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The self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theoryformulated with Green's function technique in the coordinate space is developedto investigate odd-$A$ nuclei by incorporating the blocking effect. In acalculation performed with the SLy4 parameter for the neutron-rich Mg isotopeswith $A=36-42$ around the neutron shell closure N=28, the odd-even staggeringin the neutron rms radius, i.e., a larger value in $^{39}$Mg than those in$^{38}$Mg and $^{40}$Mg, is found. The large neutron radius in $^{39}$Mg is dueto the blocking effect on the pair correlation energy, for which theconfiguration occupying the weakly-bound quasiparticle state $2p_{3/2}$ becomesthe ground state instead of the $1f_{7/2}$ configuration. Performing systematiccalculations with different Skyrme parameters we find that the ground stateconfiguration for the odd-$A$ Mg isotopes, and hence the odd-even staggering ofneutron radii, are sensitive to the details in the single-particle spectra,especially the gap between orbits $1f_{7/2}$ and $2p_{3/2}$.

Odd-even staggering of neutron radii for neutron-rich Mg isotopes in continuum Skyrme-Hartree-Fock-Bogoliubov theory