Model-independent determination of the astrophysical S-factor in laser-induced fusion plasmas

TL;DR

This paper introduces a novel, model-independent method to measure the astrophysical S-factor in laser-induced fusion plasmas, applied to deuterium reactions, emphasizing precise ion energy and fusion yield measurements.

Contribution

The work presents a general approach to determine the S-factor without assumptions on plasma state, using laser-induced fusion data, applicable to various nuclear reactions.

Findings

Method yields consistent S-factor values with existing experiments within errors.

Accurate ion energy distribution measurement is crucial for reliable S-factor determination.

Differences in plasma environment may affect S-factor values compared to traditional experiments.

Abstract

In this work, we present a new and general method for measuring the astrophysical S-factor of nuclear reactions in laser-induced plasmas and we apply it to d(d,n)$^{3}$He. The experiment was performed with the Texas Petawatt laser, which delivered 150-270 fs pulses of energy ranging from 90 to 180 J to D$_{2}$ or CD$_{4}$ molecular clusters. After removing the background noise, we used the measured time-of-flight data of energetic deuterium ions to obtain their energy distribution. We derive the S-factor using the measured energy distribution of the ions, the measured volume of the fusion plasma and the measured fusion yields. This method is model-independent in the sense that no assumption on the state of the system is required, but it requires an accurate measurement of the ion energy distribution especially at high energies and of the relevant fusion yields. In the d(d,n)$^{3}$He and $^{3}$He(d,p)$^{4}$He cases discussed here, it is very important to apply the background subtraction for the energetic ions and to measure the fusion yields with high precision. While the available data on both ion distribution and fusion yields allow us to determine with good precision the S-factor in the d+d case (lower Gamow energies), for the d+$^3$He case the data are not precise enough to obtain the S-factor using this method. Our results agree with other experiments within the experimental error, even though smaller values of the S-factor were obtained. This might be due to the plasma environment differing from the beam target conditions in a conventional accelerator experiment.