论文标题
使用有效的野外理论和贝叶斯方法分析奇数核中旋转带
Analyzing rotational bands in odd-mass nuclei using Effective Field Theory and Bayesian methods
论文作者
论文摘要
我们最近为奇数核核中的旋转带开发了一种有效的场理论（EFT）。 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和$ {}^{239} $ pu。我们的贝叶斯分析中的误差模型包括实验和EFT截断不确定性。这也解释了以下事实：低能量常数（LEC）均匀，奇数订单有望具有不同的尺寸。我们使用马尔可夫链蒙特卡洛（MCMC）采样来探索EFT和误差模型参数的关节后部，并可以可靠地确定LEC和扩展参数，$ Q $。我们将LEC提取到EFT中的第四阶，并发现，只要我们正确地说明了可能性的EFT截断错误，那么低阶LEC的结果是稳定的，因为我们进入了更高的订单。与添加更高能量数据相对于LEC结果也稳定。我们提取上述所有核的扩展参数，并根据单粒子和振动能量尺度找到提取的$ Q $之间的明显相关性。但是，实际上决定EFT扩展的收敛性的$ Q $明显小于根据这些量表的预期。
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.
