[Paper Review] Neutron-skin thickness of $^{208}$Pb, and symmetry-energy constraints from the study of the anti-analog giant dipole resonance

A. Krasznahorkay, M. Csatlós+13 more|arXiv (Cornell University)|Nov 6, 2013

Nuclear physics research studies3 citations

TL;DR

This study measures the energy difference between the anti-analog giant dipole resonance (AGDR) and the isobaric analog state (IAS) in $^{208}$Pb via the $^{208}$Pb($p$, $n\gamma\bar{p}$) reaction at 30 MeV, using coincidence detection of $\gamma$-rays and protons. The AGDR energy shift is found to be linearly correlated with neutron-skin thickness, yielding $\Delta R_{pn} = 0.190 \pm 0.028$ fm and constraining the symmetry energy to $J = 32.7 \pm 0.6$ MeV and $L = 49.7 \pm 4.4$ MeV, offering tighter constraints than most prior methods.

ABSTRACT

The $^{208}$Pb($p$,$nγ\bar p$) $^{207}$Pb reaction at a beam energy of 30 MeV has been used to excite the anti-analog of the giant dipole resonance (AGDR) and to measure its $γ$-decay to the isobaric analog state in coincidence with proton decay of IAS. The energy of the transition has also been calculated with the self-consistent relativistic random-phase approximation (RRPA), and found to be linearly correlated to the predicted value of the neutron-skin thickness ($ΔR_{pn}$). By comparing the theoretical results with the measured transition energy, the value of 0.190 $\pm$ 0.028 fm has been determined for $ΔR_{pn}$ of $^{208}$Pb, in agreement with previous experimental results. The AGDR excitation energy has also been used to calculate the symmetry energy at saturation ($J=32.7 \pm 0.6$ MeV) and the slope of the symmetry energy ($L=49.7 \pm 4.4$ MeV), resulting in more stringent constraints than most of the previous studies.

Motivation & Objective

• To determine the neutron-skin thickness $\Delta R_{pn}$ in $^{208}$Pb with high precision using a novel method based on the anti-analog giant dipole resonance (AGDR).
• To constrain the symmetry energy at saturation density ($J$) and its slope ($L$) using the measured AGDR-IAS energy difference.
• To test the consistency of the AGDR method with other established probes such as dipole polarizability ($\alpha_D$) and pygmy dipole resonances (PDR).
• To assess the sensitivity of the AGDR transition energy to neutron skin thickness using relativistic random-phase approximation (RRPA) calculations.

Proposed method

• The $^{208}$Pb($p$, $n\gamma\bar{p}$) reaction at 30 MeV beam energy was used to coherently excite the AGDR and detect its $\gamma$-decay to the IAS in coincidence with proton decay from the IAS.
• Coincidence detection of $\gamma$-rays and protons enabled precise measurement of the energy difference between the AGDR and IAS states.
• Theoretical predictions of the AGDR energy were calculated using a self-consistent relativistic proton-neutron quasi-particle random-phase approximation (RRPA) model.
• The measured AGDR-IAS energy difference was compared to RRPA-calculated values to extract $\Delta R_{pn}$, with uncertainties propagated from both experiment and theory.
• The same theoretical framework was used to derive constraints on the symmetry energy parameters $J$ (at saturation) and $L$ (slope) by mapping the AGDR energy to the EoS.

Experimental results

Research questions

• RQ1 What is the neutron-skin thickness $\Delta R_{pn}$ of $^{208}$Pb as determined from the $\gamma$-decay of the AGDR?
• RQ2 How precisely can the AGDR-IAS energy difference constrain the symmetry energy parameters $J$ and $L$?
• RQ3 Is the AGDR method consistent with other experimental probes such as dipole polarizability ($\alpha_D$) and pygmy dipole resonances (PDR)?
• RQ4 Does the measured AGDR energy difference support a linear correlation with neutron-skin thickness as predicted by relativistic RRPA models?

Key findings

• The neutron-skin thickness of $^{208}$Pb was determined to be $\Delta R_{pn} = 0.190 \pm 0.028$ fm using the AGDR-IAS energy difference and self-consistent RRPA calculations.
• The symmetry energy at saturation density is constrained to $J = 32.7 \pm 0.6$ MeV, with a slope of $L = 49.7 \pm 4.4$ MeV.
• The AGDR-based constraints on $J$ and $L$ are more stringent than those from most previous studies, including those based on pygmy dipole resonances.
• The results show excellent agreement with recent measurements of dipole polarizability ($\alpha_D$), indicating that AGDR and $\alpha_D$ probe the same underlying symmetry energy physics.
• Discrepancies with PDR-based constraints are attributed to missing strength in PDR experiments, suggesting AGDR measurements may offer a more reliable probe.
• The linear correlation between AGDR energy and $\Delta R_{pn}$, as predicted by RRPA, is validated experimentally, confirming the method's theoretical foundation.