Numerical Investigation on the Thomas–Fermi Model and Its Quantum and Exchange Corrections

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper deals with the Thomas-Fermi model, and proposes an interesting and potentially useful method to solve it numerically. In my view, it could be accepted for publication, after some revision. These are my main comments:

• First of all, there is a problem of language, and a deep revision of the English should be made.
• There is also a problem of presentation, when referring to the equations. For instance, authors should write eq. (1), and not just (1).
• There is also a conceptual problem, which could confuse the readers. The “exchange” correction is also a “quantum correction”. Therefore, the distinction between “exchange” and “quantum” should be better explained.
• The physical meaning of the different quantities should be clearly stated. In particular, the meaning of que quantities $u_i$ and $\psi_i$, and their relation with the original electron potential should be clarified.
• Some of the equations included in the main text should be better presented as numbered equations, separated from the text.
• The method proposed to solve integrals with a singularity is poorly explained at the end of page 8. In my view, this explanation should be improved.

Comments on the Quality of English Language

The quality of the English is inadequate.

Author Response

Please find the attached file.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The paper uses TF and TFC models for calculation of electron potential, energy and pressure for a bulk matter. The authors introduce several computational tricks in order to facilitate numerical solution of the TFC equation. The paper contains many equations derived previously whose physical meaning escapes the reader. In addition, the paper contains a lot of grammar mistakes. Before the paper can be recommended for publication, the authors should fix the English and give physics interpretation of their equations. In addition, the authors should address the following comments.

Equations should be quoted *after* they have been introduced, not before.

Line 71: Not clear if the reference is to Ref. [1], or Eq. (1)?

Eq. (1): x is apparently a dimensionless distance, but it is not defined.

Eq. (3): why there is r_0 in the denominator, instead of r? 

Eq. (4): it just states \phi_{TF}(1)=\phi_{TF}(1). What is the meaning of this?

Caption to Fig. 1: what does A1 mean?

Fig. 1: For what value of Z was the potential calculated?

Line 119: "...taking consideration of coulomb interaction between charged particles within an atom". In addition to poor grammar, there is a physics problem: I think the TF model *neglects* electron-electron interaction.

Line 129 and below: the physical meaning of \delta_1\phi and \delta_2\phi is unclear.
Also, what is the difference between the "quantum" and "exchange" corrections? Exchange *is* a quantum phenomenon.

p. 5, first paragraph: The authors discuss the "quantum" and "exchange" corrections. The reader wonders what is the role of the Coulomb attraction between electrons and positive ions.

Fig. 3: the drop of pressure at higher densities in the TFC model is very dramatic, and the fact that the electron-ion interaction does not play role in it is very surprising. The authors should explain the physical reason for all this. Obviously, they should explain first what is the physical meaning of the "quantum correction" and how it is different from the "exchange correction".

Fig. 3: not clear what the two dashed lines on the extreme right side of the graph correspond to.

I don't see how (26) can be obtained from (25).

 

Comments on the Quality of English Language

The paper contains many grammar mistakes which should be fixed.

Author Response

Please see the attached file.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

In the revised version of the manuscript, the authors have taken into account all the remarks made by the reviewer. As a result, the quality of the paper was significantly improved.

In my opinion, the paper can now be accepted for publication.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have satisfactorily addressed the comments from the first report, and the paper can be published in its present form.