Speaker
Description
Coulomb-excitation measurements provide a direct and model-independent probe of electromagnetic matrix elements, which are essential for understanding collective motion, shape coexistence, and configuration mixing in atomic nuclei [1]. The extraction of these quantities relies on a global least-squares analysis of experimental γ-ray yields against calculated excitation probabilities, where the absolute normalization plays a critical role in determining the final matrix elements and their uncertainties. Consequently, a statistical estimation of the uncertainties in the multidimensional χ2 minimization is crucial for ensuring the reliability of nuclear-structure information obtained from such analysis.
In this context, the semiclassical coupled-channels code GOSIA is widely used for Coulomb-excitation analysis, performing a simultaneous fit of electromagnetic matrix elements and normalization parameters through minimization of a global χ2 function [2]. The normalization coefficients, which connect calculated yields to measured intensities, are strongly correlated with the fitted matrix elements. As a result, their uncertainties propagate non-trivially into the extracted physical observables. In the typical GOSIA approach, parameter uncertainties are obtained from the linearization of the χ2 surface around its minimum using the Δχ2 criterion. However, this procedure relies on several internal approximations in the treatment of normalization, which may influence the estimated uncertainties and parameter correlations. Additionally more and more often in the analysis of Coulomb excitation of exotic nuclei with a modified version of the code GOSIA2, a manual two-dimensional error estimation is performed as it was described by Zielińska et al. [3].
In this work, we present a Monte Carlo (MC) based study of the χ2 normalization error estimation in GOSIA. Starting from a set of a priori electromagnetic matrix elements, ensembles of synthetic experimental yields are generated using MC method by incorporating realistic statistical fluctuations [4]. These pseudo-data sets are then analyzed using the standard GOSIA framework, allowing the propagation of statistical uncertainties through the full fitting procedure to be examined. By comparing the distribution of fitted parameters with the nominal Δχ2-based uncertainties, we assess the impact of approximations in the normalization treatment and quantify their effect on extracted matrix elements.
The present study provides insight into the robustness of the current error-estimation methodology and highlights potential limitations in the treatment of normalization within GOSIA. In particular, the MC approach offers a systematic framework for benchmarking the statistical reliability of Coulomb-excitation analysis and for investigating possible improvements to the normalization procedure and uncertainty evaluation. The results of this study will be presented and discussed in the context of their impact on the extraction of electromagnetic matrix elements.
References:
[1] K. Alder, A. Bohr, T. Huus, B. Mottelson, and A. Winther, Rev. Mod. Phys. 28, 432 (1956).
[2] T. Czosnyka, D. Cline, and C. Wu, Bull. Am. Phys. Soc. 28, 745 (1982).
[3] M. Zielińska et al., Eur. Phys. J. A 52, 99 (2016).
[4] Siegmund Brandt, Data Analysis - Statistical and Computational Methods for Scientists and Engineers, 4th ed., Springer (2014).