Proton decays in ${}^{16}\mathrm{Ne}$ and ${}^{18}\mathrm{Mg}$ and isospin-symmetry breaking in carbon isotopes and isotones

Proton-rich nuclei possess unique properties in the nuclear chart. Due to the presence of both continuum coupling and Coulomb interaction, phenomena such as halos, Thomas-Ehrman shift, and proton emissions can occur. Relevant experimental data are difficult to obtain, so that theoretical calculations are needed to understand nuclei at drip lines and to guide experimentalists. In particular, the ${}^{16}\mathrm{Ne}$ and ${}^{18}\mathrm{Mg}$ isotopes are supposed to be one-proton and/or two-proton emitting nuclei, but associated experimental data are either incomplete or even unavailable. Consequently, we performed Gamow shell model calculations of carbon isotones bearing $A=15\text{–}18$. Isospin-symmetry breaking occurring in carbon isotones and isotopes is also discussed. It is hereby shown that the mixed effects of continuum coupling and Coulomb interaction at drip lines generate complex patterns in isospin multiplets. Added to that, it is possible to determine the one-proton and two-proton widths of ${}^{16}\mathrm{Ne}$ and ${}^{18}\mathrm{Mg}$. Obtained decay patterns are in agreement with those obtained in previous experimental and theoretical works. Moreover, to our knowledge, this is the first theoretical calculation of binding energy and partial decay widths of ${}^{18}\mathrm{Mg}$ in a configuration interaction picture.

Figure 1

Excitation energies ($E_x$, in MeV) and widths (in keV) of ground and excited states of carbon isotones. The GSM calculations are compared to available experimental data. Energies are given with respect to the ${}^{14}\mathrm{O}$ core. Widths are represented by green striped squares, and their explicit values are written above. Experimental data of ${}^{15}\mathrm{F}$ are taken from Ref. [27] and those of ${}^{16}\mathrm{Ne}$ from Ref. [66].

Figure 2

Comparison of the excitation energies and widths of mirroring nuclear states of carbon isotones and isotopes. Excitation energies of a nucleus are given with respect to its ground state energy. Experimental data of ${}^{16}\mathrm{Ne}$ are taken from Ref. [66], whereas all other data are taken from Ref. [27]. See Fig. 1 for details and notations.

Figure 3

Calculated binding energies of carbon isotopes and isotones (GSM, black squares and blue lozenges, respectively), binding energies of carbon isotones minus the Coulomb two-body part contribution (GSM-2BC, purple crosses) and binding energies of carbon isotones minus one- and two-body Coulomb total contributions (GSM-1BC-2BC, red lozenges), as a function of mass number $A$. Experimental data are represented by green and red stars for carbon isotopes and isotones, respectively. All energies ($E$, in MeV) are given with respect to ${}^{14}\mathrm{C}$ and ${}^{14}\mathrm{O}$ cores for carbon isotopes and isotones, respectively. The arrow next to the ground state energy of ${}^{17}\mathrm{Na}$ indicates that the experimental datum is an upper limit.

Figure 4

Calculated energies and widths (in MeV) of ${}^{15}\mathrm{F}$ and ${}^{16}\mathrm{Ne}$ (upper panel) and of ${}^{17}\mathrm{Na}$ and ${}^{16}\mathrm{Mg}$ (lower panel) as a function of the difference $\mathrm{\Delta }{V}_0=V_0-V_0^{\text{(fit)}}$ of the Woods-Saxon central potential depths (see text for definition). Energies are depicted by blue disks and red lozenges for even and odd nuclei, respectively. Widths are represented by segments centered on disks and lozenges. The widths of ${}^{16}\mathrm{Ne}$ and ${}^{18}\mathrm{Mg}$ have been multiplied by 20 for readability. Energies are given with respect to the ${}^{14}\mathrm{O}$ core. The physical GSM calculation, for which $V_0=V_0^{\text{(fit)}}$, is indicated by an arrow.