Excited states in certain atomic nuclei possess an unusual structure, where the dominant degrees of freedom are those of $\alpha$ clusters rather than individual nucleons. It has been proposed that the diffuse $3\alpha$ system of the ${}^{12}\mathrm{C}$ Hoyle state may behave like a Bose-Einstein condensate, where the $\alpha$ clusters maintain their bosonic identities. By measuring the decay of the Hoyle state into three $\alpha$ particles, we obtained an upper limit for the rare direct $3\alpha$ decay branch of 0.047%. This value is now at a level comparable with theoretical predictions and could be a sensitive probe of the structure of this state.

We investigate an implication of the most recent observation of a second $J^{\pi }=2^{+}$ state in ${}^{12}\mathrm{C}$, which was measured using the ${}^{12}\mathrm{C}(\gamma ,\alpha ){}^8\mathrm{Be}_{(\mathrm{g}.\mathrm{s}.)}$ reaction. In addition to the dissociation of ${}^{12}\mathrm{C}$ to an $\alpha$-particle and ${}^8\mathrm{Be}$ in its ground state, a small fraction of events (2%) were identified as direct decays and decays to excited states in ${}^8\mathrm{Be}$. This allowed a limit on the direct $3\alpha$ partial decay width to be determined as ${\mathrm{\Gamma }}_{3\alpha }<32\left(4\right)$ keV. Since this $2^{+}$ state is predicted by all theoretical models to be a collective excitation of the Hoyle state, the $3\alpha$ partial width of the Hoyle state is calculable from the ratio of $3\alpha$ decay penetrabilities of the Hoyle and $2^{+}$ states. This was calculated by using the semiclassical Wenzel-Kramers-Brillouin approach and we deduce a stringent upper limit for the direct decay branching ratio of the Hoyle state of $\frac{{\mathrm{\Gamma }}_{3\alpha }}{\mathrm{\Gamma }}<5.7\times {10}^{-6}$, over an order of magnitude lower than previously reported. This result places the direct measurement of this rare decay mode beyond current experimental capabilities.

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).

The carbon/oxygen (C/O) ratio at the end of stellar helium burning is the single most important nuclear input to stellar evolution theory. However, it is not known with sufficient accuracy, due to large uncertainties in the cross-section for the fusion of helium with ¹²C to form ¹⁶O, denoted as ¹²C(α, γ)¹⁶O. Here we present results based on a method that is significantly different from the experimental efforts of the past four decades. With data measured inside one detector and with vanishingly small background, angular distributions of the ¹²C(α, γ)¹⁶O reaction were obtained by measuring the inverse ¹⁶O(γ, α)¹²C reaction with gamma-beams and a Time Projection Chamber (TPC) detector. We agree with current world data for the total reaction cross-section and further evidence the strength of our method with accurate angular distributions measured over the 1⁻ resonance at E_cm ~ 2.4 MeV. Our technique promises to yield results that will surpass the quality of the currently available data.

A novel experimental analysis method has been developed, making use of the continuous wavelet transform and machine learning to rapidly identify $$\alpha $$α -clustering in nuclei in regions of high nuclear state density. This technique was applied to resonant scattering measurements of the $$^\text {4}$$4 He( $$^\text {40,44,48}$$40,44,48 Ca, $$\alpha $$α ) resonant reactions, allowing the $$\alpha $$α -cluster structure of $$^\text {44,48,52}$$44,48,52 Ti to be investigated. Fragmented $$\alpha $$α -clustering was identified in $$^\text {44}$$44 Ti and $$^\text {52}$$52 Ti, while the results for $$^\text {48}$$48 Ti were less conclusive, but suggest no such clustering.