Shell-model phenomenology of low-momentum interactions

• Published in: Physical review. C, Nuclear physics Vol. 74; no. 6
• Main Authors: Schwenk, Achim, Zuker, Andrés P.
• Format: Journal Article
• Language: English
• Published: United States 01-12-2006
• Subjects: BINDING ENERGY; COMPARATIVE EVALUATIONS; G MATRIX; HAMILTONIANS; HARMONIC OSCILLATORS; L-S COUPLING; MATRIX ELEMENTS; MEAN-FIELD THEORY; NUCLEAR PHYSICS AND RADIATION PHYSICS; NUCLEI; NUCLEON-NUCLEON INTERACTIONS; OSCILLATORS; SHELL MODELS; SINGLE-PARTICLE MODEL; SPIN
• ISSN: 0556-2813; 1089-490X
• DOI: 10.1103/PhysRevC.74.061302

The first detailed comparison of the low-momentum interaction V{sub lowk} 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{sub lowk} matrix elements can be approximately obtained from a universal set by a simple scaling. In an oscillator mean-field approach, V{sub lowk} 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{sub lowk} makes it possible to define directly a meaningful unperturbed monopole Hamiltonian, for which the inclusion of three-nucleon forces is tractable.