Shell Model Description of Spin-Dependent Elastic and Inelastic WIMP Scattering off 119Sn and 121Sb
Round 1
Reviewer 1 Report
The authors calculate in the framework of the nuclear shell model
(NSM) the spin structure functions for spin-dependent elastic and inelastic WIMP
scattering off 119Sn and 121Sb.
The subject is of great interest given the present experimental
efforts for the search for dark matter.
However, I cannot recommend the publication of the paper in its
present form.
I could reconsider my decision only after some major revisions dealing
with the following points.
1) The nuclear wave functions employed in the study are obtained in
the framework of the NSM, therefore the authors should provide much
more information regarding the effective shell-model hamiltonian
employed.
2) The normal ordering approximation employed to treat the two-body
WIMP-nucleus interaction should be at least qualitatively described.
Are the final results affected by the choice of the value for the
nuclear density?
3) From the inspection of Table 1 it seems that the low
energy constants appearing in the WIMP-nucleus current are not
univocally determined, having a range of values.
What is the effect on the final results when varying the constants
within their definition interval? It is not explicitly reported
anywhere.
4) A discussion about the role of effective operators employed should
be in order.
The E2 operators employed are defined in terms of effective charge,
but this is not the case for the M1 operator (by the way it is not
reported the value employed for the orbital g-factor g_l)
and for the WIMP-nucleus current.
Why?
Author Response
Thank you for your feedback. The article has been revised. Here are the "patch notes":
* Titles added to references.
* Added explanation on what "high" means for structure functions.
* Introduction now explains in what way Sn-119 and Sb-121 are the "last" ones.
* Introduction now briefly mentions the trouble with Hg-201.
* Citation to where the S functions are precisely defined.
* Mention on what the thickness of the S curves represents.
* Mention that Eq. (1) comes from EFT.
* Explained the role of renormalization (perturbative G-matrix).
* Explained that three-body forces are taken into account by effective energies.
* Elaborated on what harmonic oscillator length b is.
* Explicitly mention how uncertainty in the parameters propagate to the results.
* Updated Table 3 and 4 descriptions: value of g_l.
* Added more about CD-Bonn/Hamiltonian.
* Added paragraph about competing dark matter theories to the introduction.
* Self-citation rate is now below 15%.
Response to your particular points:
1) More about CD-Bonn/Hamiltonian was added. We have also provided citations so it is possible to work out exactly what kind of interaction/Hamiltonian was used.
2) When it comes to the WIMP calculation, nuclear density was among the parameters with a range of values leading to a range of possible structure functions. As such different possible values have been taken into account. I have updated the text to make it more clear. The normal ordering approximation has been referenced.
3) I have revised the text to make it clear that all possible values were used to get a minimum and maximum for the structure functions. This was a very good point, I did not realize that it was not mentioned anywhere in the text.
4) Added g_l. Forgetting it was a silly mistake.
Reviewer 2 Report
This paper addresses whether some nuclei are good candidates for dark matter detection (provided dark matter is made by WIMPs, see my comment below). Two specific nuclei are selected, and shell-model calculations are performed using particular model spaces, interactions and effective charges.
There is no basic flaw in these ideas and calculations, and, aside from minor issues, the presentation is complete, and the paper reads well.
However, my main concern is that the reader cannot understand the error(s) associated with these results for the structure functions. I know this is a difficult task, but still, the reader should know what the best possible error estimates are.
This being my major concern, I have a few other questions or comments that the authors should carefully consider before the manuscript can be considered for publication.
1) What is the meaning of the sentence "119Sn and 121Sb are the only ones still not explored ... for their potential of detection"? I imagine not all 300 stable nuclei have been explored. The main text seems to be more complete, but the abstract, although briefly, should reflect the main text.
2) WIMPs are strong candidates for dark matter, but alternative explanations do exist. For the non-expert reader's convenience, a few words in the introduction would be in order.
3) What is the precise definition of S(A), and why does Eq. (1) have the given form?
4) If no three-body forces are included in the calculations, how can this be justified?
5) In Sec. 4, a harmonic oscillator length is mentioned: which oscillator do the authors refer to?
6) Another statement which is unclear to me (and, I guess. to other readers) is that the authors say that structure functions are "high". What is the benchmark to judge if such a function is large or small?
Author Response
Thank you for your feedback. The article has been revised. Here are the "patch notes":
* Titles added to references.
* Added explanation on what "high" means for structure functions.
* Introduction now explains in what way Sn-119 and Sb-121 are the "last" ones.
* Introduction now briefly mentions the trouble with Hg-201.
* Citation to where the S functions are precisely defined.
* Mention on what the thickness of the S curves represents.
* Mention that Eq. (1) comes from EFT.
* Explained the role of renormalization (perturbative G-matrix).
* Explained that three-body forces are taken into account by effective energies.
* Elaborated on what harmonic oscillator length b is.
* Explicitly mention how uncertainty in the parameters propagate to the results.
* Updated Table 3 and 4 descriptions: value of g_l.
* Added more about CD-Bonn/Hamiltonian.
* Added paragraph about competing dark matter theories to the introduction.
* Self-citation rate is now below 15%.
Response to your particular points:
1) Text has been revised. It is now clearer than before, I hope.
2) Paragraph about dark matter explanations added to introduction.
3) It can be derived using EFT. Text has been revised, and this should now be more clear.
4) Three-body forces are taken into account in the effective energies. Updated the text to mention this.
5) This is now cited and explained in the text.
6) Clarified what "high" means for structure functions: high is high compared to other nuclei for which similar calculations have been performed.
Reviewer 3 Report
The problem of dark matter and the corresponding WIMP scattering has been a hot topic in recent years, both on the theoretically and experimentally. This group presents a theoretical investigation of the inelastic scattering of WIMP particles on an odd-N Sn- and an odd-Z Sb-isotope. They use state-of-the-art nuclear CI-calculations with a residual interaction derived by standard ab-initio calculations from high precision scattering data and calculate the spin structure functions for spin-dependent elastic and inelastic WIMP scattering. These are very interesting and new results, which can be used for future experiments.
The paper is clearly written by a group of well known specialized in this field. It contains all the essential references in this context. I, therefore, can recommend publication in the journal Universe.
Author Response
Thank you for your feedback. The article has been revised. Here are the "patch notes":
* Titles added to references.
* Added explanation on what "high" means for structure functions.
* Introduction now explains in what way Sn-119 and Sb-121 are the "last" ones.
* Introduction now briefly mentions the trouble with Hg-201.
* Citation to where the S functions are precisely defined.
* Mention on what the thickness of the S curves represents.
* Mention that Eq. (1) comes from EFT.
* Explained the role of renormalization (perturbative G-matrix).
* Explained that three-body forces are taken into account by effective energies.
* Elaborated on what harmonic oscillator length b is.
* Explicitly mention how uncertainty in the parameters propagate to the results.
* Updated Table 3 and 4 descriptions: value of g_l.
* Added more about CD-Bonn/Hamiltonian.
* Added paragraph about competing dark matter theories to the introduction.
* Self-citation rate is now below 15%.
(These are to address the concerns of the other two reviewers.)
Thank you for reviewing!
Round 2
Reviewer 1 Report
The authors have addressed my questions, and therefore the article can be published in its present form.
Reviewer 2 Report
I think that the authors have responded in a reasonable way to the points raised in my first report.
