Ab initio no-core shell model description of ${}^{10-14}$C isotopes

Abstract

We present a systematic study of the ${}^{10-14}\text{C}$ isotopes within the \textit{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 non-local outside Yukawa (INOY) potential (iii) the next-to-next-to-next-to-leading order (N${}^3$LO) potential, and (iv) the optimized next-to-next-to-leading order (N${}^2$LO${}_{opt}$) potential. We report the low-lying energy spectra of both positive and negative parity states for the ${}^{10-14}\text{C}$ isotopes and investigate the level structures. We also calculate electromagnetic properties such as transition strengths, quadrupole 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 $10\hslash \Omega$ for ${}^{10}\text{C}$ and $8\hslash \Omega$ for ${}^{11-14}\text{C}$, with a maximum M-scheme dimension of $1.3\times 10^9$ for ${}^{10}\text{C}$. We found that while the INOY interaction gives the best description of the ground state energies, the N${}^3$LO interaction best reproduces the point-proton radii.

21 pages, 12 figures

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