Precision calculation of hyperfine-structure constants for extracting nuclear quadrupole moment of ${}^{43}$Ca

There have been several reported values for the nuclear quadrupole moment of ${}^{43}$Ca, but significant discrepancies exist among these reported values, ranging from $-0.0408(8)$~b to $-0.065(20)$~b. In this work, we performed an accurate calculation of the electric field gradients of the $4s4p{}^3\text{\hspace{0.17em}⁣}{P}_1$, $4s4p{}^3\text{\hspace{0.17em}⁣}{P}_2$ and $4s3d{}^1\text{\hspace{0.17em}⁣}{D}_2$ states in the ${}^{43}$Ca atom using a hybrid method. This hybrid method integrates the advantages of the configuration interaction method and the coupled-cluster method, and can simultaneously account for core-core, core-valence, and valence-valence correlations. By combining our calculated results with the experimental values of the electric quadrupole hyperfine-structure constants of these three states, an accurate and reliable nuclear quadrupole moment of ${}^{43}$Ca was determined to be $-0.0479(6)$~b, which could be recommended as a reference for ${}^{43}\text{Ca}$.