The relativistic coupled-cluster method has been employed to calculate the energies, magnetic dipole, electric quadrupole and magnetic octupole hyperfine-structure constants of the low-lying states of Ra + . The validity of our calculations is substantiated by comparing the calculated binding energies and magnetic dipole hyperfine-structure constants with the corresponding available experimental results. The combination of our theoretical results with the available experimental values of the electric quadrupole hyperfine-structure constant, makes it possible to extract the electric quadrupole moments Q of the 209,211,221,223 Ra nuclei. Our Q( 221 Ra) = 1.968(34) and Q( 223 Ra) = 1.248( 22) are consistent with the referenced values 1.978(106) and 1.254(66) from a semi-empirical analysis (1988 Z. Phys. D 11 105), but Q( 211 Ra) = 0.33(2) is smaller than the referenced value 0.48(4) by about 30%. Furthermore, we also performed a procedure for assessing the contributions of magnetic octupole hyperfine interaction to the hyperfine splitting considering the preliminary value of magnetic octupole moment from the single-particle nuclear structure model. The sensitivity of hyperfine-structure interval measurements in 223 Ra + that can reveal the effect caused by the nuclear octupole moment are found to be on the order of kHz.

Hyperfine-structure constants of odd Ra + due to the interactions of nuclear magnetic dipole, electric quadrupole, and magnetic octupole moments with the electrons are investigated in the framework of relativistic coupled-cluster method within single-and double-excitation approximation. The calculated energies and magnetic dipole hyperfine-structure constants A exhibit a good agreement with available experimental values. Combining with the experimental electric quadrupole hyperfinestructure constant, we also extracted the electric quadrupole moments Q of 209,211,221,223 Ra. Our Q( 221 Ra) and Q( 223 Ra) are consistent with the referenced values from a semi-empirical analysis (Z. Phys. D: At., Mol. Clusters 11, 105 (1988)), but Q( 211 Ra)=0.33(2) is smaller than the referenced value 0.48(4) by about 30%. Furthermore, we also performed a procedure for assessing the contributions of magnetic octupole moment to the hyperfine splitting. The sensitivity of hyperfine-structure interval measurements in 223 Ra + that can reveal the effect caused by the nuclear octupole moment are found to be on the order of kHz.