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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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Analyzing rotational bands in odd-mass nuclei using effective field theory and Bayesian methods
We recently developed an Effective Field Theory (EFT) for rotational bands in odd-mass nuclei. Here we use EFT expressions to perform a Bayesian analysis of data on the rotational energy levels of 99 Tc, 155,157 Gd, 159 Dy, 167,169 Er, 167,169 Tm, 183 W, 235 U and 239 Pu. The error model in our Bayesian analysis includes both experimental and EFT truncation uncertainties. It also accounts for the fact that low-energy constants (LECs) at even and odd orders are expected to have different sizes. We use Markov Chain Monte Carlo (MCMC) sampling to explore the joint posterior of the EFT and error-model parameters and show both the LECs and the breakdown scale can be reliably determined. We extract the LECs up to fourth order in the EFT and find that, provided we correctly account for EFT truncation errors in our likelihood, results for lower-order LECs are stable as we go to higher orders. LEC results are also stable with respect to the addition of higher-energy data. We extract the expansion parameter for all the nuclei listed above and find a clear correlation between the extracted and the expected value of the inverse breakdown scale, W , based on the single-particle and vibrational energy scales. However, the W that actually determines the convergence of the EFT expansion is markedly smaller than would be naively expected based on those scales.
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- Award ID(s):
- 2004601
- PAR ID:
- 10432246
- Date Published:
- Journal Name:
- Frontiers in Physics
- Volume:
- 10
- ISSN:
- 2296-424X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fphy.2022.901954
