Speaker
Description
The structure of the excited states in $^{12}$C plays a fundamental role in both nuclear structure and nuclear astrophysics, particularly in modeling stellar nucleosynthesis and understanding the production of $^{12}$ C through the triple-alpha process. Of particular interest is the Hoyle state [1] confirmed experimentally as the $^{12}{\rm C} (0^+_2 , 7.65{\rm MeV})$ [2] and its proposed rotational excitations, which exhibit pronounced $\alpha$-cluster configurations. Subsequent studies and experimental work have confirmed the existence of a rotational excitation band built on the Hoyle state, well above the $3\alpha$ decay threshold ($S_{3\alpha} = 7.36 {\rm MeV}$) referred to as high-lying excited states ($2^+_2 , {\rm 9.6 MeV}, 4^+_1 , {\rm 13.3 MeV}$) of the Hoyle state. The $2^+_2$ and $4^+_1$ states are considered the first and second excitation of the Hoyle state as a rotational band of $\alpha$-clusters, while the $3^−_1$ state (negative parity) constitutes a triangular set of vibrating $\alpha$-clusters. Since the direct synthesis of $^{12}$C from $3\alpha$ particles is improbable in a laboratory setting due to the transient nature of intermediate states, a selective high-precision experimental set-up is essential to probe the nuclear structure of $^{12}$C in detail. This study aims to investigate $\alpha$-cluster states in $^{12}$C through a selective $\alpha$-transfer $^9{\rm Be}(^6{\rm Li}, t)^{12}{\rm C}$ reaction using the C-Line Tandem accelerator at iThemba LABS (Gauteng). This reaction, proceeding through a direct $\alpha$-transfer ($^6{\rm Li}\to\alpha+d$), will preferentially populate states in $^{12}$C with a strong α-cluster sub-structure such as the Hoyle state and its rotational excitation band, rather than states characterised by a pure shell-model configuration.
Furthermore, since $^9{\rm Be}$ is itself a weakly bound, deformed cluster nucleus ($2\alpha+n$), the use of a $^6{\rm Li}$ beam at energies near the Coulomb barrier is expected to enhance the population of high-lying cluster states in $^{12}$C through favourable spectroscopic overlap between the cluster like configurations of the target and the final states. A high-resolution $\Delta E-E$ gas ionisation detector will be utilised to measure the reaction products from a beam of $^6{\rm Li}$ ions at $E_{Lab} = 20$\,MeV incident on a thin $^9{\rm Be}$
target at forward scattering angles from $\theta_{Lab} = 15^\circ$ in steps of $10^\circ$ up to $\theta_{lab} = 45^\circ$. The reaction channel of the outgoing triton will be isolated and the excitation energy spectrum of the excited $^{12}$C reconstructed from standard kinematic equations.
The strengths of the populated states in $^{12}$C , including the Hoyle state ($0^+_2$ ) , and its rotational excitation band ($2^+_2$ , $4^+_1$ ) will be extracted from the measured excitation energy spectrum, and compared with strengths measured previously in the $^{10}{\rm B}(^6{\rm Li},\alpha)^{12}{\rm C}$ reaction [3]. Continuous Wavelet Transform (CWT) analysis will be used to improve the identification and characterisation of weak, broad, or overlapping resonant structures. The extracted excitation energies, widths and population strengths will also be compared with predictions from Antisymmetrised Molecular Dynamics (AMD) [4] calculations to assess the degree of $\alpha$-clustering in $^{12}$C, and establish connections between experimentally observed states and theoretical cluster configurations. These measurements will provide an independent assessment of states previously observed in the $^{10}{\rm B}(^6{\rm Li},\alpha)^{12}{\rm C}$ reaction and contribute to resolving uncertainties concerning the Hoyle-state rotational band, including the reported narrow width of the $4^+_1$ resonance [3]. The results are expected to provide new constraints on cluster-model descriptions of $^{12}$C, improve our understanding of clustering phenomena in light nuclei, and contribute to more reliable models of stellar nucleosynthesis.
References
[1] Fred Hoyle. On Nuclear Reactions Occuring in Very Hot STARS. I. the Synthesis of Elements from Carbon to Nickel.
Astrophysical Journal Supplement, vol. 1, p. 121 (1954) 1, 121 (1954).
[2] Charles W Cook, William A Fowler, Charles C Lauritsen, and Thomas Lauritsen. B 12, C 12, and the Red Giants.
Physical Review 107, 508 (1957).
[3] John Carter et al. “Investigation of the Alpha-Cluster Continuum Structure of 12C using ContinuousWavelet Transform
Analysis”. Proceedings of the 69th Annual Conference of the South African Institute of Physics (SAIP 2025). South Africa,
2025.
[4] Yoshiko Kanada-En’yo. The structure of ground and excited states of 12C. Progress of Theoretical Physics 117, 655–680
(2007).