A no-core shell model for 48Ca, 48Sc and 48Ti

Abstract

We report the first no-core shell model results for 48Ca, 48Sc and 48Ti with derived and modified two-body Hamiltonians. We use an oscillator basis with a limited ℏΩ range around 45/A1/3 − 25/A2/3 = 10.5 MeV and a limited model space up to 1ℏΩ. 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 (ββ) decay process.