Neutron radii and semi-phenomenological treatment of neutron distributions for Mg isotopes
Involving the charge radii of \rm Mg isotopes, as calculated using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), we have extracted the neutron radii of $^{24-38}$\rm Mg isotopes by studying their reaction cross sections ($σ_{R}$) from $^{12}$\rm C at 240 MeV/nucleon within the framework of Glauber model. The calculations use (i) descriptions of nuclei in terms of the Slater determinant involving harmonic oscillator single-particle wave functions (SDHO), and (ii) two-parameter Fermi (2pF) shape of density distribution, with the aim to assess the density dependence of neutron skin in $^{24-38}$\rm Mg isotopes. To understand the asymptotic behavior (spread) of neutron distribution, we propose to introduce the use of core+n ($S_{n} S_{2n}$) description for stable as well as unstable isotopes; $S_{n}$ ($S_{2n}$) is the one-neutron (two-neutron) separation energy of the considered isotope. The core+n (core+2n) is treated semi-phenomenologically. In this work, the core+n is employed for $^{25-38}$\rm Mg isotopes, and is subjected to reproduce the same neutron radius of the given isotope, as we obtained from $σ_{R}$ calculations. To validate the core+n description, we have revisited the reaction cross sections of $^{25-38}$\rm Mg isotopes. The results are found to agree well with the experimental values. Moreover, the core+n neutron distributions clearly demonstrate the one-neutron halo structure of $^{37}$\rm Mg. These findings motivated us to use the core+2n description for the neutron distribution of $^{40}$\rm Mg in predicting its neutron radius, and $σ_{R}$ from $^{12}$\rm C at 240 and 1000 MeV/nucleon. The trend of the neutron radius and $σ_{R}$ suggests that $^{40}$\rm Mg exhibits two-neutron halo like structure.