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

The self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with Green's function technique in the coordinate space is developed to investigate odd-$A$ nuclei by incorporating the blocking effect. In a calculation performed with the SLy4 parameter for the neutron-rich Mg isotopes with $A=36-42$ around the neutron shell closure N=28, the odd-even staggering in 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 due to the blocking effect on the pair correlation energy, for which the configuration occupying the weakly-bound quasiparticle state $2p_{3/2}$ becomes the ground state instead of the $1f_{7/2}$ configuration. Performing systematic calculations with different Skyrme parameters we find that the ground state configuration for the odd-$A$ Mg isotopes, and hence the odd-even staggering of neutron radii, are sensitive to the details in the single-particle spectra, especially the gap between orbits $1f_{7/2}$ and $2p_{3/2}$.