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  • Vary, J P; Popescu, S; Stoica, S; Navratil, P

    arXiv.org, 03/2009
    Paper

    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 \(\hbar\Omega\) range around \(45/A^{1/3}-25/A^{2/3} = 10.5 MeV\) and a limited model space up to \(1\hbar\Omega\). 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.