Analyzing rotational bands in odd-mass nuclei using Effective Field Theory and Bayesian methods

TL;DR

This paper applies an Effective Field Theory combined with Bayesian analysis to study rotational energy levels in various odd-mass nuclei, providing reliable LECs and insights into EFT convergence.

Contribution

It introduces a Bayesian framework with EFT for analyzing nuclear rotational bands, accounting for uncertainties and extracting low-energy constants up to fourth order.

Findings

LECs are stable across orders and data sets.

The EFT expansion parameter Q is smaller than expected.

Reliable extraction of LECs and Q from nuclear data.

Abstract

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 expansion parameter, $Q$, 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 $Q$ based on the single-particle and vibrational energy scales. However, the $Q$ that actually determines the convergence of the EFT expansion is markedly smaller than would be naively expected based on those scales.