Radiative Lifetimes for the A and C1Σ+ States of the (SrK)+ Ion Molecular
Round 1
Reviewer 1 Report
The authors investigated radiative lifetimes and absorption spectra of states A and C for the SrK+ ion molecular at the vibrational levels. For this purpose the authors used the results of their previous research, related to Potential Dipole Moments (PDM) and Transition Dipole Moment (TDM). The results of the research seems no problem and hence can be publishable in Applied Sciences, if the authors revise their manuscript as follows before its publication:
1. In abstract part, the authors represented as “We have been investigated, in a previous work, the transition dipole moments (TDM) of the 13 1Σ+ states of the (SrK)+ molecular ion by using the ab initio method based on the pseudopotential approach.” However, it is not clear which reference is the “previous work” designated here.
The author should clarify it by revising, for example, as:
in a previous work -> in a previous work (Phys. Rev. A XX, XXX (2022))
2. The English of the paper should be improved.
For example, the followings should be revised.
Line 26 (and line 102)
“a huge number of molecular ions and molecules” should be a sentence.
“Two possible transitions” in line 102 should also be a sentence.
3. The arrangement of equations is crude. This problem can be settled by authors, or by a typesetter in the production/publication stage.
Author Response
Corrections requested by the referee 1
Q1. In abstract part, the authors represented as “We have been investigated, in a previous work, the transition dipole moments(TDM) of the 13 1Σ+ states of the (SrK)+ molecular ion by using the ab initio method based on the pseudo potential approach.”However, it is not clear which reference is the “previous work” designated here. The author should clarify it by revising, for example, as: in a previous work -> in a previous work (Phys. Rev. A XX, XXX (2022)):
-We have added this reference in the text to clarify the previous work: “We have been investigated, in a previous work” 2H. Souissi, L. Mejrissi, H. Habli, At. A. Al-Ghamdi, B. Oujia, F. X. Gadea, Chem. Phys. 490, 19–28 (2017)”, the transition dipole moments (TDM) of the 13 1Σ+ states of the (SrK)+ molecular ion by using the ab initio method based on the pseudo-potential approach.
Q2. The English of the paper should be improved. For example, the followings should be revised.
Line 26 (and line 102)
“a huge number of molecular ions and molecules” should be a sentence.
“Two possible transitions” in line 102 should also be a sentence.
- A major revision has been performed and almost all the manuscript has been rewritten.
Q3. The arrangement of equations is crude. This problem can be settled by authors or by a type setter in the production/publication stage.
-We have arranged all the equations in the text.
- A major revision has been performed and almost all the manuscript has been rewritten.
-We have reordered all the number of the references.
The authors thank the referee for its careful reading of the manuscript and its comments and suggestions.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
I have read this work carefully and suggest the authors to improve it along with the following points.
1) There are many grammatical mistakes in the manuscript. Please ask native English speaker to improve it.
2) The authors claimed the exact results. How to use (1) to calculate? How to get the exact solutions of the system? What wave function was used for the initial and final states?
Author Response
Comments and suggestions for authors 2:
I have read this work carefully and suggest the authors to improve it along with the following points.
Corrections requested by the referee 2
Q1. There are many grammatical mistakes in the manuscript. Please ask native English speaker to improve it.
-We have improved all the manuscript and we have corrected all the grammatical mistakes.
Q2. The authors claimed the exact results. How to use (1) to calculate? How to get the exact solutions of the system? What wave function was used for the initial and final states?
- During the absorption process, an electron in the initial state of energy Ei transits to a final state of energy Ef by the absorption of a photon. The rate of this transition is given to us by Fermi's Model (equation 1). We use this equation in the program to investigate the result of absorption and emission spectra.
- A major revision has been performed and almost all the manuscript has been rewritten.
-We have reordered all the number of the references.
The authors thank the referee for its careful reading of the manuscript and its comments and suggestions.
Author Response File: Author Response.pdf
Reviewer 3 Report
This work presents the modeling of absorption and emission spectra for the SrK+ molecule, implying the calculation of intensities of transitions X(ν=0)→A(ν=0,1,..), X(ν=0)→C(ν=0,1,..), A(ν=0)→C(ν=0,1,..), A(ν=0)→X(ν=0, 1…), C(ν=0)→A(ν=0, 1…), C(ν=0)→X(ν=0, 1…), as the functions of the excitation energy. Radiative-lifetimes of the vibrational levels of the molecular states A1Σ+ and C1Σ+ of the SrK+ were calculated by means of exact calculation of the integral of the bound-free contribution and, alternatively, by using the Franck-Condon approximation scheme.
This work is potentially publishable in Applied Sciences, however, there are some issues that should be fixed prior publication.
11. English grammar requires serious checking. Style correction is also desirable. For example (line 12): “We have been investigated, in a previous work, the transition dipole moments (TDM) of …”. It is more correct to rephrase the sentence as follows: “We have investigated the transition dipole moments (TDM) of … in our previous work.” Please, correct such issues throughout the whole manuscript.
22. Theoretical sections 2.1, 2.2, 2.3 are very succinct. For example, there is not a single word about the way of evaluation of the multidimensional Franck-Condon overlap integrals.
33. Correct the misprint on line 113 (tau).
44. Adsorption (figs. 3.1, 3.3, 3.5)? Did you mean the absorption?
55. Where the comparison with the experiment? If there is not, the simulated spectral data is not validated. How do you prove that your calculations are correct?
66. Correct the references (for example, line 233-234, plus remove the additional numbering).
77. What conceptually new do you propose in your work?
Author Response
Comments and suggestions for authors 3:
This work presents the modelling of absorption and emission spectra for the SrK molecule, implying the calculation of intensities of transitions X(ν=0)→A(ν=0,1,..), X(ν=0)→C(ν=0,1,..), A(ν=0)→C(ν=0,1,..), A(ν=0)→X(ν=0, 1…), C(ν=0)→A(ν=0, 1…),C(ν=0)→X(ν=0, 1…), as the functions of the excitation energy.
Radiative-lifetimes of the vibrational levels of the molecular states AΣ+ and CΣ+ of the SrK were calculated by means of exact calculation of the integral of the bound-free contribution and, alternatively, by using the Franck-Condon approximation scheme.
This work is potentially publishable in Applied Sciences; however, there are some issues that should be fixed prior publication.
Corrections requested by the referee 3
Q1. English grammar requires serious checking. Style correction is also desirable. For example (line 12): “We have been investigated, in a previous work, the transition dipole moments (TDM) of …”. It is more correct to rephrase the sentence as follows: “We have investigated the transition dipole moments (TDM) of … in our previous work.” Please, correct such issues throughout the whole manuscript.
-We have improved all the manuscript and we have corrected all the grammatical mistakes.
Q2. Theoretical sections 2.1, 2.2, 2.3 are very succinct. For example, there is not a single word about the way of evaluation of the multidimensional Franck-Condon overlap integrals.
-We have presented in this section the different methods and we have explained more the results in the section 3.1, 3.2, 3.3, 3.4.
Q3. Correct the misprint on line 113 (tau).
-We have been corrected this mistake.
Q4. Adsorption (figs. 3.1, 3.3, 3.5)? Did you mean the absorption?
-You are all right, we have corrected this mistake.
Q5. Where the comparison with the experiment? If there is not, the simulated spectral data is not validated. How do you prove that your calculations are correct?
-we don’t have a comparison with the experimental. However, our result helps the experimenter to finish their experiences. Our result for the ground state of the dipole moment is in very good agreement with the best theoretical and experimental works which is menshed in the preview work.
Q6. Correct the references (for example, line 233-234, plus remove the additional numbering).
-we have corrected and have reordered the number the references.
Q7. What conceptually new do you propose in your work?
-The calculated radiative lifetimes in nanoseconds are presented here for the first time. These results are important for the experimenter researchers which they need the parameters of our results.
- A major revision has been performed and almost all the manuscript has been rewritten.
-We have reordered all the number of the references.
The authors thank the referee for its careful reading of the manuscript and its comments and suggestions.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
I have read the revised manuscript and have the following suggestions even though some of them have been improved.
1) The English writing has to be improved,e .g. the mathematical formulae or mathematical symbols should be prepared in mathematical style, e.g in page 2, v=0. It should be $v=0$ or Italian style v=0. Please modify them completely.
2) The authors only answered me the use of Eq. (1), but the authors did not answer my questions, the wave function, exact solution? What is the mathematical expression of H_{int}? Only mention the fermi program is not enough.
3) It seems that many French or other language words were used in the text, e.g. Adiabatique, Exacte, etc.
4) In Table 2, what is representive of the "Bonded-free Exacte"? The difference between "Bonded-free Exacte" and "Bonded-free F.C." is too big. Please explain it in detail. The similar problem is Table 3. In Table 4, v=0-40, "Bonded-free Exacte" is zero, but after v=41, it is not equal to zero. Why?
Author Response
Response to the referee reports
Comments and suggestions for authors 2:
I have read the revised manuscript and have the following suggestions even though some of them have been improved.
Corrections requested by the referee 2
Q1. The English writing has to be improved, e .g. the mathematical formulae or mathematical symbols should be prepared in mathematical style, e.g in page 2, v=0. It should be $v=0$ or Italian style v=0. Please modify them completely.
- A major revision has been performed and almost all the manuscript has been rewritten.
-We have prepared the mathematical formulae or mathematical symbols in mathematical style.
-We have been modified the “v” to “v” in all the text.
Q2. The authors only answered me the use of Eq. (1), but the authors did not answer my questions, the wave function, and exact solution? What is the mathematical expression of H_{int}? Only mention the Fermi program is not enough.
- We have simplified the explication of the using of Fermi's golden rule and the other expression is written in general form.
-This paragraph explains more the Fermi model:
For isolated states, the undulations in the potentials clearly reflect the nodal pattern of the Rydberg state involved and the magnitude is fixed in the Fermi approach by the electron-ground-state atom scattering length. When several atomic states are close in energy, in the Fermi model because of the factorizable nature of the interaction, only a single non-zero potential emerges from the remaining flat manifold.
-We added this paragraph:
“To determine the transitions between a vibrational level and another level of a bound state, it is necessary to perform a calculation of the transition probability.
Consider a system whose unperturbed Hamiltonian H0 Eigen values En and Eigen states. The transition probability of a bound vibrational state towards a continuum state, under the effect of a disturbance W (external field) is given by Fermi's Golden Rule:
|
where ρ(E) is the density of states in the continuum such that ρ(E) dE is the number of states in a energy interval dE, and the matrix element of the disturbance W.
The probability of transition per unit time is written:
|
The transition probability makes a sense when the perturbation is applied for a sufficient interval of time () for the system to feel the disturbance.”
Q3. It seems that many French or other language words were used in the text, e.g. Adiabatique, Exacte, etc.
-You are all right, we have been corrected all these mistakes in the text.
Q4. In Table 2, what is representive of the "Bonded-free Exact"? The difference between "Bonded-free Exact" and "Bonded-free F.C." is too big. Please explain it in detail. The similar problem is Table 3. In Table 4, v=0-40, "Bonded-free Exact" is zero, but after v=41, it is not equal to zero. Why?
-We have recomputed the result of the radiative lifetimes and we found the correct result.
- A major revision has been performed and almost all the manuscript has been rewritten.
-We have reordered all the number of the references.
The authors thank the referee for its careful reading of the manuscript and its comments and suggestions.
Author Response File: Author Response.pdf
