Relativistic Chiral Mean Field Model for Finite Nuclei

TL;DR

This paper introduces a relativistic chiral mean field model that accurately incorporates pion-exchange interactions in finite nuclei, extending previous models to include higher spin states and applying it to helium-4 to analyze pionic correlations.

Contribution

The paper develops the RCMF model with higher spin quantum states for pionic correlations and demonstrates its application to ^4He, including short-range correlations via UCOM, advancing nuclear many-body modeling.

Findings

Energy convergence occurs around J^{pi}_{max} = 6^{-}.

Approximately 50% of the two-body interaction energy is from tensor parts.

20% of the energy comes from spin-spin central parts of pion-exchange.

Abstract

We present a relativistic chiral mean field (RCMF) model, which is a method for the proper treatment of pion-exchange interaction in the nuclear many-body problem. There the dominant term of the pionic correlation is expressed in two-particle two-hole (2p-2h) states with particle-holes having pionic quantum number, J^{pi}. The charge-and-parity-projected relativistic mean field (CPPRMF) model developed so far treats surface properties of pionic correlation in 2p-2h states with J^{pi} = 0^{-} (spherical ansatz). We extend the CPPRMF model by taking 2p-2h states with higher spin quantum numbers, J^{pi} = 1^{+}, 2^{-}, 3^{+}, ... to describe the full strength of the pionic correlation in the intermediate range (r > 0.5 fm). We apply the RCMF model to the ^{4}He nucleus as a pilot calculation for the study of medium and heavy nuclei. We study the behavior of energy convergence with the pionic quantum number, J^{pi}, and find convergence around J^{pi}_{max} = 6^{-}. We include further the effect of the short-range repulsion in terms of the unitary correlation operator method (UCOM) for the central part of the pion-exchange interaction. The energy contribution of about 50% of the net two-body interaction comes from the tensor part and 20% comes from the spin-spin central part of the pion-exchange interaction.