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arXiv · 0909.1707

Hypernuclear single particle spectra based on in-medium chiral SU(3) dynamics

P. Finelli·N. Kaiser·D. Vretenar·W. Weise
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Abstract

A previously derived relativistic energy density functional for nuclei, based on low-energy in-medium chiral dynamics, is generalized to implement constraints from chiral SU(3) effective field theory and applied to $Λ$ hypernuclei. Density-dependent central and spin-orbit mean fields are calculated for a $Λ$ hyperon using the SU(3) extension of in-medium chiral perturbation theory to two-loop order. Long range $ΛN$ interactions arise from kaon-exchange and from two-pion-exchange with a $Σ$ hyperon in the intermediate state. Short-distance dynamics is encoded in contact interactions. They include scalar and vector mean fields reflecting in-medium changes of quark condensates, constrained by QCD sum rules. The $Λ$ single particle orbitals are computed for a series of hypernuclei from $^{13}_Λ$C to $^{208}_Λ$Pb. The role of a surface (derivative) term is studied. Its strength is found to be compatible with a corresponding estimate from in-medium chiral perturbation theory. Very good agreement with hypernuclear spectroscopic data is achieved. The smallness of the $Λ$-nuclear spin-orbit interaction finds a natural explanation in terms of an almost complete cancellation between short-range scalar/vector contributions and longer range terms generated by two-pion exchange.

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P. Finelli, N. Kaiser, D. Vretenar, W. Weise. 2009-10-02. Hypernuclear single particle spectra based on in-medium chiral SU(3) dynamics. https://doi.org/10.1016/j.nuclphysa.2009.10.083

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