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A time-dependent Hartree-Fock study of triple-alpha dynamics

by P. D. Stevenson, J. L. Willerton

This is not the current version.

Submission summary

As Contributors: Paul Stevenson
Arxiv Link: (pdf)
Date submitted: 2019-09-05 02:00
Submitted by: Stevenson, Paul
Submitted to: SciPost Physics Proceedings
Proceedings issue: 24th European Few Body Conference (University of Surrey, U.K.)
Academic field: Physics
  • Nuclear Physics - Theory
Approaches: Theoretical, Computational


Time-dependent Hartree-Fock calculations have been performed for fusion reactions of He-4 + He-4 -> Be*-8, followed by He-4 + Be*-8 . Depending on the orientation of the initial state, a linear chain vibrational state or a triangular vibration is found in 12C, with transitions between these states observed. The vibrations of the linear chain state and the triangular state occur at ~9 and 4 MeV respectively.

Current status:
Has been resubmitted

Submission & Refereeing History

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Submission 1909.01924v1 on 5 September 2019

Reports on this Submission

Anonymous Report 1 on 2019-9-9 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1909.01924v1, delivered 2019-09-09, doi: 10.21468/SciPost.Report.1159


The paper address the delicate issue of forming carbon 12 from three alphas collisions. They used quite advances microscopic theories.


This is an intermediate step study and maybe some more systematic study varying input parameters would be desirable


In this article, the authors reanalyze the possibility to obtain a 12C from the reactions of three alphas using the TDHF approach. As mentioned by the authors, such studies were already made in the past, the novelty here being the consideration of a two-step process and the method to extract the excited state energy. Some of the result are interesting and I understand that the present article is an intermediate step towards more systematic studies.
I have a few comments that the authors might consider:
1) It is not clear in general if the HF/TDHF approach can describe light systems such as alpha particles or carbon. Can the authors give the ground state energy of these two nuclei obtained at the HF level and also compare with experiments? This would give an indirect hint on the precision one could achieve on energies.
2) Regarding the sentence “The centre of mass collision energy is fixed at Ecm = 2.0 MeV.”.
Can the authors motivate physically their choice of energy? If the authors have made tests with different energy, a comment on how the peaks obtained from the spectral analysis depends on the beam energy might be of interest.
3) Another delicate issue is that one usually discuss the formation of the 12C to the Hoyle state that has a definite spin. TDHF simulation leads to a final state which is a combination of different spins. Isolating a given spin can be made with some effort by projecting on total spins at the intermediate and/or final time. Another way would be to use the approximate relation between initial impact parameter and final internal spin. I am not asking the authors to solve this issue, but maybe a comment on this might enrich the article.
4) As a final remark, there are numerous misprints in the text that should be corrected in the final version. I collected some of them in the text: analsis, tracjectory, multinucles, resononance, calcualtion, lablled…
As I say above, the calculations are of interest and deserve to be published. I hope the authors will however follow some of my recommendation to improve the manuscript.

  • validity: ok
  • significance: good
  • originality: good
  • clarity: ok
  • formatting: reasonable
  • grammar: acceptable

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