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

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

This Submission thread is now published as SciPost Phys. Proc. 3, 047 (2020)

Submission summary

As Contributors: Paul Stevenson
Arxiv Link: (pdf)
Date accepted: 2019-10-18
Date submitted: 2019-10-07 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.

Published as SciPost Phys. Proc. 3, 047 (2020)

Author comments upon resubmission

We thank the referee for the comments.

Yes, the paper is an intermediate step, though we hope the results as presented are interesting in themselves. They reflect what was presetned at the conference for which the paper is intended as a proceeding article (which also has a 6 page limit, as a poster contribution). I agree with the stated weakness that more variation of the input parameters is needed to give a clearer picture of the validity of this approach

In answer to the particlar points in the report

1) We included a sentence about the calculated (17.67 MeV) vs experimental (28.30) binding energy of He-4 at the beginning of the "Results" section. This serious underbinding is commented on in the same section - that it may be expected to have qualitative effects on the results, but that we wish to start from a known interaction to give a starting point for the study

2) 2 MeV was chosen as being just above the Coulomb barrier which is between 1 and 2 MeV (since 1 MeV is too low to fuse, we found) and we are interested in low-energy behaviour. For much higher energy qualitatively different dynamics would be expected - e.g. fusion-fission. I'd expect the resonances that we saw to be governed more by the properties of the force; with the oscillations' frequencies governed by a restoring force that does not depend too much on entrance channel behaviour except to the extent of how many cycles the oscillation can happen. This is of course speculation until more calculations are performed and analysed, which await future work. In section 3.2 I have expanded the second paragraph which previously stopped at the sentence "The centre of mass collision energy is fixed at E_cm=2.0 MeV" to give a motivation for this energy. I note that the similar previous study by Umar et al. (our [4]) used 2.0 MeV as the collision energy, by coincidence (our value was not chosen because they used it, but for the motivation mentioned above)

3) Agreed. Ultimately we see this work as a stepping stone to something like a time-dependent generator coordinate method (with time as the generator coordinate) from which a spectrum with good angular momentum could be generated from projected and mixed Slater Determinants. The referee's suggestion of using the approximate relation between impact parameter and spin would be a computationally cheap way of getting an idea of the spin, and we'll look at this suggestion for the followup work. An extra paragraph has been added to section 3.2 at the end of the section to discuss obtaining spins.

4) Sorry. Numerous typos changed, and run through a spell checker.

Other changes: * changed the postcode in my affiliation which I had typed incorrectly

  • in the conlcusions I have been more explicit about which parameters deserve further study, in line with the referee's comments.

List of changes

changes all detailed in the "author comments" field

Submission & Refereeing History

Published as SciPost Phys. Proc. 3, 047 (2020)

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Resubmission 1909.01924v2 on 7 October 2019

Reports on this Submission

Anonymous Report 1 on 2019-10-14 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1909.01924v2, delivered 2019-10-14, doi: 10.21468/SciPost.Report.1223


The article present novel aspects related to the formation of carbon from triple alpha process


The authors have accounted for all the recommendations I asked for in my previous report. For this reason, I recommend the article for publication.

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

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