[Paper Review] Resonance Contribution to Radiative Neutron Capture on Lithium-7

Lakma Fernando, R. Higa+1 more|Data Archiving and Networked Services (DANS)|Sep 9, 2011

Nuclear physics research studies3 citations

TL;DR

This paper uses halo effective field theory to model radiative neutron capture on $^7$Li, incorporating the $3^+$ resonance and electromagnetic currents. It finds that a resonance width three times larger than the experimental value is required for consistency, highlighting limitations in current data and the need for improved constraints in astrophysical reaction rate extrapolations.

ABSTRACT

Using halo effective field theory, we provide a model-independent calculation of the radiative neutron capture on lithium-7 over an energy range where the contribution from the 3+ resonance becomes important. One finds that a satisfactory description of the capture reaction, in the present single-particle approximation, suggests the use of a resonance width about three times larger than the experimental value. We also present power counting arguments that establish a hierarchy for electromagnetic one- and two-body currents.

Motivation & Objective

• To provide a model-independent description of radiative neutron capture on $^7$Li using halo effective field theory.
• To include the contribution of the $3^+$ resonance at ~0.22 MeV, which becomes significant at low energies.
• To improve constraints on the $p$-wave effective range and resonance width by incorporating two-body electromagnetic currents.
• To establish a power counting scheme for electromagnetic currents in the EFT framework for halo nuclei.
• To benchmark the $^7$Li(n,γ)$^8$Li reaction as a mirror system to $^7$Be(p,γ)$^8$B for solar neutrino physics.

Proposed method

• Employ halo effective field theory (EFT) with neutron and $^7$Li core as degrees of freedom, treating the system as a single-particle approximation.
• Construct EFT Lagrangians for $s$- and $p$-wave elastic scattering and radiative capture, including one- and two-body electromagnetic currents.
• Use power counting to organize contributions by order in the expansion parameter $Q/\Lambda$, ensuring systematic uncertainty control.
• Derive projector operators for $^3P_1$, $^3P_2$, $^5P_1$, $^5P_2$, and $^5P_3$ partial waves using tensor structures $R_{ijlm}$, $T_{ijklm}$, and $G_{ijklmq}$.
• Implement photon polarization sums and gauge-invariant current operators to preserve symmetry constraints.
• Solve the Schrödinger equation with a Woods-Saxon potential and match to EFT amplitudes, including resonance width as a free parameter.

Experimental results

Research questions

• RQ1 How does the inclusion of the $3^+$ resonance affect the radiative neutron capture cross section on $^7$Li at low energies?
• RQ2 What is the required resonance width for the $^8$Li $3^+$ state to reproduce the observed capture rate in the halo EFT framework?
• RQ3 How do one- and two-body electromagnetic currents contribute to the radiative capture amplitude, and what is their power-counting hierarchy?
• RQ4 Can the $^7$Li(n,γ)$^8$Li reaction serve as a reliable mirror system for constraining $^7$Be(p,γ)$^8$B in solar neutrino models?
• RQ5 What are the dominant sources of uncertainty in the EFT description of this reaction, and how do they compare to potential model calculations?

Key findings

• The inclusion of the $3^+$ resonance significantly improves the description of the radiative neutron capture cross section on $^7$Li at low energies.
• A resonance width approximately three times larger than the experimental value is required to achieve a satisfactory fit to the data in the single-particle EFT framework.
• The power counting analysis shows a clear hierarchy: one-body currents dominate over two-body currents, with the latter suppressed by $Q/\Lambda$.
• The $p$-wave effective range remains the leading source of uncertainty in the capture cross section, even with resonance and EM current inclusion.
• The model-independent EFT approach successfully incorporates gauge invariance and symmetry constraints, validating its use for low-energy astrophysical reactions.
• The results suggest that current experimental data on the $^7$Li(n,γ)$^8$Li reaction may be inconsistent with the measured resonance width unless higher-order effects or three-body dynamics are included.