Ab initio no-core shell model study of neutron-rich ${}^{18,19,20}$C isotopes

We implement the ab initio no-core shell model approach to study neutron-rich ${}^{18}$C, ${}^{19}$C and ${}^{20}$C isotopes. For this purpose, we employ charge-dependent Bonn 2000 (CDB2K), inside non-local outside Yukawa (INOY) and chiral next-to-next-to-next-to-leading order (N${}^3$LO) nucleon-nucleon interactions. Low-lying energy spectra, electromagnetic properties and point-proton radii for these nuclei up to basis space $N_{\mathrm{m}\mathrm{a}\mathrm{x}}$ = 4 are calculated. Binding energies obtained with INOY interaction are in better agreement with the experimental values as compared to other $\mathit{\text{ab}}\mathit{\text{initio}}$ interactions. We also show the behavior of ground state energy and point-proton radii with the NCSM parameters, $\mathrm{\hslash }$$\mathrm{\Omega }$ and $N_{\mathrm{m}\mathrm{a}\mathrm{x}}$. We report a strong sensitivity of the B(E2) values from the first excited $2^{+}$ to the ground state of ${}^{18}$C and ${}^{20}$C to the nuclear interaction. Shell model calculations with YSOX interaction are also performed, and corresponding results are compared with ab initio one.