Abstract We treat low-energy 3 He– α elastic scattering in an effective field theory (EFT) that exploits the separation of scales in this reaction. We compute the amplitude up to next-to-next-to-leading order, developing a hierarchy of the effective-range parameters (ERPs) that contribute at various orders. We use the resulting formalism to analyse data for recent measurements at center-of-mass energies of 0.38–3.12 MeV using the scattering of nuclei in inverse kinematics (SONIK) gas target at TRIUMF as well as older data in this energy regime. We employ a likelihood function that incorporates the theoretical uncertainty due to truncation of the EFT and use Markov chain Monte Carlo sampling to obtain the resulting posterior probability distribution. We find that the inclusion of a small amount of data on the analysing power A y is crucial to determine the sign of the p-wave splitting in such an analysis. The combination of A y and SONIK data constrains all ERPs up to O ( p 4 ) in both s- and p-waves quite well. The asymptotic normalisation coefficients and s-wave scattering length are consistent with a recent EFT analysis of the capture reaction 3 He( α , γ ) 7 Be.
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This content will become publicly available on December 17, 2025
Variational inference of effective range parameters for 3 He− 4 He scattering
Abstract We use two different methods, Monte Carlo sampling and variational inference (VI), to perform a Bayesian calibration of the effective-range parameters in3He–4He elastic scattering. The parameters are calibrated to data from a recent set of3He–4He elastic scattering differential cross section measurements. Analysis of these data forElab≤ 4.3 MeV yields a unimodal posterior for which both methods obtain the same structure. However, the effective-range expansion amplitude does not account for the 7/2−state of7Be so, even after calibration, the description of data at the upper end of this energy range is poor. The data up toElab = 2.6 MeV can be well described, but calibration to this lower-energy subset of the data yields a bimodal posterior. After adapting VI to treat such a multi-modal posterior we find good agreement between the VI results and those obtained with parallel-tempered Monte Carlo sampling.
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- Award ID(s):
- 2004601
- PAR ID:
- 10606734
- Publisher / Repository:
- Institute of Physics, UK
- Date Published:
- Journal Name:
- Journal of Physics G: Nuclear and Particle Physics
- Volume:
- 52
- Issue:
- 1
- ISSN:
- 0954-3899
- Page Range / eLocation ID:
- 015109
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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