Pear-shaped atomic nuclei

This review presents the current status of experimental evidence for the occurrence of reflection-asymmetric or ‘pear’ shapes in atomic nuclei, which arises from the presence of strong octupole correlations in the nucleon–nucleon interactions. The behaviour of energy levels and electric octupole transition moments is reviewed, with particular emphasis on recent measurements. The relevance of nuclear pear shapes to measurements of fundamental interactions is also discussed.


Comments to the Author(s)
The manuscript is well written update and summary of octupole deformation in medium heavy and heavy nuclei. In addition to addressing the relevant points with respect to nuclear structure physics also potential role of these nuclei in the searches for permanent electric dipole moment in atoms are addressed.The author has played central role in recent studies of this phenomena using Coulomb excitation of radioactive ion beams.
I only have only two comments on the text itself: page 5, line 5: will be large .... page 6, line 45: instead of using the word "statistical fluctuation" I would suggest to use "statistical uncertainty" Review form: Referee 2

Is the paper of sufficient general interest? Excellent
Is the overall quality of the paper suitable? Excellent Can the paper be shortened without overall detriment to the main message? Yes Do you think some of the material would be more appropriate as an electronic appendix? No

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
This is an excellent review article, and I recommend its publication in Proceedings A. I have only minor and rather technical suggestions. In page 6, line 5, "will large fluctuations ..." seems to be an incomplete sentence. In Fig. 1, 3 ¥hoar is not visible. In Fig. 2, axes may help, and some letters are too small. In Fig. 3. some letters are too small. In Fig. 4, Q_2, Q_3 and A are too large out of balance. In Fig. 6, there are four panels, which is not clear. They should be divided. The legend is common to all panels, but this is not obvious. Caption of Fig. 6, line 3, "The upper dashed line" does not exist in the figure.

Review form: Referee 3
Is the manuscript an original and important contribution to its field? Excellent

Is the paper of sufficient general interest? Excellent
Is the overall quality of the paper suitable? Excellent Can the paper be shortened without overall detriment to the main message? Yes Do you think some of the material would be more appropriate as an electronic appendix? No

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
This paper presents the present status of experimental evidence for the occurrence of octupole shapes in atomic nuclei and reviews the behaviour of energy levels and electric octupole transition moments.
The work is thoroughly implemented, the manuscript is well written and the subject is of a high actuality. Therefore, I would recommend for publication after the author provide a clarification of the following point. 1) In lines 30,31 of page 5, there is a sentence "Deviations from this ideal behaviour will occur for low-lying states because of the dominant effect of nucleonic pairing." Could the author say some more words to explain this comment or cite some relevant references?

Review form: Referee 4
Is the manuscript an original and important contribution to its field? Excellent

Is the paper of sufficient general interest? Good
Is the overall quality of the paper suitable? Excellent Can the paper be shortened without overall detriment to the main message? Yes Do you think some of the material would be more appropriate as an electronic appendix? No Do you have any ethical concerns with this paper? No

Recommendation?
Accept as is

Comments to the Author(s)
The manuscript is very compact yet informative (I've learned that Rn appears to be less suitable to the EDM measurement than Ra). I do not have any suggestions for its improvement.
Perhaps a word in "defence" of Hg EDM experiment: while of course the octupole-shaped deformations provide a way of enhancing the Schiff moment, the final utility of the bound/measurement comes down to the size of the errors on EDMs. 199Hg is a stable isotope that can be used in copious amounts in the EDM measurement, while suitable Ra exists in tiny quantities -which will lead to a constraint on atomic Ra EDM to be less stringent than in Hg simply because the statistical errors in Hg EDM are the smallest across all EDM experiments. It remains to be seen whether the deformation-induced enhancement of the effects in Ra would in the future make it competitive with, or better than Hg.
Decision letter (RSPA-2020-0202.R0) 08-May-2020 Dear Professor Butler, On behalf of the Reviews Editor, I am pleased to inform you that your Manuscript RSPA-2020-0202 entitled "Pear-shaped atomic nuclei" has been accepted for publication subject to minor revisions in Proceedings A. Please find the referees' comments below. We were fortunate in that all the invited referees accepted and returned their reviews promptly, a tribute to you and the excellence of your paper. Thank you.
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We welcome submissions of images for possible use on the cover of Proceedings A. Images should be square in dimension and please ensure that you obtain all relevant copyright permissions before submitting the image to us. If you would like to submit an image for consideration please send your image to proceedingsa@royalsociety.org Once again, thank you for submitting your manuscript to Proceedings A and I look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Comments to the Author(s) The manuscript is well written update and summary of octupole deformation in medium heavy and heavy nuclei. In addition to addressing the relevant points with respect to nuclear structure physics also potential role of these nuclei in the searches for permanent electric dipole moment in atoms are addressed.The author has played central role in recent studies of this phenomena using Coulomb excitation of radioactive ion beams.

Best wishes
I only have only two comments on the text itself: page 5, line 5: will be large .... page 6, line 45: instead of using the word "statistical fluctuation" I would suggest to use "statistical uncertainty" Referee: 2 Comments to the Author(s) This is an excellent review article, and I recommend its publication in Proceedings A. I have only minor and rather technical suggestions. In page 6, line 5, "will large fluctuations ..." seems to be an incomplete sentence. In Fig. 1, 3 ¥hoar is not visible. In Fig. 2, axes may help, and some letters are too small. In Fig. 3. some letters are too small. In Fig. 4, Q_2, Q_3 and A are too large out of balance. In Fig. 6, there are four panels, which is not clear. They should be divided. The legend is common to all panels, but this is not obvious. Caption of Fig. 6,  Comments to the Author(s) This paper presents the present status of experimental evidence for the occurrence of octupole shapes in atomic nuclei and reviews the behaviour of energy levels and electric octupole transition moments.
The work is thoroughly implemented, the manuscript is well written and the subject is of a high actuality. Therefore, I would recommend for publication after the author provide a clarification of the following point. 1) In lines 30,31 of page 5, there is a sentence "Deviations from this ideal behaviour will occur for low-lying states because of the dominant effect of nucleonic pairing." Could the author say some more words to explain this comment or cite some relevant references?
Referee: 4 Comments to the Author(s) The manuscript is very compact yet informative (I've learned that Rn appears to be less suitable to the EDM measurement than Ra). I do not have any suggestions for its improvement.
Perhaps a word in "defence" of Hg EDM experiment: while of course the octupole-shaped deformations provide a way of enhancing the Schiff moment, the final utility of the bound/measurement comes down to the size of the errors on EDMs. 199Hg is a stable isotope that can be used in copious amounts in the EDM measurement, while suitable Ra exists in tiny quantities -which will lead to a constraint on atomic Ra EDM to be less stringent than in Hg simply because the statistical errors in Hg EDM are the smallest across all EDM experiments. It remains to be seen whether the deformation-induced enhancement of the effects in Ra would in the future make it competitive with, or better than Hg.

18-May-2020
Dear Professor Butler On behalf of the Editor, I am pleased to inform you that your manuscript entitled "Pear-shaped atomic nuclei" has been accepted in its final form for publication in Proceedings A.
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Best wishes
Raminder Shergill, Proceedings A Editorial Office proceedingsa@royalsociety.org I thank all referees for their careful reading of the paper, and have made the following changes to address their comments:

Referee 1
I have corrected the phrase in section 3 to read "…there will be large fluctuations in its value…" For the other phrase I have replaced it by "… whether this dip arises from an experimental artifact or there is a real physical effect." Referee 2 (Prof. Otsuka) I have corrected the phrase in section 3, see above.

Referee 3
I have expanded this sentence (section 2) to read: "Deviations from this ideal behaviour will occur for low-spin states where nucleonic pairing will try to maintain a reflection-symmetric shape" and inserted a reference to Egido JL, Robledo LM 1989 (Microscopic study of the octupole degree of freedom in the radium and thorium isotopes with Gogny forces. Nucl. Phys. A 494, 85-101).
Referee 4 (Prof. Pospelov) I agree with the comment regarding how competitive EDM measurements in unstable 225Ra will be compared to those in stable 199Hg. It is clear that the 225Ra experimental programme at Argonne (and FRIB) requires possibly decades of development to reach the sensitivity achieved by the Seattle group. However, even if only the same sensitivity is reached, it is (apparently) more straightforward to calculate the Schiff moment and atomic EDM for the deformed Ra system than for the nearspherical Hg system.
In addition I have made the following clarifications, corrections and additions:

Introduction
I have added "in nuclei" in "For a review of generalised spontaneous symmetry breaking in nuclei…".

Section 3
I have replaced the theoretical calculations "Skyrme Hartree-Fock (SkO' variant)" (Engel et al., 2003) by "Skyrme Hartree-Fock-Bogoliubov (UNEDF0 variant)" (Cao et al., 2020). The former publication did not contain explicit calculations of E3 moments; these I estimated from the shape parameters. The latter paper, made available to me recently, presents E3 moments properly calculated from the octupole charge distribution.