Shape Coexistence in Odd-Z Isotopes from Fluorine to Potassium
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
The authors studied the quadrupole-deformation dependence of
the energy of odd-Z isotopes with Z in the range 9-19. The
analysis is aimed at the identification of candidate isotopes
exhibiting shape coexistence, the signature of which is the
occurrence of nearly degenerate minima of the nuclear potential
energy as a function of the quadrupole deformation parameter β2.
The calculations have been performed using a well-established
formalism and the covariant energy-density functional known as
PC-PK1 model.
The paper is well written and the results reported are interesting
and potentially useful. In order to fully achieve publication
level, however, the manuscript needs to be improved to fix two
weak points.
1. In the Introduction, the authors state that investigating exotic
nuclear features, such as shape cohexistence, "offers valuable
insights into the formation of nuclei from neutrons and protons".
This is way too generic. The authors' claim needs to be properly
justified.
2. Setting the degeneracy threshold to 300 MeV involves a degree
of arbitrariness. The authors should clarify what would be the
effects of using a different theshold.
A revised manustript, amended to take into account the above remarks,
will be suitable for publication in Particles.
Author Response
We would like to thank the referee for the helpful comments.
Below, we provide responses to the referee's comments.
(Referee) In the Introduction, the authors state that investigating exotic nuclear features, such as shape coexistence, "offers valuable insights into the formation of nuclei from neutrons and protons". This is way too generic. The authors' claim needs to be properly justified.
(Our reply) In the Introduction, we have rephrased the sentence as follows:
The investigation of these exotic nuclear features provides invaluable insights into the complex nature of nuclear forces that govern the formation and structure of atomic nuclei. By exploring how neutrons and protons arrange themselves within these unusual shapes, one can gain a deeper understanding of the underlying nuclear forces and quantum mechanical effects at play.
(Referee) Setting the degeneracy threshold to 300 MeV involves a degree of arbitrariness. The authors should clarify what would be the effects of using a different threshold.
(Our reply)
We use 500 MeV as the criterion and found 24 additional candidates for shape coexistence.
We have included these additional isotopes in Figure 2.
We also revised Introduction further by including more references relevant to our current study and expanded its last paragraph to better motivate the present work.
In addition, we compared our results with those from D1S.
We hope that our responses adequately address the concerns and suggestions raised by the referee.
Reviewer 2 Report
Comments and Suggestions for AuthorsSee attached file report155.pdf
Comments for author File: 
Comments.pdf
Author Response
We thank the referee for their helpful comments.
Please see the attached file
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsPlease see attached file.
Comments for author File: Comments.pdf
Author Response
We would like to thank the referee for the helpful comments.
Below, we provide responses to the referee's comments.
(Referee) Ref. [1] regards shape coexistence in even-even nuclei, for which more recent reviews exist, including [Heyde2011] by two of the authors of {1]. More recent reviews of shape coexistence in even-even nuclei
have been given in [Garrett2022,Bonatsos2023,Leoni2024].
(Our reply) We thank the referee for providing relevant references, which have been incorporated as Refs. 3, 5, and 6.
(Referee) Shape coexistence in odd nuclei has been considered in the early review [Heyde1983]. I am not aware of any more recent review on shape coexistence in odd nuclei.
(Our reply) We included the review article and tow more recent studies on shape coexistence in odd-nuclei.
(Referee) A mechanism for predicting regions of the nuclear chart in which shape coexistence can be expected, has been introduced in [Martinou2021} and reviewed in Martinou2023]. It would be interesting to
compare the predictions of the present work to the regions predicted in these references.
(Our reply) We added the reference just above Summary and briefly compared our results with the ones from the references.
(Referee) In the region of light nuclei considered by the authors, islands of inversion have been proposed [Brown2010,Scheit2011], which are related to shape coexistence. These have been considered by a
variety of methods, including large scale shell model calculations [Caurier2014] and ab initio calculations [Miyagi2020]. The authors might try to compare their results with the predictions of these alternative
methods
(Our reply) We thank the referee for helpful comments. We added the papers as Refs. [7,8,9,10] in Introduction with some additional comments.
In addition, we have compared these findings with those obtained from the D1S model and also presented our results using the 500 MeV criterion for shape coexistence.
We also expanded the Introduction in its last paragraph to better motivate the present work.
We hope that our responses adequately address the concerns and suggestions raised by the referee.
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors have improved this revised version of the paper by adding new discussions along the lines suggested in my first report. Therefore, I recommend the manuscript for publication in the MDPI Journal Particles.
Please check the values reported in Table 2 for the nuclei 56Cl, 34K, 38K,43K, and 52K, where some black characters appear in addition to the red(old) and blue(new) data.
