Electron Impact Ionization Cross-Section Maxima of Atoms
Round 1
Reviewer 1 Report (Previous Reviewer 1)
The authors have made substantial improvements to the original manuscript. It is in much better condition now.
Author Response
Reviewer 1: The authors have made substantial improvements to the original manuscript. It is in much better condition now.
Authors’s Answer: The authors are grateful to the referee for positive acceptance of the paper.
Reviewer 2 Report (Previous Reviewer 2)
In my previous report I asked:
More broadly, what is the point of this work? How does it improve on the work of Kim and Rudd of 1994, see https://journals.aps.org/pra/pdf/10.1103/PhysRevA.50.3954?
Authors’ answer:
We believe that the present work can guide theoretical studies of ionization of multieletronic systems by electron impact by indicating what parameters are relevant in a region where Born Approximation is no longer valid.
This answer is not relevant to the question. The work of Kim and Rudd is not the Born approximation, but does yield excellent agreement with experiment for many targets. The present work does not, and thereby does not advance the field.
Author Response
Referee #2:
The authors thank to the reviewer for the critical reading of the manuscript. Here we give the detailed answers for the questions.
Q1: More broadly, what is the point of this work? How does it improve on the work of Kim and Rudd of 1994, see https://journals.aps.org/pra/pdf/10.1103/PhysRevA.50.3954? Authors’ answer: We believe that the present work can guide theoretical studies of ionization of multieletronic systems by electron impact by indicating what parameters are relevant in a region where Born Approximation is no longer valid.
This answer is not relevant to the question. The work of Kim and Rudd is not the Born approximation, but does yield excellent agreement with experiment for many targets. The present work does not, and thereby does not advance the field.
A1: As pointed out by Kim and Rudd, a systematic application of the their model to more complex targets than those presented in Kim and Rudd 1995 is needed to understand the validity of their model. They conclude that reliable total photoionization cross sections and cross sections for each of the outer subshells of atoms and molecules are needed. In the present paper, we compare our fitting with complex atomic targets. The scope of the present work, which is a comment, is quite different from Kim and Rudd’s. By using a single parameter, the target polarizability, one can estimate the maximum cross sections.
Moreover, we applied a quite common classical theoretical model to justify the experimental observations. The classical trajectory Monte Carlo model has proven its suitability in recent decades in many applications. Although it is classical, most of the time give reasonable results as it was in our recent case. Maybe the absolute cross sections are not exactly the same as for the experimental data but at least the estimation of the cross section maximums are reasonable.
Reviewer 3 Report (New Reviewer)
This paper presents a correlation between the maximum value of the electron impact ionization cross sections of some atoms and their respective static polarizabilities. There is nothing new in this study and, for the reasons explained below, we consider is not suitable for publication in Atoms .
- The main result of the paper is based on a simple linear fit of data taken from the literature. There are many empirical formulae to reproduce ionization cross section (see for instance the review of Younger and Mark, Springer-Verlag, New York, Berlin, 1985) but authors do not compare with them or even discuss the important uncertainties related to these formulae.
- It is well known that the atomic polarizability plays an important role in the scattering of electrons by atoms, affecting mainly to the scattering angles and in particular for the lower energies. In the case of ionization processes, even in a classical representation, apart from the scattering of the incident electron, dominated by the charged distribution of the target and its atomic polarizability, there is a direct electron-electron collision which lead to the ejection of the target electron. Obviously, the probability to ionize the target should depend not only on the target polarizability but also on the number of target electrons.
- It is not explained why they chose these atoms and not others. We can expect a clear dependence of the ionization cross section on the atomic polarizability for closed shell atoms and particularly for noble gases but for open shell atoms other parameters may be relevant and should be included in any empirical study, in order to obtain a useful formula. Authors mentioned the cases of Mg, Fe, Cu that do not follow the linear fit but we are sure that many other do not follow it either (alkali metals, alkaline earths, halogens….)
- Most of data have been taken from Ref. [5]. We are respectful with the work of Freund et al. but measuring ionization cross sections is a difficult task, even for atomic gases. A serious empirical or semiempirical analysis would require compare results from different sources, in order to look for possible systematic errors. Just to illustrate how complicated could be to find the right maximum value of the ionization cross section we recommend to see the case of In , recently summarized by Hamilton et al. (J. Phys. Chem. Ref. Data 50, 013101 (2021)). In Fig. 5 of Hamilton’s paper is shown that the peak cross sections, including all the available experimental and theoretical values, varies from less to 4e-16 cm2 to more than 12e-16 cm2 and choosing a correct value requires a deep analysis of different methods used by different authors. Note that the value given in the Ref [5] of the paper we are reviewing is 1217 Mb in the case of In, which would be out of the scale of Fig. 2. However, the value for In shown in Table 1, supposed to be taken from Ref. [5], is 832 Mb. Is there any reason to choose this value or is simply a mistake?
- The calculation procedure they use is quite naive. It is a simple calculation of the classical trajectories of electrons scattered by a static potential. Any consideration about the target properties such as the atomic polarizability or the ionization energy is ignored. Authors mentioned they applied an additional Monte Carlo method, which is practically say nothing. A Monte Carlo procedure is based on a random number generator to fit the possible results of the calculation to a given probability distribution function. No information about the input of this Monte Carlo procedure is given. In addition, more elaborated methods, easy to be used, such as the BEB and Optical Potential methods, are available in the literature. We don’t see the advantages of the presented calculation.
Author Response
Dear Editor,
We hereby submit the corrected manuscript, submission ID: atoms-2254942, to ATOMS. We have carefully revised the manuscript according to the reports. Our revisions are highlighted in yellow in the revised manuscript. We hope that in view the revision of our paper, it is now fully ready for publication.
Sincerely Yours,
Prof. A C F Santos
Author Response File: 
Author Response.pdf
Reviewer 4 Report (New Reviewer)
Dear Editor,
The authors are presenting a scaling rule for electron impact cross sections maxima as a function of the atomic target polarizability. The cross section and polarizability data were obtained from the literature. To confirm this scaling rule they also perform CTMC calculations for certain elements showing a good agreement. I find their result quite interesting and worthy of publications.
A suggestion for the better presentation of the paper would be to include legends inside the graphs 3, 4, and 5, for a clearer picture of the graph. Also, the caption of figure 3 needs to be revised as the corresponding descriptions are not exact in all cases.
Author Response
Referee #4:
The authors thank to the reviewer for the critical reading of the manuscript. Here we give the detailed answers for the questions.
Q1: The authors are presenting a scaling rule for electron impact cross sections maxima as a function of the atomic target polarizability. The cross section and polarizability data were obtained from the literature. To confirm this scaling rule they also perform CTMC calculations for certain elements showing a good agreement. I find their result quite interesting and worthy of publications.
A suggestion for the better presentation of the paper would be to include legends inside the graphs 3, 4, and 5, for a clearer picture of the graph. Also, the caption of figure 3 needs to be revised as the corresponding descriptions are not exact in all cases.
A1:
We are grateful for the referee to call our attention to these modifications.
We did corrections for the caption of figure 3. However we would like to keep our original figure style that the curves description is in the fihure caption. According to our experiences if we add the description in the figure then the figure become to crowded.
Reviewer 5 Report (New Reviewer)
The authors measured the cross-section of electron-atom impact ionization for the collisional energy from the range of 20..120 eV. They used three-body classical-trajectory Monte-Carlo simulation for theoretical interpretation of their results. The authors found an empirically linear dependence of the maximum cross-section on the polarizability of the target atom. The manuscript is clear and well-written. The connection with the results of other authors is shown. The scientific significance of the obtained results is emphasized.
The manuscript may be accepted for publication if the authors improve it in accordance with the comments below.
1. Target polarizability plays an important role not only in impact ionization, but also in polarization bremsstrahlung (see book [Tsytovich V. N. and Oiringel I. M. 1992 Polarization Bremsstrahlung (New York: Plenum Press) translated from Russian] and paper [Beilin E. L. and Zon B. A. 1983 J. Phys. B: At. Mol. Phys. 16, L159]). The author should mention this fact anywhere and cite the publications.
2. Since the simulations require the target mass m_T, the authors should indicate the atomic isotopes they used in their experiments and simulations.
3. Does potential (1) account for exchange effects? They could contribute at low energies. The authors should explain it.
4. The authors should have improved the readability of the manuscript. Particularly,
Line 23: "velocity" should be replaced with "speed" (here, v is not a vector).
Line 87: The reference to figure 1 should be inserted here. The phrase "In the case under condideration m_P=m_e" should be added here.
Line 91: The authors should have reformulated this paragraph, as the phrase "for a given set..." is repeated.
5. The authors should eliminate carelessness in the presentation of information. Namely,
Line 112: Add units of R.
Figures 3-5 contain abbreviation Mbarn, whereas in the thext the unit is Mb. Please unify the designations. Please use [...] to cite literature here.
Line 252: The last bibliography source is not enumerated; no reference to it in the text. I suggest to fix this point.
Tables 1, 2 are numbered with Roman numerals in the text (e.g. lines 106-116) but with Arabic ones in captions. Please consist the numeration.
Please append suitable punctuation marks to equations and remove indents in paragraphs following them.
6. It seems, the authors used MS Word instead of TeX, and therefore formulas are sometimes difficult to perceive, and they look carelessly. The authors should fix them. Particularly, single Latin letters should be typed in math italics and not in Roman font (e.g. R in line 112, Z in line 104; see also lines 137, 138, 129-131, equation (8), table 2 etc.). These corrections should be made throughout the text.
7. Some typos should be fixed.
Line 127: insert a space between sigma_{max} and "is";
Line 138: insert a space before "see Table...".
Author Response
Referee #5:
The authors thank to the reviewer for the critical reading of the manuscript. Here we give the detailed answers for the questions.
Q1: Target polarizability plays an important role not only in impact ionization, but also in polarization bremsstrahlung (see book [Tsytovich V. N. and Oiringel I. M. 1992 Polarization Bremsstrahlung (New York: Plenum Press) translated from Russian] and paper [Beilin E. L. and Zon B. A. 1983 J. Phys. B: At. Mol. Phys. 16, L159]). The author should mention this fact anywhere and cite the publications.
A1: It is done.
Q2. Since the simulations require the target mass m_T, the authors should indicate the atomic isotopes they used in their experiments and simulations.
A2: We include the isotope number of the simulations. Unfortunately, we do not know the isotope number used in the experiments.
Q3. Does potential (1) account for exchange effects? They could contribute at low energies. The authors should explain it.
A3: The description of the collision system is based on the classical treatment. The interaction potential between the projectile and the target system is a pure Coulomb one. The interaction between the active target electron and the target nucleus is describing by the screened Garvey type potential. This potential takes care of the target nucleus charge and the remaining electrons interaction with the active electron. During the CTMC simulation we take care of the channel when the projectile electron replaced the active target electron. If the referee was thinking to this channel as exchange effect than we take into account.
Q4: The authors should have improved the readability of the manuscript. Particularly,
Line 23: "velocity" should be replaced with "speed" (here, v is not a vector).
A4: It is done.
Q5: Line 87: The reference to figure 1 should be inserted here. The phrase "In the case under condideration m_P=m_e" should be added here.
A5: We did the modifications according to the referee request.
Q6: Line 91: The authors should have reformulated this paragraph, as the phrase "for a given set..." is repeated.
A6: It is done.
Q7: The authors should eliminate carelessness in the presentation of information. Namely,
Line 112: Add units of R.
A7: The correlation coefficient does not have any units
Q8: Figures 3-5 contain abbreviation Mbarn, whereas in the thext the unit is Mb. Please unify the designations. Please use [...] to cite literature here.
A8: We did the modifications according to the referee request.
Q9: Line 252: The last bibliography source is not enumerated; no reference to it in the text. I suggest to fix this point.
A8: done
Q9: Tables 1, 2 are numbered with Roman numerals in the text (e.g. lines 106-116) but with Arabic ones in captions. Please consist the numeration.
A9: done
Q10: Please append suitable punctuation marks to equations and remove indents in paragraphs following them.
A10: done
Q11: It seems, the authors used MS Word instead of TeX, and therefore formulas are sometimes difficult to perceive, and they look carelessly. The authors should fix them. Particularly, single Latin letters should be typed in math italics and not in Roman font (e.g. R in line 112, Z in line 104; see also lines 137, 138, 129-131, equation (8), table 2 etc.). These corrections should be made throughout the text.
A11: done
Q12: Some typos should be fixed.
Line 127: insert a space between sigma_{max} and "is";
A12: done
Q13: Line 138: insert a space before "see Table...".
A13: done
Round 2
Reviewer 2 Report (Previous Reviewer 2)
publish as is
Author Response
We thank the reviewer for his/her comments. We have performed spell check
Reviewer 3 Report (New Reviewer)
Not all previous questions and comments are properly adressed
Author Response
We thank the reviewer for his/her comments.
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
Please see attached file.
Comments for author File: Comments.pdf
Reviewer 2 Report
This appears to be a very rushed presentation. It has a number of glaring errors such as: "anyregime", "well-knownlnv2/v2expression", and poor English such as "the accuracies are usually limited". Furthermore, there are major mistakes: the cross section units in Figs. 3 and 4 are obviously wrong. Also, no comparison with experiment in Figs. 3 or 4 is presented, but should be. More broadly, what is the point of this work? How does it improve on the work of Kim and Rudd of 1994, see https://journals.aps.org/pra/pdf/10.1103/PhysRevA.50.3954?
