Absolute hydrogen depth profiling using the resonant $^{1}$H($^{15}$N,$\alpha\gamma$)$^{12}$C nuclear reaction

TL;DR

This paper improves hydrogen depth profiling by re-measuring key nuclear reaction data, enabling standard-less, absolute hydrogen quantification in materials with practical formulas and real-world examples.

Contribution

It provides new measurements of angular distribution coefficients and resonance strength for the $^{1}$H($^{15}$N,$eta ext{-} ext{gamma}$)$^{12}$C reaction, enhancing hydrogen profiling accuracy.

Findings

Re-measured gamma-ray angular distribution coefficients.

Re-evaluated resonance strength to 25.0±1.5 eV.

Provided a practical formula for hydrogen concentration calculation.

Abstract

Resonant nuclear reactions are a powerful tool for the determination of the amount and profile of hydrogen in thin layers of material. Usually, this tool requires the use of a standard of well-known composition. The present work, by contrast, deals with standard-less hydrogen depth profiling. This approach requires precise nuclear data, e.g. on the widely used $^{1}$H($^{15}$N,$\alpha\gamma$)$^{12}$C reaction, resonant at 6.4\,MeV $^{15}$N beam energy. Here, the strongly anisotropic angular distribution of the emitted $\gamma$-rays from this resonance has been re-measured, resolving a previous discrepancy. Coefficients of (0.38$\pm$0.04) and (0.80$\pm$0.04) have been deduced for the second and fourth order Legendre polynomials, respectively. In addition, the resonance strength has been re-evaluated to (25.0$\pm$1.5)\,eV, 10\% higher than previously reported. A simple working formula for the hydrogen concentration is given for cases with known $\gamma$-ray detection efficiency. Finally, the absolute approach is illustrated using two examples.