Proton Spectra from ${}^3\mathrm{He}+\mathrm{T}$ and ${}^3\mathrm{He}+{}^3\mathrm{He}$ Fusion at Low Center-of-Mass Energy, with Potential Implications for Solar Fusion Cross Sections

Few-body nuclear physics often relies upon phenomenological models, with new efforts at the ab initio theory reported recently; both need high-quality benchmark data, particularly at low center-of-mass energies. We use high-energy-density plasmas to measure the proton spectra from ${}^3\mathrm{He}+\mathrm{T}$ and ${}^3\mathrm{He}+{}^3\mathrm{He}$ fusion. The data disagree with $R$-matrix predictions constrained by neutron spectra from $\mathrm{T}+\mathrm{T}$ fusion. We present a new analysis of the ${}^3\mathrm{He}+{}^3\mathrm{He}$ proton spectrum; these benchmarked spectral shapes should be used for interpreting low-resolution data, such as solar fusion cross-section measurements.

Figure 1

Experimental schematic. Left: A capsule containing fuel is illuminated by the 60 OMEGA laser beams. Right: The capsules used in this experiment were thin-glass microballoons filled with a mixture of ${\mathrm{T}}_2$ and ${}^3\mathrm{He}$ or pure ${}^3\mathrm{He}$.

Figure 2

Top row: $R$-matrix calculations of the total proton spectrum and components for ${}^3\mathrm{He}+{}^3\mathrm{He}$ (a) and ${}^3\mathrm{He}+\mathrm{T}$ (b). Bottom row: Comparison of the calculated $R$-matrix spectrum to the data for ${}^3\mathrm{He}+{}^3\mathrm{He}$ (c) and ${}^3\mathrm{He}+\mathrm{T}$ (d). Dashed curves are using feeding factors from the Wong, Anderson, and McClure data, and solid curves are from the fit to our data.

Figure 3

Second $R$-matrix calculation for ${}^3\mathrm{He}+{}^3\mathrm{He}$ (model 2) constrained using lower-energy TT data. (a) Comparison of the total spectrum (area normalized). (b) Comparison of each model to the data. For each model, the dashed curve is as predicted using $\mathrm{T}+\mathrm{T}$ data in the literature, and the solid curve is the best fit to our data.