Al^+离子3s^2 ~1S_0→3s3p~ (3,1)P_1~o跃迁同位素偏移的理论研究

Theoretical study on the isotope shift factors for the 3s^2 ~1S_0→3s3p ^(3,1)P_1~o transitions in Al^+ ion

在多组态Dirac-Hartree-Fock方法对Al^+离子3s^2~1S_0→3s3p^(3,1)p_1~o两个跃迁同位素偏移因子精细计算工作的基础上,细致研究了同位素偏移因子和能量本征值(或跃迁能)随着电子关联的收敛过程.研究发现:单个能级的同位素质量偏移因子随电子关联的收敛性与能量本征值随电子关联的收敛性之间有线性关系;对于跃迁而言,对电子关联的描述越充分,质量偏移因子和跃迁能随电子关联的收敛性之间的线性关系越明显.因此,在计算模型中包含大规模的电子关联的情况下,可以利用该线性关系根据跃迁能的误差评估同位素偏移因子的不确定度.

The accurate calculation of the isotope shift factors is helpful in extracting the mean-square charge radius of the nucleus, which is an important nuclear parameter to investigate the nuclear properties and improve nuclear structure theories. However, for atomic systems with many electrons the uncertainties of the calculated isotope shift factors are difficult to evaluate accurately, since high sensitivity of the isotope shift factor to the electron correlation and limitation of the computational resource. Based on the calculations of the isotope shift factors of the 3 s2 1 S0→3 s3 p 3,1P1o transitions in Al＋ by using the multi-configuration Dirac-Hartree-Fock method, the convergences of these physical quantities with the expansion of the configuration space are investigated in detail. In our calculation, the electron correlations are divided into the first-order correlation and the higher-order correlations according to the perturbation theory, and captured by using the active space approach. The effect of the first-order correlation are considered by including configuration state functions（CSFs） that are generated by the single and double substitutions from the occupied orbitals in the single reference configuration set. After the first-order correlation effect are taken into account adequately, the reference configuration sets are augumented by adding the dominant CSFs from the first-order correlation configuration space, in order to consider the higher-order correlation effect. We find that the convergence of the mass shift factors（including the normal shift factor and the specific mass shift factor） is linearly correlated with the convergence of the level energies in our computational model. For the transitions, the linear correlation of the convergence between the mass shift factors and the transition energies is not so good as that for the levels involved in the transitions due to the limited computational resource, but it can be improved with the expansion by including more higher-order correlation related 2 s and 2 p core electrons. Furthermore, we made use of the linear correlation to estimate the uncertainties of our isotope shift factors,and obtain the reasonable value of error. The authors hope that the linear correlation between the convergence of the mass shift factors and the level or transition energies can be proved and explained in more atomic systems, and the linear correlation can be used to evaluate accurately the uncertainties of the mass shift factors for the atoms and ions with many electrons in the near future.