclei are 0.271b and 0.226b respectively for the deformation parameters which were obtained from WS4 model and HFB27* model. The rms of the magic nuclei shows that the global formula of this paper reasonably consider the shell effect and isospin effect through the nuclear charge radius. (3) The results of this paper had been also compared with the calculations of the microscopic shell model and the experimental data results of least-squares fitting. The calculation results based on the deformation parame-ters obtained from WS4 model have little difference with the results of microcosmic shell model and the experimental data results of least-squares fitting. And the calculation re-sults which the deformation parameters were obtained from HFB27* model is less precise. (4) Electric quadrupole moment is closely related to the nuclear charge radius. In this pa-per, we use of the experimental and theoretical values of the nuclear charge radius as input parameters to calculate the NQM. The results calculated with the deformation parameters derived from WS4 and HFB27* respectively are compared with the 385 experimental data, which exist both NQM and nuclear charge radius. Their root mean square deviation are 0.477b and 0.598b, respectively. It shows that the accuracy of the nuclear charge radius is very important to calculate NQM. (5) In the end of this paper, we also have employed this global formula to predict 161 NQMs, which only have the experimental spin value of the ground states. The result shows the heavier nucleus have larger NQM. This indicates that there may be large deformation for most heavy mass nuclei. The trend is consistent with the results of all existing experimental values.In summary, the systematic studies in this paper indicate that electric quadrupole moment is closely related to the shell effect, isospin effect and nuclear deformation. The shell effect and isospin effect can be reasonably considered through the nuclear charge radius. Furthermore, the global formula of the electric quadrupole moment proposed in this paper can be used to test if the deformation parameters given by different models are reasonable.