Abstract
We have calculated the ground-state energy of the doubly-magic nucleus $^{40}\mathrm{Ca}$ within the framework of the Goldstone expansion using the CD-Bonn nucleon-nucleon potential. The short-range repulsion of this potential has been renormalized by integrating out its high-momentum components so as to derive a low-momentum potential ${V}_{\mathrm{low}\ensuremath{-}k}$ defined up to a cutoff momentum \ensuremath{\Lambda}. A simple criterion has been employed to establish a connection between this cutoff momentum and the size of the two-nucleon model space in the harmonic oscillator basis. This model-space truncation approach provides a reliable way to renormalize the free nucleon-nucleon potential preserving its many-body physics. The role of the $3p\text{\ensuremath{-}}3h$ and $4p\text{\ensuremath{-}}4h$ excitations in the description of the ground state of $^{40}\mathrm{Ca}$ is discussed.
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