Theoretical study of the hyperfine-interaction constants and the isotope-shift factors for the $3s^2{}^1{S}_0\text{–}3s3p{}^{3,1}{P}_1^o$ transitions in ${\mathrm{Al}}^{+}$

We calculated the magnetic dipole and the electric quadrupole hyperfine interaction constants of $3s3p{}^{3,1}{P}_1^o$ states and the isotope shift, including mass and field shift, factors for transitions from these two states to the ground state $3\mathrm{s}{}^{21}{S}_0$ in ${\mathrm{Al}}^{+}$ ions using the multiconfiguration Dirac-Hartree-Fock method. The effects of the electron correlations and the Breit interaction on these physical quantities were investigated in detail based on the active space approach. It is found that the core-core and the higher order correlations are considerable for evaluating the uncertainties of the atomic parameters concerned. The uncertainties of the hyperfine interaction constants in this work are less than 1.6%. Although the isotope shift factors are highly sensitive to the electron correlations, reasonable uncertainties were obtained by exploring the effects of the electron correlations. Moreover, we found that the relativistic nuclear recoil corrections to the mass shift factors are very small and insensitive to the electron correlations for ${\mathrm{Al}}^{+}$. These atomic parameters present in this work are valuable for extracting the nuclear electric quadrupole moments and the mean-square charge radii of Al isotopes.

Figure 1

The hyperfine interaction constants (in MHz) $A$ (a) and $B$ (b) of $3s3p{}^{3,1}{P}_1^o$ states in the ${\mathrm{Al}}^{+}$ ion as functions of the computational models.

Figure 2

The relativistic nuclear recoil corrections of the NMS (a) and SMS (b) factors for the transitions $3s^2{}^1{S}_0\text{–}3s3p{}^{3,1}{P}_1^o$ in the ${\mathrm{Al}}^{+}$ ion as functions of the computational models.