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

TL;DR

This paper uses ab initio no-core shell model calculations with four realistic NN interactions to study energy spectra, electromagnetic properties, and density distributions of $^{10-14}$C isotopes, revealing how different interactions affect various nuclear properties.

Contribution

It provides a systematic comparison of four realistic NN interactions within the no-core shell model for carbon isotopes, including detailed spectra, electromagnetic properties, and density distributions.

Findings

INOY interaction best describes ground state energies.

N$^3$LO interaction best reproduces point-proton radii.

Calculations reach up to $10 abla ext{h} abla ext{O}$ basis space.

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 $10 \hbar \Omega$ for $^{10}\text{C}$ and $8 \hbar \Omega$ 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.