Shell-model phenomenology of low-momentum interactions

Abstract

The first detailed comparison of the low-momentum interaction V_{low k} with G matrices is presented. We use overlaps to measure quantitatively the similarity of shell-model matrix elements for different cutoffs and oscillator frequencies. Over a wide range, all sets of V_{low k} matrix elements can be approximately obtained from a universal set by a simple scaling. In an oscillator mean-field approach, V_{low k} reproduces satisfactorily many features of the single-particle and single-hole spectra on closed-shell nuclei, in particular through remarkably good splittings between spin-orbit partners on top of harmonic oscillator closures. The main deficiencies of pure two-nucleon interactions are associated with binding energies and with the failure to ensure magicity for the extruder-intruder closures. Here, calculations including three-nucleon interactions are most needed. V_{low k} makes it possible to define directly a meaningful unperturbed monopole Hamiltonian, for which the inclusion of three-nucleon forces is tractable.

5 pages, 4 figures, minor additions, to appear as Rapid Comm. in Phys. Rev. C

References in corpus (4)

• The Shell Model as Unified View of Nuclear Structure
• Quantum Monte Carlo calculations of excited states in A = 6--8 nuclei
• Is nuclear matter perturbative with low-momentum interactions?
• Low-momentum interaction in few-nucleon systems

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