Precision calculation of hyperfine-structure constants for extracting the nuclear quadrupole moment of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>Ca</mml:mi> <mml:mprescripts/> <mml:none/> <mml:mn>43</mml:mn

There have been several reported values for the nuclear quadrupole moment of $^{43}\mathrm{Ca}$, but significant discrepancies exist among these reported values, ranging from $\ensuremath{-}0.0408(8)$ b to $\ensuremath{-}0.065(20)$ b. In this work we perform an accurate calculation of the electric-field gradients of the $4s4p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}, 4s4p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{2}$, and $4s3d{\phantom{\rule{0.16em}{0ex}}}^{1}{D}_{2}$ states in the $^{43}\mathrm{Ca}$ 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 $^{43}\mathrm{Ca}$ is determined to be $\ensuremath{-}0.0479(6)$ b, which could be recommended as a reference for $^{43}\mathrm{Ca}$.