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 \(4s4p~^3\!P_{1}\), \(4s4p~^3\!P_{2}\) and \(4s3d~^1\!D_2\) 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 \(^{43}\text{Ca}\).