- 董 晨钟1,
- 1. 西北师范大学
- 2. Key Laboratory of Atomic and Molecular Physics-Northwest Normal University, Lanzhou 730070, China
- 3. 西北师范大学物理与电子工程学院
Theoretical study on the polarizabilities and hyperpolarizabilities of Be+ ions and Li atoms
- Received Date:
24 August 2020
Abstract: The wave functions, energy levels, and oscillator strengths of Be+ ions and Li atoms are calculated by using a relativistic model potential method, which is named the relativistic configuration interaction plus core polarization method(RCICP). The presently calculated energy levels are in good agreement with experimental levels tabulated in NIST Atomic Spectra Database, and the difference appears in the sixth digits after the decimal point. The present oscillator strengths are in good agreement with the existing theoretical and experimental results. By means of these energy levels and oscillator strengths, the electric-dipole static polarizabilities and hyperpolarizabilities of the ground states are determined. The contributions of different intermediate states to the hyperpolarizabilities of the ground state are further discussed. For Be+ ions, the present electric-dipole polarizability and hyperpolarizability are in good agreement with the results calculated by Hartree-Fock plus core polarization method, the finite field method and relativistic many-body method. The largest contribution to the hyperpolarizability is the term of α01β0. For Li atoms, the present electric-dipole polarizability is in good agreement with the available theoretical and experimental results. However, the present hyperpolarizability is different with the other theoretical results significantly. Moreover, the hyperpolarizabilities calculated by different theoretical methods are quite different. The biggest difference is more than an order of magnitude. In order to explain the reason for these differences, we analyzed the contributions of different intermediate states to the hyperpolarizability in detail. It is found that the sum of the contributions of the 2s→npj(n>=3) and npj→ndj(n>=3) to hyperpolarizability is approximately equal to that term of α01β0. The total hyperpolarizability, which is the subtraction between the sum of the contributions of the 2s→npj(n>=3) and npj→ndj(n>=3) to hyperpolarizability and α01β0, is relatively small. Consequently, this subtraction magnifies the calculated error. If the uncertainties of the transition matrix elements are less than 0.1%, the uncertainty of hyperpolarizability would be more than 100%. Therefore, the differences of hyperpolarizabilities for the ground state of Li atoms calculated by various theoretical methods are more than 100% or an order of magnitude.