Fine and hyperfine splitting of the low-lying states of ${}^9$Be

We perform accurate calculations of energy levels as well as fine and hyperfine splittings of the lowest ${}^{1,3}\text{\hspace{0.17em}⁣}{P}_J$, ${}^3\text{\hspace{0.17em}⁣}{S}_1$, ${}^3\text{\hspace{0.17em}⁣}{P}_J^e$, and ${}^{1,3}\text{\hspace{0.17em}⁣}{D}_J$ excited states of the ${}^9$Be atom using explicitly correlated Gaussian functions and report on the breakdown of the standard hyperfine structure theory. Because of the strong hyperfine mixing, which prevents the use of common hyperfine constants, we formulate a description of the fine and hyperfine structure that is valid for an arbitrary coupling strength and may have wide applications in many other atomic systems.