[论文解读] Single-Particle Resonant States in Relativistic Hartree-Fock Theory: A Green's Function Approach

Wei Gao, Ting Ting Sun+1 more|arXiv (Cornell University)|Mar 5, 2026

Nuclear physics research studies被引用 0

一句话总结

该论文建立了 RHF-GF 框架，在坐标空间处理束缚态与共振单粒子态，并分析了 N=82 同位素中质子共振的 exact Coulomb 交换效应。

ABSTRACT

Relativistic Hartree-Fock theory is combined with the Green's function method in coordinate space to study both single-particle bound and resonant states within a unified framework. Within this approach, single-particle resonance energies and widths are unambiguously extracted from the density of states, and the influence of the Coulomb exchange effects on proton resonances in $N=82$ isotones are systematically examined. It is found that the exact treatment of Coulomb exchange terms reduces proton resonance energies of approximate $0.09\sim0.21$ MeV, a significantly smaller effect than that obtained from the phenomenological treatment. Moreover, except for rather narrow resonances, the proton resonance widths are visibly reduced by the Coulomb exchange terms, also being much less pronounced than the phenomenological approach. Notably, clear shell effects are observed in the isotonic evolutions of the resonance energy reductions for specific resonances. All these highlight the necessity of a microscopical and exact treatment of the Coulomb exchange terms.

研究动机与目标

• Motivate the need to treat resonant states within a microscopic RHF framework with exact Coulomb exchange.
• Develop a Green’s function in coordinate space to extract resonance energies and widths from the density of states.
• Demonstrate self-consistency by incorporating non-local Fock terms and non-local densities.
• Quantify the impact of exact Coulomb exchange on proton resonances in N=82 isotones.
• Showcase the method on Sn-120 as a benchmark and compare with other approaches.

提出的方法

• Formulate the radial Dirac equation with local (Hartree) and non-local (Fock) terms within RHF.
• Construct the Green’s function G_kappa(r,r';epsilon) as the inverse of (epsilon - h) and express it via incoming/outgoing solutions.
• Obtain the non-local density R_a^{munu}(r,r') from contour integration of G_kappa; use it to derive the local and non-local potentials.
• Compute the density of states from Im G^{++}+Im G^{--} to identify bound and resonant poles.
• Locate resonance poles and extract energies and widths from the density of states and sign-change behavior with respect to the probing energy.
• Compare RHF-GF results with RMF-GF, CMR, S-matrix, ACCC, and CSM methods.

实验结果

研究问题

• RQ1 How can single-particle bound and resonant states be described in a unified RHF framework using Green’s functions?
• RQ2 What is the impact of exact Coulomb exchange terms on proton resonances in N=82 isotones within RHF-GF?
• RQ3 How do RHF-GF results for proton resonances compare with other state-of-the-art methods?
• RQ4 What shell-effects emerge in the evolution of resonance energies and widths across isotones as Z varies near magic numbers?

主要发现

• The RHF-GF method yields resonance energies and widths from the density of states, validated against other approaches for 120Sn.
• Exact treatment of Coulomb exchange reduces proton resonance energies by about 0.09–0.21 MeV, smaller than phenomenological estimates.
• Coulomb exchange generally reduces resonance widths, with a more pronounced effect for certain resonances; results show shell-dependent behavior.
• High-l resonances exhibit clear spin-orbit driven splittings and shell effects impacting their couplings.
• Narrow proton resonances show substantial lifetime sensitivity to Coulomb exchange, while broad resonances are less affected.
• The method captures both bound and resonant states on equal footing and demonstrates the importance of non-local Fock terms.