SciPost Submission Page
Beryllium-9 in Cluster Effective Field Theory
by Elena Filandri, Paolo Andreatta, Carlo A. Manzata, Chen Ji, W. Leidemann and G. Orlandini
This is not the current version.
|As Contributors:||Elena Filandri|
|Submitted by:||Filandri, Elena|
|Submitted to:||SciPost Physics Proceedings|
|Proceedings issue:||24th European Few Body Conference (University of Surrey, U.K.)|
|Subject area:||Nuclear Physics - Theory|
We study the 9 Be ground-state energy with non-local αn and αα potentials derived from Cluster Effective Field Theory. The short-distance dependence of the interaction is regulated with a momentum cutoff. The potential parameters are fitted to reproduce scattering length and effective range. We implement such potential models in a Non-Symmetrized Hyperspherical Harmonics (NSHH) code in momentum space. In addition we calculate ground-state energies of various alpha nuclei. Work is in progress in view of the calculation of the photodisintegration of 9 Be with the Lorentz Integral Transform (LIT) method.
Submission & Refereeing History
Reports on this Submission
Report 1 by Daniel Phillips on 2020-1-2 Invited Report
1. The approach is sound.
2. The calculations are well explained
3. The results are interesting.
There are no significant weaknesses. The paper is short–as is appropriate for a conference proceedings. In the longer term I would like to see how this approach performs for excited states of these systems, e.g., the full spectrum of 9Be is interesting, and historically several states have been identified as "molecules" of a neutron and two alpha particles.
There are a couple of technical points I am puzzled about, and I have noted these in the "Requested changes".
This paper develops calculations of alpha-clustered nuclei that employ separable momentum-space interactions motivated by effective field theory. The Non-Symmetrized Hyperspherical Harmonics method is used to solve the three-, four-, five-, and six-body problems with these potentials. Results are shown for the ground state energy of 9Be, 12C, 16O, 20Ne, and 24Si.
Several of these are simply suggestions for improvements to the English, but I also have some physics questions I would like the authors to discuss in a revised manuscript, if space permits.
1. Abstract, fourth line: should read “are fitted to reproduce the scattering length and effective range”.
2. Abstract, third-last line: I would suggest “Work is in progress on a calculation of the photodisintegration….”
3. Introduction, first line: I suggest “The idea of alpha clustering has a long history, that goes back to the 1930s.”
4. Introduction, third line: “…there is much experimental evidence for alpha clustering in nuclei”
5. Introduction, second paragraph, second line: I am not sure I would describe the energies of interest as “very low”. Energies up to almost 20 MeV should be accessible within this clustered approach, yes?
6. One of the authors of this work is a co-author of an excellent review on Halo/Cluster EFT: Hammer, Ji, Phillips, J. Phys. G 44, 103002 (2017). It would be worth citing that work, as well as the original papers already cited, when introducing the Cluster/Halo EFT concept in the text.
7. Luna and Papenbrock has recently suggested that the large scattering length found in the αα case is not the result of fine tuning, but instead is an outcome of Coulomb barrier penetration in a system with a moderately strong Coulomb repulsion (Phys. Rev. C 100, 054307 (2019)). How would this suggestion affect the power counting for the alpha-alpha system? It may also be worth comparing to Luna and Papenbrock's αα phase shifts, since they also use a finite-range regularization of the EFT potential.
8. The power counting of Eq. (2) seems to be the same as that adopted by Higa, Hammer, and van Kolck in MS Ref. . A citation at this point in the text would be appropriate.
9. Do I understand correctly that the authors are only claiming LO accuracy, i.e., they have neglected NLO effects in both the α-α and α-n scattering? If so, maybe they can say that explicitly. Some readers might think “expanding up to NLO” means that NLO terms are kept.
10. The expression (8) is fine in the absence of Coulomb interactions, but–as I'm sure the authors are aware–does not apply to the α-α case, where Coulomb is present.
11. I do not think Eq. (13) is correct. Isn’t GC(+) accounted for via the denominator (p^2-k^2+i epsilon), at least if p is replaced by p’’? I therefore think that GC(+) should not appear with V inside the matrix element under the integral. Or am I missing something?
12. Why is the Non-Symmetrized Hyperspherical Harmonics basis used? Is it because these are not fermions? How is the Bose symmetry of the alpha particles imposed on the wave function of these nuclei?
13. The caption of Figs. 3 and 5 should specify that what is plotted on the x-axis is the hyper radial quantum number K. (Even though this is staled in the text.)
14. The caption of Fig. 4 should read “9Be ground state energy as a function of the cutoff…”. The same suggested change to the English applies to the opening sentence of the first full paragraph on p.6.
15. Ideally the value of K would also be quoted in the caption of Fig. 4, but since it’s in the text I suppose that is okay.
16. The first full paragraph on p.6 clarifies that the binding energy computed here does not include the binding energy of the alpha particles. That makes it the binding energy of the three-body ααn system, or, equivalently, the 1n separation energy of 9Be. Maybe these definitions of the binding energy that is being shown can be added to the text.
17. Looking at Fig. 4 & 6 it seems counter-intuitive that the repulsive αα potential leads to more binding in the 3B system. I originally wondered if my intuition is violated because this is a non-local potential. However, the one-term separable employed here seems to me to not change sign, and so be repulsive for all momenta as long as λ0>0. And the second paragraph on page 6 includes the statement “Furthermore, one sees that the parameter set with a positive λ0 leads to about 0.5 MeV less binding.”. Is it possible that the blue curves are actually for the repulsive case, in spite of the labeling in the figures?
18. Associatedly, do the authors have any insight into why the nominally attractive αα potential produces α-conjugate nuclei that are underbound, and also produces much weaker cutoff dependence than the nominally repulsive potential?