Ab initio no-core shell-model description of C10–14 isotopes

Abstract

We present a systematic study of the $^{10--14}\mathrm{C}$ isotopes within the ab initio no-core shell-model theory. We apply four different realistic nucleon-nucleon $(NN)$ interactions: (i) the charge-dependent Bonn 2000 (CDB2K) potential; (ii) the inside nonlocal outside Yukawa (INOY) potential; (iii) the next-to-next-to-next-to-leading order $({\mathrm{N}}^{3}\mathrm{LO})$ potential; and (iv) the optimized next-to-next-to-leading order $({\mathrm{N}}^{2}{\mathrm{LO}}_{\mathrm{opt}})$ potential. We report the low-lying energy spectra of both positive- and negative-parity states for $^{10--14}\mathrm{C}$ isotopes and investigate the level structures. We also calculate electromagnetic properties such as transition strengths, quadrupole moments, and magnetic moments. The dependence of point-proton radii on the harmonic-oscillator frequency and basis space is shown. We present calculations of the translation invariant one-body density matrix in the no-core shell-model and discuss isotopic trends in the density distribution. The maximum basis space reached is $10\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}$ for $^{10}\mathrm{C}$ and $8\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}$ for $^{11--14}\mathrm{C}$, with a maximum M-scheme dimension of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{9}$ for $^{10}\mathrm{C}$. We found that, while the INOY interaction gives the best description of the ground-state energies, the ${\mathrm{N}}^{3}\mathrm{LO}$ interaction best reproduces the point-proton radii.