Neutron-upscattering enhancement of the triple-alpha process

Abstract

The neutron inelastic scattering of carbon-12, populating the Hoyle state, is a reaction of interest for the triple-alpha process. The inverse process (neutron upscattering) can enhance the Hoyle state's decay rate to the bound states of ¹²C, effectively increasing the overall triple-alpha reaction rate. The cross section of this reaction is impossible to measure experimentally but has been determined here at astrophysically-relevant energies using detailed balance. Using a highly-collimated monoenergetic beam, here we measure neutrons incident on the Texas Active Target Time Projection Chamber (TexAT TPC) filled with CO₂ gas, we measure the 3α-particles (arising from the decay of the Hoyle state following inelastic scattering) and a cross section is extracted. Here we show the neutron-upscattering enhancement is observed to be much smaller than previously expected. The importance of the neutron-upscattering enhancement may therefore not be significant aside from in very particular astrophysical sites (e.g. neutron star mergers).

Fig. 1. Overview schematic diagram.

This details the steps involved in the triple-alpha process, showing the contribution of neutron upscattering to the decay width to bound states. A low-energy neutron interacts with the Hoyle state leaving carbon-12 in the ground-state (or first-excited state) and the extra energy is carried away with the neutron.

Fig. 2. Cross sections as a function of neutron energy for channels of interest.

a ¹²C(n, n₂)3α cross section (blue error bars) measured across the energy range of astrophysical interest with the Hauser-Feshbach (HF) predictions from ref.  overlaid in dashed magenta. The ¹²C(n, α₀) cross section, scaled by a factor of 0.1 is overlaid with green triangles with data from ref.  (Table III) to show the similarity in form with the experimental data from this work. The cross section below the threshold was determined to be < 0.25 mb at the 95% C.L. where zero Hoyle events were observed. b ${}^{12}\mathrm{C}{\left(n,{\alpha }_{1,2}\right)}^9{\mathrm{Be}}^{\star }$ cross section with the two thresholds for the centroid of the ⁹Be^⋆ states marked by solid red lines. The lowest two energy points had zero observed events so the upper limit at the 95% C.L. is shown. For both plots, the x-axis error bars represent the total width of the neutron energy spectrum rather than its standard deviation due to the non-Gaussian nature of the beam energy profile. The y-axis shows purely statistical error bars at the 1σ level.

Fig. 3. Enhancement of the Hoyle radiative-width via neutron upscattering as a function of temperature.

Contributions from upscattering to the ¹²C ground state (green dashed) and to the ¹²C first-excited state (black solid). The sum of these is shown in dotted blue for a neutron density of 10⁶ g cm⁻³. The comparable contribution from protons as calculated in ref.  is shown by the dot-dashed red line.

Fig. 4. Incident neutron energy spectrum.

The spectrum is shown from the NE-213 detector placed at 30 m with a pulsed beam (magenta points) with corrections for the interaction location within the gas cell applied. The neutron energy spectrum from the 7.98-cm gas cell as predicted by GEANT4 is overlaid (solid blue line) and normalised to reproduce the amplitude of the flat region between 8.2 and 8.36 MeV. Error bars correspond to a statistical uncertainty of 1σ.