[Paper Review] Elastic scattering of 3He+4He with SONIK

S. N. Paneru, C. R. Brune+23 more|arXiv (Cornell University)|Nov 26, 2022

Spacecraft and Cryogenic Technologies4 citations

TL;DR

This study presents the first low-energy elastic scattering measurement of 3He+4He below 500 keV using the SONIK inverse kinematics setup at TRIUMF, achieving higher angular coverage and precision than prior experiments. Using R-matrix and Halo EFT frameworks with full uncertainty propagation, it extracts s-wave scattering length and effective range, reducing uncertainty in the astrophysical S-factor S34(0) for solar neutrino production and Big Bang nucleosynthesis.

ABSTRACT

Measurements of the elastic scattering cross section of 3He and 4He are important in order to improve constraints on theoretical models of 4He(3He,g)7Be, a key reaction in Big Bang nucleosynthesis and solar neutrino production. The astrophysical S-factor for this reaction is a significant source of uncertainty in the standard solar-model prediction of the 7Be and 8B solar neutrino fluxes. The elastic scattering measurements reported in the literature do not extend to low energies and lack proper uncertainty quantification. A new measurement of the 4He(3He,3He)4He reaction has been made at center-of-mass energies Ec.m. = 0.38-3.13 MeV using the Scattering of Nuclei in Inverse Kinematics (SONIK) scattering chamber: a windowless, extended gas target surrounded by an array of 30 collimated silicon charged particle detectors situated at TRIUMF. This is the first elastic scattering measurement of 3He+4He made below 500 keV and it has greater angular range and better precision than previous measurements. The elastic scattering data were analyzed using both R-matrix and Halo Effective Field Theory (Halo EFT) frameworks, and values of the s-wave scattering length and effective range were extracted. The resulting improvement in knowledge of the s-wave effective-range function at low energies will reduce the overall uncertainty in S34 at solar energies.

Motivation & Objective

• To measure the elastic scattering cross section of 3He+4He at center-of-mass energies from 0.38 to 3.13 MeV, extending previous measurements to lower energies.
• To reduce the uncertainty in the astrophysical S-factor S34(0) for the 4He(3He,γ)7Be reaction, a key input for solar neutrino flux predictions.
• To extract precise s-wave scattering parameters (scattering length a0 and effective range r0) using both R-matrix and Halo Effective Field Theory (Halo EFT) frameworks.
• To resolve discrepancies between theoretical models and experimental data by providing a high-precision dataset with full uncertainty quantification.
• To enable improved global fits of 4He(3He,γ)7Be data, reducing extrapolation errors in standard solar model predictions.

Proposed method

• Employed the Scattering of Nuclei in Inverse Kinematics (SONIK) chamber at TRIUMF, featuring a windowless, extended gas target and 30 collimated silicon detectors.
• Conducted measurements in inverse kinematics using a 3He beam on a 4He gas target at E_c.m. = 0.38–3.13 MeV, achieving high angular resolution and low background.
• Analyzed data using the R-matrix formalism to extract s-wave scattering parameters with full propagation of statistical and systematic uncertainties.
• Applied Halo EFT at next-to-next-to-leading order (NNLO) to the same dataset, incorporating model uncertainties and testing EFT breakdown at higher energies.
• Combined SONIK data with existing Barnard scattering data to improve constraints on phase shifts and effective range functions.
• Performed χ² comparisons between R-matrix and Halo EFT fits to assess model consistency, especially near the 7/2− resonance.

Experimental results

Research questions

• RQ1 What is the precise s-wave scattering length and effective range for 3He+4He at low center-of-mass energies below 500 keV?
• RQ2 How do R-matrix and Halo EFT analyses compare in describing the elastic scattering data, and what accounts for their differing results?
• RQ3 To what extent does the description of the 5/2− and 7/2− resonances affect the inferred low-energy scattering parameters?
• RQ4 Can the discrepancy in s-wave scattering length between R-matrix and Halo EFT be resolved by focusing on low-energy data alone?
• RQ5 How does the inclusion of this new high-precision dataset improve the uncertainty in the astrophysical S-factor S34(0) for solar neutrino production?

Key findings

• This is the first experimental measurement of 3He+4He elastic scattering below 500 keV, extending the energy reach of prior studies.
• The R-matrix analysis yields a s-wave scattering length of a0 = 33.10 ± 0.13 (stat) +7.5/-3.0 (analysis) fm, with full uncertainty propagation.
• The Halo EFT analysis at NNLO yields a0 = 42 ± 1 fm, showing a significant discrepancy with the R-matrix result.
• The two models agree on phase shifts over most of the energy range, but diverge at higher energies (E_c.m. > 2 MeV), where R-matrix better describes data from Spiger and Tombrello (1967).
• The EFT fit shows a large χ² at E_c.m. > 2 MeV despite inclusion of theoretical error components, indicating breakdown in EFT description at backward angles.
• The inferred s-wave parameters are highly sensitive to the description of the 5/2− phase shift and the width of the 5/2− level, suggesting a need for improved modeling of these states.