Relativistic single particle motion and spin-orbit coupling in nuclei and hypernuclei

doi:10.1016/0375-9474(81)90533-9

Nuclear Physics A

Volume 355, Issue 2, 9 March 1981, Pages 365-382

https://doi.org/10.1016/0375-9474(81)90533-9 Get rights and content

Abstract

Within the framework of a relativistic mean field approach, a comparison is made between the single particle potentials and spin-orbit interactions for nucleons and Λ-particles. The phenomenological observation that scalar and vector exchange interactions of the Λ turn out to be roughly a factor of three weaker than the corresponding nuclear forces is related back to properties of the ΛN interaction using boson exchange models. K and K^∗ exchange terms for hypernuclei are also calculated. Their combined effect is found to be small.

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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_ΛC to ²⁰⁸_ΛPb. 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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In this work we present an extension to hypernuclei of a relativistic nuclear energy density functional [14–16] that combines relevant features of chiral dynamics and the symmetry breaking pattern of low-energy QCD. Chiral pionic fluctuations in combination with Pauli blocking effects [11], Δ excitations and three-nucleon (3N) interactions [12] are superimposed on the condensate background fields and produce the nuclear binding. Scalar and vector mean fields representing the in-medium changes of the quark condensates, which cancel almost completely in their sum, act coherently in their difference to generate the large spin–orbit potential for nucleons in nuclei.
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^∗: Supported in part by USDOE Contract No. EY-76-S-02-3001 and by Deutsche Forschungs-gemeinschaft; on leave from University of Regensburg.

^∗∗: Permanent address: Institute of Theoretical Physics, University of Regensburg, D-8400 Regensburg; work supported in part by German Bundesministerium für Forschung und Technologie under contract MEP 3200 X.

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Relativistic single particle motion and spin-orbit coupling in nuclei and hypernuclei

Abstract

Phys. Lett.

Phys. Lett.

Ann. Rev. Nucl. Part. Sci.

Ann. of Phys.

Phys. Rev. Lett.

Phys. Lett.

Nucl. Phys.

Phys. Lett.

Phys. Lett.

Phys. Lett.

Ann. of Phys.

Phys. Lett.

Phys. Lett.

Ann. of Phys.

Ann. of Phys.

Phys. Lett.

Ann. of Phys.

J. of Phys.

Phys. Rev.

Ann. of Phys.

Nucl. Phys.

Nuovo Cim.