采用相对论多组态Dirac-Hartree-Fock方法对Mg原子同位素位移的理论研究

利用相对论多组态Dirac-Hartree-Fock方法研究了Mg原子基态到低激发态~1S_0-~1P_1和~1S_0-~3P_1两条跃迁谱线的同位素位移参数,包括正常质量位移系数,特殊质量位移系数和场位移因子,并计算了~(24)Mg,~(25)Mg和~(26)Mg三个稳定同位素的同位素位移.在计算中采用了一种受限制的双电子激发模式,并将同位素位移计算结果与已有的实验测量和理论计算结果进行了对比.结果表明,用本文的研究方法计算的Mg原子同位素位移与其他理论结果和实验测量值十分符合.本文的计算结果可以为~(20-40)Mg同位素位移测量实验提供必要的参考,所用的计算方法也可以应用到其他类Mg体系(核外电子数等于12的离子)等多电子离子的光谱结构计算和同位素位移的研究中.

Theoretical calculations on isotope shifts of Mg I by using relativistic multiconfiguration Dirac-Hartree-Fock method

The isotope shift parameters for the atomic transitions ¹S₀-¹P₁ and ¹S₀-³P₁ of Mg are calculated by the relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) method, including the normal mass shift (NMS) coefficients, the specific mass shift (SMS) coefficients and the field shift (FS) factors. The detailed calculations of the isotope shifts for the three stable isotopes ²⁴Mg, ²⁵Mg and ²⁶Mg are also carried out, in which the GRASP2K package is used together with another modified relativistic isotope shift computation code package RIS3. The two-parameter Fermi model is used here to describe the nuclear charge distribution in order to calculate the field shift by the first-order perturbation. A restricted double excitation mode is used in our calculations, one electron is excited from the two electrons in the 3s shell (3s²), another electron is excited from the eight electrons in the 2s or 2p shells (2s²2p⁶), and the two electrons in the 1s shell (1s²) are not excited. The active configurations are expanded from the occupied orbitals to some active sets layer by layer, each correlation layer is numbered by the principal quantum numbers n (n= 3, 4, 5, …) and contains the corresponding orbitals s, p, d, …. The active configurations with the mixing coefficients in the added layer can be optimized by the MCDHF calculations. In this work, the atomic state functions are optimized simultaneously by the self-consistent field method and the relativistic configuration interaction approach in which the Breit interaction is taken into account perturbatively as well. The maximum principal quantum number n equals 10 and the largest orbital quantum number l_max is g. In our calculations, the NMS coefficients are -576.8 and -359.9 GHz·u, the SMS coefficients are 133.9 and -479.6 GHz·u, and the FS factors are -62.7 and -78.0 MHz·fm^-2 for the ¹S₀-¹P₁ and ¹S₀-³P₁ transitions of Mg, respectively. The difference between our isotope shift calculations and the previous experimental measurements is in a range from 6 MHz to 20 MHz with the relative error range from 0.6% to 1.3%, which shows that our results are in good agreement with experimental values. Our calculations are also coincident with other theoretical results. The isotope shift parameters provided here can be applied to the quick calculations of isotope shifts for the short-lived Mg isotopes, including ^20-23Mg and ^27-40Mg, and can be referred to for the corresponding isotope shift experiments. The methods used here canbe applied to calculating the isotope shifts and the atomic spectroscopic structures for other Mg-like ions with twelve extranuclear electrons.