Beta Decay Properties of Waiting-Point N = 50 and 82 Isotopes
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsI agree that it is important to develop a reliable theory to calculate the beta-decay rates of the nuclei on the waiting points of the r-process nucleosynthesis for better understanding of the r-process. The present work is important since it quantitatively showed the importance of the contribution of first forbidden (FF) transitions. According to Table 2, the contributions of FF evaluated in Ref. 33 are negligibly small compared to the ones predicted by the other theories including the present work. Since such a kind of the point was not discussed in Ref. 33 itself, it will be interested by the readers if the present paper can argue its reason. In page 7, it is mentioned that the quenched gA was not employed in the present work. It is interesting to hear why non-quenched value was employed. Is it simply because non-quenched value gave better agreement with the experimental data?
It is not clear what is the merit or new point of the present calculation method.
In addition, the following notations or maybe typo are recommended to be corrected;
p.1, L.36, 10^90 K --- is this an approximate temperature of the region where the r-process is working? It should not be as high as 10^90 K, and maybe it is around 10^9 K.
Author Response
Comment 1: It is interesting to hear why non-quenched value was employed. Is it simply because non-quenched value gave better agreement with the experimental data?
Response 1: We sincerely thank the reviewer for pointing out this important aspect of our calculation.
In our study, we did not apply a quenching factor to the axial-vector coupling constant (gA) because our pn-QRPA calculations already produced results in very good agreement with the available experimental data. Therefore, the use of a quenched (gA) was not necessary to improve the accuracy of our theoretical predictions .
Comment 2: p.1, L.36, 10^90 K --- is this an approximate temperature of the region where the r-process is working? It should not be as high as 10^90 K, and maybe it is around 10^9 K .
Response 2: We thank the reviewer for this valuable observation. Indeed, the value 10^90 K was a typographical error. The correct temperature value is 10^9 K, which is consistent with the typical astrophysical conditions for the r-process. We have corrected this mistake in the revised version of the manuscript .
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors of the manuscript present new calculations of beta – decay properties of several nuclei with N=50 and N=82. The proton-neutron quasiparticle random phase approximation (𝑝𝑛-QRPA) with a Woods – Saxon potential was used. The formalism used was discussed in detail. The computed beta – decay half – lives were compared with other works (when available) and the experimental values. The present work is a continuation of previous works of the same group reported in the literature.
The present manuscript is a part of a systematic work worth publishing and useful for the scientific community. The topic is certainly appropriate for particles. As a part of a systematic work special care should be given discussing the comparisons between the present results and the ones reported in the literature (experimental and theoretical ones). Before suggesting the publication of the manuscript, I strongly recommend the authors to address several comments presented below:
Major points:
- A more careful use of English language is necessary since, in the present form some parts of the text such as the introduction, are hard to read.
- Results and discussion, first paragraph: the authors state that the selection of the values was chosen to give better results which are close to the experimental values. What does it mean “better results”? Also, if I understood correctly, the authors fixed the values such as to reproduce some experimental ones. Did the authors perform any sensitivity test or minimization procedure for the selection of the values? The experimental values used should be also cited.
- A spherical shape was assumed for the nuclei under study. A comment on whether this is a good assumption or not may be added.
- I would expect a more detailed discussion on the 𝛽-decay half-lives results presented in tables 1, 2 and especially in what concerns the discrepancies between calculations and experimental values.
Specific points:
- The authors are advised to be careful with the standard nuclear symbol notation. A nucleus X with atomic number (number of protons) Z and mass number A=N+Z where, N is the number of neutrons is written as: . Therefore, all the nuclei mentioned in the abstract (lines 16,17) are written in a wrong way.
- The introduction starts with some confusing sentences. In page 1, lines 29-31 the authors mentioned that there is a lack in the available data providing also a reference of 2006 while, in the next sentence it is stated that “This understanding has improved with time due to modern references [6,7,8,9].” providing references starting from year 1994. Please rephrase.
- Introduction, page 1, line 37 it is stated “nuclear safety in reactors depends on data about the beta decay…”. Since the sentence is confusing, I propose rephrasing that in something like: “data about the beta decay…are useful in the sector of nuclear safety in reactors”.
- Introduction, page 2, line 60-61: “Borzov adopted…”. A reference is needed here. A reference is also missing in line 72 “Wang et al…”.
- Introduction, page 2, line 79: “(e.g., 208 Pb )”. I suggest the use of the same notation in all cases. It is quite confusing to use different notations along the text. Also, if the authors prefer to use this notation, it should be written 208
- Mathematical formalism, page 4, equations in line 129: please double check the index of summation. Also, the authors are advised to define/explain in the text all the parameters presented in the equations.
Minor suggestions/corrections:
- Page 3, lines 120-121: “and the particleparticle channels,…” →“and the particle-particle channels,…”
- Page 8, line 288: “In Table 1, In the absence of prior theoretical predictions, this study provided”. Please rephrase since the sentence is hard to read.
- Page 8, line 290-291: “Nuclei like Ge-82, As-83, Se-84, Br-85, and Rb-87 did not have previous computational results in the literature,…” →please rephrase. For example, it may be written as “For nuclei like Ge-82, As-83, Se-84, Br-85, and Rb-87 no computational results can be found in the literature,…”
Dear Editor,
please find herewith the referee report for the manuscript entitled "Beta Decay Properties of Waiting-Point N=50 and 82 Isotopes".
Sincerely Yours
Author Response
Major points:
Comment 1: A more careful use of the English language is necessary since, in the present form some parts of the text such as the introduction, are hard to read.
Response 1: We thank the reviewer for the observation. The manuscript, particularly the introduction and other relevant sections, has been carefully revised and corrected to improve the clarity and readability of the English language. We hope the revised version meets the expected standard.
Comment 2: Results and discussion, first paragraph: the authors state that the selection of the values was chosen to give better results which are close to the experimental values. What does it mean “better results”? Also, if I understood correctly, the authors fixed the values such as to reproduce some experimental ones. Did the authors perform any sensitivity test or minimization procedure for the selection of the values? The experimental values used should be also cited.
Response 2: We thank the reviewer for this important comment. In this study, we employed the schematic model, which is a self-consistent approach involving effective interaction parameters. The values used for both Gamow–Teller (GT) and First Forbidden (FF) transitions were fixed and kept the same across all considered nuclei, without tuning them individually to fit specific experimental data. These values are based on commonly used standards in the literature.
By “better results,” we meant that the calculated β-decay half-lives showed reasonable agreement with the available experimental data without requiring parameter adjustment. However, we did not perform a formal sensitivity analysis or parameter minimization procedure in this work, as the aim was to test the general predictive capability of the model with standard parameters.
The experimental values used for comparison have now been clearly cited in the revised manuscript (see Tables 1 and 2 and corresponding references).
Comment 3: A spherical shape was assumed for the nuclei under study. A comment on whether this is a good assumption or not may be added.
Response 3:
We thank the reviewer for this valuable remark. It is well known that nuclear deformation tends to become more significant as the mass number increases. However, in the present study, we assumed spherical shapes for all the nuclei under consideration. This assumption is commonly adopted in pn-QRPA calculations, especially for semi-magic or near-magic nuclei, where spherical symmetry is often a good approximation.
In our case, many of the studied nuclei are near closed shells (N=50 and N=82), where deformation effects are expected to be minimal. Therefore, the spherical assumption is justified as a first approximation. We have now added a brief clarification on this point in the revised manuscript.
Comment 4: I would expect a more detailed discussion on the ?-decay half-lives results presented in tables 1, 2, and especially in what concerns the discrepancies between calculations and experimental values.
Response 4: The results presented in Tables 1 and 2 from other studies were obtained using the specific theoretical methods adopted in each respective work. As the reviewer rightly pointed out, we can provide a summary of these methods to clarify how the referenced calculations were performed. These approaches are commonly used in theoretical nuclear physics for beta decay studies, but they differ in their underlying assumptions, approximations, and model details.
Specific points:
Comment 5: The authors are advised to be careful with the standard nuclear symbol notation. A nucleus X with atomic number (number of protons) Z and mass number A=N+Z where, N is the number of neutrons is written as: . Therefore, all the nuclei mentioned in the abstract (lines 16,17) are written in a wrong way.
Response 5: We thank the reviewer for pointing out the incorrect notation. The nuclear symbols mentioned in the abstract have been carefully reviewed and corrected to follow the standard notation, where each nucleus is written in the form. These corrections have been applied throughout the abstract and manuscript where necessary.
Comment 6: The introduction starts with some confusing sentences. In page 1, lines 29-31 the authors mentioned that there is a lack in the available data providing also a reference of 2006 while, in the next sentence it is stated that “This understanding has improved with time due to modern references [6,7,8,9].” providing references starting from year 1994. Please rephrase.
Response 6: We thank the reviewer for highlighting this inconsistency. The sentence has been rephrased in the revised manuscript to improve clarity and to ensure a logical flow regarding the development of knowledge in the field. The issue with the timeline of the references has also been addressed to avoid confusion.
Comment 7: Introduction, page 1, line 37 it is stated “nuclear safety in reactors depends on data about the beta decay…”. Since the sentence is confusing, I propose rephrasing that in something like: “data about the beta decay…are useful in the sector of nuclear safety in reactors”.
Response 7: We thank the reviewer for highlighting this inconsistency. The sentence has been rephrased in the revised manuscript to improve clarity and to ensure a logical flow regarding the development of knowledge in the field. The issue with the timeline of the references has also been addressed to avoid confusion.
Comment 8: Introduction, page 2, line 60-61: “Borzov adopted…”. A reference is needed here. A reference is also missing in line 72 “Wang et al…”.
Response 8: We thank the reviewer for pointing out the missing references. The appropriate citations have now been added for both “Borzov” and “Wang et al.” in the revised manuscript to ensure completeness and proper attribution.
Comment 9: Introduction, page 2, line 79: “(e.g., 208 Pb )”. I suggest the use of the same notation in all cases. It is quite confusing to use different notations along the text. Also, if the authors prefer to use this notation, it should be written 208
Response 9: We thank the reviewer for this helpful suggestion. The notation has been reviewed and corrected throughout the manuscript to ensure consistency. The standard nuclear notation format (e.g., ²⁰⁸Pb) has been applied uniformly across the text.
Comment 10: Mathematical formalism, page 4, equations in line 129: please double check the index of summation. Also, the authors are advised to define/explain in the text all the parameters presented in the equations.
Response 10: We thank the reviewer for this valuable comment. The summation indices in the equations on page 4 have been carefully checked and corrected where necessary. In addition, all parameters and symbols used in the equations have now been clearly defined and explained in the text to improve clarity and readability.
Minor suggestions/corrections:
Comment 11: Page 3, lines 120-121: “and the particleparticle channels,…” →“and the particle-particle channels,…”
Response 11: We thank the reviewer for pointing out this typographical error. It has been corrected to “particle-particle” in the revised manuscript.
Comment 12: Page 8, line 288: “In Table 1, In the absence of prior theoretical predictions, this study provided”. Please rephrase since the sentence is hard to read.
Response 12: We thank the reviewer for the observation. The sentence has been rephrased in the revised manuscript to improve clarity and readability.
Comment 13: Page 8, line 290-291: “Nuclei like Ge-82, As-83, Se-84, Br-85, and Rb-87 did not have previous computational results in the literature,…” →please rephrase. For example, it may be written as “For nuclei like Ge-82, As-83, Se-84, Br-85, and Rb-87 no computational results can be found in the literature,…”
Response 13: We thank the reviewer for the helpful suggestion. The sentence has been rephrased as recommended in the revised manuscript to improve clarity and correctness.
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsI appreciate the authors' response and corrections to the manuscript. A big part of my comments and suggestions were adopted in a satisfactory way. To my opinion, the manuscript was improved being appropriate for publication.
