Relativistic hyperpolarizabilities for atomic H, Li, and Be${}^{+}$ systems

Abstract

The hyperpolarizability of an atom is a property that describes the nonlinear interaction between an atom and an external electric field leading to a higher-order Stark shift. Accurate evaluations of these coefficients for various systems are crucial to improve experimental precision in advanced atom-based clocks. However, there is a dearth of reports on atomic hyperpolarizabilities, particularly regarding relativistic hyperpolarizabilities. Thus, in this paper, we use fourth-order perturbation theory to establish a universal formula for the hyperpolarizability and calculate the relativistic hyperpolarizabilities of low-lying states for the monovalent electronic atomic systems H, Li, and Be${}^{+}$. The highly accurate results given here for the H atom could serve as benchmarks for other theoretical methods.

12 pages; 1 figure

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