Neutron radii and semi-phenomenological treatment of neutron distributions for Mg isotopes

Abstract

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 (${\sigma }_R$) 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 ($S_n<S_{2n}$) or core+2n ($S_n>S_{2n}$) 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 ${\sigma }_R$ 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 ${\sigma }_R$ from ${}^{12}$\rm C at 240 and 1000 MeV/nucleon. The trend of the neutron radius and ${\sigma }_R$ suggests that ${}^{40}$\rm Mg exhibits two-neutron halo like structure.