Correlated Energy Uncertainties in Reaction Rate Calculations

TL;DR

This paper investigates how correlated uncertainties in nuclear resonance energies influence reaction rate calculations, revealing that correlations can either amplify or diminish uncertainties depending on resonance placement relative to the Gamow peak.

Contribution

It introduces a method to evaluate the impact of correlated energy uncertainties on reaction rates using Monte Carlo simulations across multiple reactions.

Findings

Correlations can increase or decrease reaction rate uncertainties.

Resonance placement relative to the Gamow peak determines the effect of correlations.

Complex reactions with multiple resonances show unpredictable correlation effects.

Abstract

Context. Monte Carlo methods can be used to evaluate the uncertainty of a reaction rate that arises from many uncertain nuclear inputs. However, until now no attempt has been made to find the effect of correlated energy uncertainties in input resonance parameters. Aims. To investigate the impact of correlated energy uncertainties on reaction rates. Methods. Using a combination of numerical and Monte Carlo variation of resonance energies, the effect of correlations are investigated. Five reactions are considered: two fictional, illustrative cases and three reactions whose rates are of current interest. Results. The effect of correlations in resonance energies depends on the specific reaction cross section and temperatures considered. When several resonances contribute equally to a reaction rate, and are located either side of the Gamow peak, correlations between their energies dilute their effect on reaction rate uncertainties. If they are both located above or below the maximum of the Gamow peak, however, correlations between their resonance energies can increase the reaction rate uncertainties. This effect can be hard to predict for complex reactions with wide and narrow resonances contributing to the reaction rate.