Wigner SU(4) symmetry, clustering, and the spectrum of $$^{12}$$C

We present lattice calculations of the low-lying spectrum of $$^{12}$$ 12 C using a simple nucleon–nucleon interaction that is independent of spin and isospin and therefore invariant under Wigner’s SU(4) symmetry. We find strong signals for all excited states up to $$\sim 15$$ ∼ 15 MeV above the ground state, and explore the structure of each state using a large variety of $$\alpha $$ α cluster and harmonic oscillator trial states, projected onto given irreducible representations of the cubic group. We are able to verify earlier findings for the $$\alpha $$ α clustering in the Hoyle state and the second $$2^+$$ 2 + state of $$^{12}$$ 12 C. The success of these calculations to describe the full low-lying energy spectrum using spin-independent interactions suggest that either the spin-orbit interactions are somewhat weak in the $$^{12}$$ 12 C system, or the effects of $$\alpha $$ α clustering are diminishing their influence. This is in agreement with previous findings from ab initio shell model calculations.

Coulomb screening correction to the Q value of the triple-alpha process in thermal plasmas

The triple-alpha reaction is key to $^{12}$C production and is expected to occur in weakly coupled thermal plasmas as encountered in normal stars. We investigate how Coulomb screening affects the structure of a system of three alpha particles in such a plasma environment by precise three-body calculations within the Debye–Hückel approximation. A three-alpha model that has the Coulomb interaction modified in the Yukawa form is employed. Precise three-body wave functions are obtained by a superposition of correlated Gaussian basis with the aid of the stochastic variational method. The energy shifts of the Hoyle state due to the Coulomb screening are obtained as a function of the Debye screening length. The results, which automatically incorporate the finite-size effect of the Hoyle state, are consistent with the conventional result based on the Coulomb correction to the chemical potentials of ions that are regarded as point charges in a weakly coupled thermal plasma. We have given a theoretical basis to the conventional point-charge approach to the Coulomb screening problem relevant for nuclear reactions in normal stars by providing the first evaluation of the Coulomb corrections to the $Q$ value of the triple-alpha process that produces a finite-size Hoyle state.

The Hoyle Family: break-up measurements to probe α-condensation in light nuclei

The ^{12}12C Hoyle state is a candidate for \alphaα-condensation, due to its large volume and \alphaα-cluster structure. This paper discusses precision break-up measurements and how they can elucidate \alphaα-condensate structures. Two experiments are discussed in detail, firstly concerning the break-up of ^{12}12C and then the decays of heavier nuclei. With more theoretical input, and increasingly complex detector setups, precision break-up measurements can, in principle, provide insight into the structures of states in \alphaα-conjugate nuclei. At present, such searches have not delivered evidence for \alphaα-condensation in ^{12}12C or ^{16}16O.