No-core shell model for 48-Ca, 48-Sc and 48-Ti

Abstract

We report the first no-core shell model results for ${}^{48}Ca$, ${}^{48}Sc$ and ${}^{48}Ti$ with derived and modified two-body Hamiltonians. We use an oscillator basis with a limited $\hslash \Omega$ range around $45/A^{1/3}-25/A^{2/3}=10.5MeV$ and a limited model space up to $1\hslash \Omega$. No single-particle energies are used. We find that the charge dependence of the bulk binding energy of eight A=48 nuclei is reasonably described with an effective Hamiltonian derived from the CD-Bonn interaction while there is an overall underbinding by about 0.4 MeV/nucleon. However, the resulting spectra exhibit deficiencies that are anticipated due to: (1) basis space limitations and/or the absence of effective many-body interactions; and, (2) the absence of genuine three-nucleon interactions. We then introduce additive isospin-dependent central terms plus a tensor force to our Hamiltonian and achieve accurate binding energies and reasonable spectra for all three nuclei. The resulting no-core shell model opens a path for applications to the double-beta ($\beta \beta$) decay process.

Comments: Revised content and added references