Evaluated 12C(4He,4He)12C cross-section and its uncertainty

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Abstract

A revision of the evaluated differential cross-section for elastic scattering of 4He from carbon was performed. The uncertainties to the evaluated data were assigned using an algorithm based on the covariance matrix of the experimental errors.

Introduction

The cross-section evaluation consists in the elaboration of the most reliable cross-section through the critical compilation and analysis of available experimental data using an appropriate theoretical model. The evaluated cross-section for elastic scattering of 4He from carbon was reported in [1]. In the energy range under consideration (from Coulomb scattering up to ∼8 MeV) the 12C(4He,4He)12C excitation function has both relatively smooth intervals convenient for elastic backscattering analysis and strong resonances suitable for resonance profiling. The theoretical model employed in [1] treated resonances as isolated and so the effect of the resonance interference was not taken into account. Since apparent discrepancies were observed between the bulk of the experimental points and the theoretical curve in some energy intervals a revision of the evaluated 12C(4He,4He)12C cross section was undertaken, the more elaborated model proved to be adequate for a similar case [2] being used. One new set of the experimental data [3] has become available since previous evaluation and these data were also included in the revision.

As any physical quantity the evaluated cross-sections have some uncertainty. While attempting to determine this uncertainty one is faced with the problem of systematic errors inherent in the experimental data. The classical statistical theory does not consider systematic errors. It is implied that these errors should be somehow eliminated before the methods of statistics are applied. Within the framework of a separate work the systematic error cannot be revealed in principle. However, the evaluated cross-section is based on the results of several measurements and this makes it possible to determine the corresponding covariance matrix for the experimental data followed by the analysis of the errors. The respective algorithm developed in [4] is employed in the present paper to estimate the evaluated cross-section uncertainties.

Section snippets

Evaluation

The analysis of the experimental data [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18] for the 12C(4He,4He)12C cross-section was made in [1]1. The main difference in the theoretical approach of the present work from [1] is the interpretation of the resonance cross-section structure in the frameworks of the R-matrix theory instead of an isolated level approximation

Uncertainties

The whole array of the available experimental data was inspected and four energy intervals (1.7–5.5 MeV, 5.5–6.0 MeV, 6.0–7.0 MeV, 7.0–7.2 MeV) with different average relative deviation of the experimental points were revealed. At energy exceeding ∼7.2 MeV the problems remained in the evaluation of the controversial sets of the experimental data and so this part of the excitation function was excluded from the consideration. In each of the intervals numbered below by K the mean value of the relative

Discussion

The discrepancies between different data sets for the cross-section under evaluation are far beyond quoted experimental errors. Therefore it is a safe assumption that the main portion of the experimental error in the data is systematic. Generally the systematic error does not obey the normal distribution. This error is as a rule strongly correlated for the different points measured in the same experiment and the mean of the distribution of the experimental data distorted by the systematic error

Conclusion

Methodologically the way of assigning uncertainties to the evaluated cross-sections is clear and the extension of the approach presented in the present paper over all the evaluated cross-sections seems to be straightforward. However, the corresponding computations have not yet been arranged for an unattended implementation and so they cannot be immediately incorporated in the online calculator SigmaCalc [26]. Another problem is that few programs applied for the IBA spectra simulation if any at

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