[Paper Review] Comments on the ${}^{12}{ m C}$-${}^{12}{ m C}$ fusion S*-factor

A. M. Mukhamedzhanov, Xiaodong Tang+1 more|arXiv (Cornell University)|Jun 15, 2018

Superconducting Materials and Applications3 citations

TL;DR

This paper challenges the astrophysical S*-factor for $^{12}$C-$^{12}$C fusion reported in a 2018 Nature study using the indirect Trojan Horse Method (THM). It argues that the original analysis is flawed due to incorrect use of the plane-wave approximation, improper normalization to direct data, and invalid R-matrix resonance assignments. The authors demonstrate that including Coulomb effects via a three-body theory and correcting data normalization lead to a significantly reduced S*-factor, rejecting the reported 1000-fold increase in reaction rate at T9 = 0.2.

ABSTRACT

The goal of this Comment is to draw attention of the readers that the results in the published letter [A Tumino {et al,}, Nature {\bf 557}, 687 (2018)] regarding ${}^{12}{ m C}-{}^{12}{ m C}$ fusion are not correct

Motivation & Objective

• To challenge the validity of the $^{12}$C-$^{12}$C fusion S*-factor reported in a 2018 Nature study using the Trojan Horse Method.
• To identify and correct methodological flaws in the original THM analysis, particularly the use of a plane-wave approximation that neglects Coulomb interactions.
• To demonstrate that the reported steep rise in S*-factor at low energies is an artifact of incorrect theoretical modeling and data normalization.
• To advocate for the use of a three-body theory including Coulomb effects in THM analyses for heavy-ion systems like $^{12}$C-$^{12}$C.
• To correct the misassignment of resonances in the R-matrix analysis, which violates quantum mechanical selection rules for identical bosons.

Proposed method

• Apply a general three-body theory with Coulomb interactions (muk2011) instead of the plane-wave approximation used in the original study.
• Re-evaluate the normalization of THM data to direct experimental measurements, excluding unreliable datasets such as mazarakis1973 (due to energy calibration errors) and barron2006 (due to resonance-smoothing methods).
• Correct the branching ratio for $\gamma$-ray transitions in direct data to ensure consistency with $^{12}$C($^{12}$C,$\alpha_1$) $^{20}$Ne cross sections.
• Reassess the R-matrix analysis by enforcing quantum mechanical selection rules: only even-spin, positive-parity resonances are allowed in the $^{12}$C-$^{12}$C channel.
• Compare the location of THM-observed resonances with those from direct experiments, accounting for three-body Coulomb effects.
• Use only consistent, uncorrected, and well-calibrated direct data for normalization and resonance validation.

Experimental results

Research questions

• RQ1 Does the plane-wave approximation used in the original THM analysis accurately describe the $^{12}$C-$^{12}$C fusion reaction at 30 MeV incident energy?
• RQ2 How do Coulomb interactions in the three-body final state affect the observed resonance positions and S*-factor in the THM method?
• RQ3 To what extent do errors in direct data normalization, such as from mazarakis1973 or barron2006, distort the THM-derived S*-factor?
• RQ4 Are the resonances identified in the R-matrix analysis of the THM data consistent with the quantum mechanical selection rules for identical bosons in the $^{12}$C-$^{12}$C system?
• RQ5 Does the inclusion of a proper three-body Coulomb theory eliminate the reported 1000-fold increase in the $^{12}$C-$^{12}$C reaction rate at T9 = 0.2?

Key findings

• The plane-wave approximation used in the original Nature study is invalid for the $^{12}$C-$^{12}$C system at 30 MeV incident energy due to strong Coulomb interactions in the d-$^{24}$Mg transfer channel.
• Including three-body Coulomb effects via the muk2011 theory significantly reduces the predicted S*-factor, contradicting the steep rise reported in NatureTHM1.
• The direct data set from mazarakis1973 is found to be unreliable due to incorrect energy calibration, and its exclusion eliminates the observed rise in the S*-factor.
• The barron2006 data set is unsuitable for normalization due to resonance-smoothing techniques that erase physical structure.
• The R-matrix analysis in the original study incorrectly includes resonances with odd spin and negative parity, violating the selection rules for identical bosons in the $^{12}$C-$^{12}$C entrance channel.
• The only observed peak in the overlapping energy range (E_c.m. = 2.56 MeV) has a wrong J^π = 3^-, making it impossible to confirm the existence of molecular $^{12}$C-$^{12}$C resonances as claimed.