# Second-order equation of state with the full Skyrme interaction: toward new effective interactions for beyond mean-field models

Abstract : In a quantum Fermi system the energy per particle calculated at the second order beyond the mean-field approximation diverges if a zero-range interaction is employed. We have previously analyzed this problem in symmetric nuclear matter by using a simplified nuclear Skyrme interaction, and proposed a strategy to treat such a divergence. In the present work, we extend the same strategy to the case of the full nuclear Skyrme interaction. Moreover we show that, in spite of the strong divergence ($\sim$ $\Lambda^5$, where $\Lambda$ is the momentum cutoff) related to the velocity-dependent terms of the interaction, the adopted cutoff regularization can be always simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratio. This paves the way to applications to finite nuclei.
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-00697623
Contributor : Sophie Heurteau <>
Submitted on : Tuesday, May 15, 2012 - 5:12:26 PM
Last modification on : Sunday, November 8, 2020 - 12:26:02 PM

### Citation

K. Moghrabi, M. Grasso, X. Roca-Maza, G. Colo'. Second-order equation of state with the full Skyrme interaction: toward new effective interactions for beyond mean-field models. Physical Review C, American Physical Society, 2012, 85, pp.044323. ⟨10.1103/PhysRevC.85.044323⟩. ⟨in2p3-00697623⟩

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