Theoretical approaches to the 3α break-up of ¹²C

Abstract

Two recent experiments have indicated that the break-up of the 12C Hoyle state is dominated by the sequential 8Be(g.s.) + α decay channel. The rare direct 3α decay was found to contribute with a branching ratio of less than 0.047% (95% C.L.). However, the ability of experimentalists to successfully disentangle these two competing decay channels relies on accurate theoretical predictions of how they each manifest in phase space distribution of the three break-up α-particles. The following paper reviews the current theoretical approaches to calculating the break-up of the Hoyle state and introduces a semi-classical WKB approach, which adequately reproduces the results of more sophisticated calculations. It is proposed that a more accurate upper limit on this branching ratio may be obtained if these new theoretical results are taken into account when analysing experimental data.

The Hoyle Family: The Search for Alpha-Condensate States in Light Nuclei

“…However, in their paper, they only consider DDE-type decays because "We expect a change less than a factor of 2 [by] adding more configurations". In contrast to this, the 3α phase space distributions calculated in references [49] and [51] demonstrate a large dependence of the barrier transmission probability on the relative energies/orientations of the three α-particles. Furthermore, the Coulomb interaction chosen by Zheng et al was modified to reflect the potential energy of two overlapping, uniformly charged spheres, parameterised for a 2-body decay as…”

“…This type of decay corresponds to points on the outer edge of the Dalitz plot. A final model, developed in references [35] and [51], is called DDP 2 (Direct Decay Phase space + Penetrability). This model accounts for the changing 3α decay penetrability depending on the relative energies and directions of the α-particles as they tunnel from the nucleus.…”

“…A simple approach to theoretically determining the BR is to evaluate the relative sequential and direct decay widths using tunnelling calculations. References [35] and [51] present WKB calculations for the 2-body and 3-body decays, which calculate the BR to be around 0.06%. This is higher than the current experimental upper limit.…”

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

“…This type of decay corresponds to points on the outer edge of the Dalitz plot. A final model, developed in references [16] and [28], is called DDP 2 (Direct Decay Phase space + Penetrability). This model accounts for the changing 3α decay penetrability depending on the relative energies and directions of the α-particles as they tunnel from the nucleus.…”

Report on scipost_201911_00026v1

“…In the 12 C( 16 O, 28 Si ) study [36], to overcome the limitations of the 4α penetrability, populating this state in the 12 C( 16 O, 12 C(0 + 2 )) 16 O reaction was attempted, by reconstruct- ing the 16 O from measuring the 12 C(0 + 2 ). From the compound nucleus, if one decay product ( 12 C(0 + 2 )) is produced which is heavily clustered, one would expect the other decay product to also be preferentially populated by heavily-clustered states.…”