Best linear unbiased estimation of the nuclear masses

This paper presents methods to provide an optimal evaluation of the nuclear masses. The techniques used for this purpose come from data assimilation that allows combining, in an optimal and consistent way, information coming from experiment and from numerical model. Using all the available information, it leads to improve not only masses evaluations, but also to decrease uncertainties. Each newly evaluated mass value is associated with some accuracy that is sensibly reduced with respect to the values given in tables, especially in the case of the less well-known masses. In this paper, we first introduce a useful tool of data assimilation, the Best Linear Unbiased Estimation (BLUE). This BLUE method is applied to nuclear mass tables and some results of improvement are shown.

💡 Research Summary

The paper introduces a data‑assimilation framework based on the Best Linear Unbiased Estimator (BLUE) to produce optimal evaluations of nuclear masses by jointly exploiting experimental measurements and theoretical model predictions. Traditional nuclear mass evaluations treat experimental data and model outputs separately, which leads to inconsistencies and relatively large uncertainties, especially for nuclei far from stability where measurements are scarce. BLUE offers a mathematically rigorous solution: it combines a prior estimate (theoretical mass model) with observations (experimental masses) through a linear, unbiased weighting that minimizes the posterior variance.

The authors first formulate the problem in the standard linear observation model y = H x + ε, where x is the vector of prior mass values supplied by a chosen nuclear mass model (e.g., Finite‑Range Droplet Model, HFB‑21), y is the vector of measured masses from the latest Atomic Mass Evaluation (AME2020), H is the observation operator (essentially the identity matrix for direct mass measurements), and ε represents measurement noise. Two covariance matrices are required: B, the prior error covariance that quantifies uncertainties and correlations inherent to the theoretical model, and R, the observation error covariance derived from reported experimental uncertainties. The authors construct B by analysing residuals of the chosen model against the full experimental database, fitting a distance‑dependent correlation function of the form exp