Error analysis of nuclear mass fits

TL;DR

This paper analyzes the methods used for fitting nuclear mass models, highlighting differences in error analysis for accurate versus approximate models, and demonstrates the impact of weighting schemes on parameter uncertainties.

Contribution

It provides a detailed comparison of least-square and linear-regression methods for nuclear mass fits, emphasizing the importance of model accuracy and weighting in error estimation.

Findings

Standard error analysis may be inaccurate for approximate models

Mass-number dependent weights significantly affect parameter uncertainties

Explicit illustration using simple analytic models

Abstract

We discuss the least-square and linear-regression methods, which are relevant for a reliable determination of good nuclear-mass-model parameter sets and their errors. In this perspective, we define exact and inaccurate models and point out differences in using the standard error analyses for them. As an illustration, we use simple analytic models for nuclear binding energies and study the validity and errors of models' parameters, and uncertainties of its mass predictions. In particular, we show explicitly the influence of mass-number dependent weights on uncertainties of liquid-drop global parameters.