No-core shell model for A = 47 and A = 49

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We apply the no-core shell model to the nuclear structure of odd-mass nuclei straddling 48Ca. Starting with the NN interaction, that fits two-body scattering and bound state data, we evaluate the nuclear properties of A = 47 and A = 49 nuclei while preserving all the underlying symmetries. Due to model space limitations and the absence of three-body interactions, we incorporate phenomenological interaction terms determined by fits to A = 48 nuclei in a previous effort. Our modified Hamiltonian produces reasonable spectra for these odd-mass nuclei. In addition to the differences in single-particle basis states, the absence of a single-particle Hamiltonian in our no-core approach complicates comparisons with valence effective NN interactions. We focus on purely off-diagonal two-body matrix elements since they are not affected by ambiguities in the different roles for one-body potentials and we compare selected sets of fp-shell matrix elements of our initial and modified Hamiltonians in the harmonic oscillator basis with those of a recent model fp-shell interaction, the GXPF1 interaction of Honma et al. While some significant differences emerge from these comparisons, there is an overall reasonably good correlation between our off-diagonal matrix elements and those of GXPF1.