A Program Library for Computing Pure Spin–Angular Coefficients for One- and Two-Particle Operators in Relativistic Atomic Theory

Round 1

Reviewer 1 Report

The manuscript entitled 'A Program Library for Computing Pure Spin-Angular Coefficients for One-  and Two-Particle Operators in Relativistic Atomic Theory' by G. Gaigalas reports on a program library for computing pure spin-angular coefficients in jj-coupling that are used in the expression of matrix elements of one- and two-particle operators for the evaluation of atomic structure relativistic Dirac-Coulomb or  Dirac-Coulomb-Breit hamiltonian matrix elements, and different atomic properties in the relativistic theory framework. The method used for the elaboration of the different library's subroutines is based on the combination of the second quantization, the quasispin and the irreducible tensorial sets techniques. The author is a well-known (I would say the) world expert on the above-mentioned approaches and on their  implementation in the different GRASP packages. I have though a general remark concerning the structure of the manuscript; it should be more "linear" to ease the reading. Indeed the reader has to jump to subsequent sections in too many places in the text and go back and forth. For instance, in Subsection 3.1.1, it is written that the detailed description of the routine WJ is given in Subsection 3.3.3; why not given it directly in Subsection 3.1.1 as a "subsubsection" 3.1.1.1, and so on and so forth ...  I would thus recommend this manuscript for publication provided the author consider, in addition to the above-mentioned general remark on the manuscript structure, the following minor remarks/corrections:

- Page 1, line 5: please add 'the' just before 'General ...'.

- Page 1, line 7: please delete the comma just before 'too'.

- Page 3, line 76: please add 'the' just before 'GRASP-2018'.

- Page 3, line 77: please delete the comma just before 'too'. 

- Page 5, line 136: please add 'total' just before 'angular'.

- Page 5, Table 1, in the second part of the second group, please define the triangular delta as you did for the [Q]=(2Q+1) notation. 

- Page 6, formula (9): please define the notation J_12...u-1.

- Page 6, line 143: please replace 'a=max(i,j)' by 'b=max(i,j)'.

- Page 10, line 198: Greek symbol capital Xi is not defined.

- Page 11, line between 215 and 216: please replace 'sumbatrix' by 'submatrix'.

- Page 11, formula (31): please replace the operator 'g' by 'g_12'.

- Page 12, line 255: beta should be also defined like alpha.

- Page 12, line 259: please replace 'quantuma' by 'quantum'.

- Page 12, end of line 267: replace 'a(def=)n_il_ij_i.' by 'b(def=)n_il_ij_i.'.

- Page 13, legend of Figure 1 (and all the other figures): please give more details such as what are the numbers in the different boxes, what is the meaning of the colored box , etc ...

- Page 16, line 337 and 338: the subroutines SPEAK, TALK and WW1 do not appear in Figure 3. Why?

- Page 17, line 355: '... off-diagonal matrix elements' ... of what type of operator? Two-body?

- Page 22, lines 402 and 415: please replace 'RECO2' by respectively 'RECOONESCALAR' and 'RECOP00'.

- Page 26, lines 505 and 506: please move 'are satisfied' just after '(see Tables 1, 2, and 3)'. 

- Page 28, lines 580, 581, 586, 587: please add '(see (92))'.

- Page 29, line 612 and page 29, line 613: please add '(see (93))'.

- Page 29, line 630: please add '(see (94))'.

- Page 30, Table 4: 'Nr' should be defined.

- Page 30-31, lines between 635 and 636: these lines should be part of an additional table (Table 5) and this new table should be introduced in the text. Also, concerning 'ribojj_C', 'ribojj9_C' and 'ribojj11_C', 'or' should be replaced by 'for' and '1/2-9/2' by '1/2-7/2'?

- Page 31, line 659: replace 'All this, in its entity,' by simply 'It'.

- Page 32, line 675: please add a full-stop between 'matrices' and 'Hence'.

- Page 32, line 677: please replace 'leading' by 'lead'.

Author Response

Dear Reviewer,

Thank you very much for your valuable comments. I have taken all of them into account and am sending a revised version of the article. All modifications are marked in red.

In addition, I would like to draw your attention to the comment “For instance, in Subsection 3.1.1, it is written that the detailed description of the routine WJ is given in Subsection 3.3.3; why not given it directly in Subsection 3.1.1 as a "subsubsection" 3.1.1.1, and so on and so forth”, where, thanks to it, I have inserted the sentence “The program library is divided into three routines groups, METWO, REC, and SQ according to the  peculiarity of the expressions (8), (21), and (24).” (see line 280).

Best wishes,

Gediminas

Reviewer 2 Report

Based on the combination of the second quantization and quasispin techniques with the angular momentum theory and with the generalized graphical method, the method of irreducible tensorial sets, the author developed a program library for computing pure spin-angular coefficients for any one- and scalar two-particle operator, which have many advantages comparing with traditional approaches. I recommend the article for publication.   I have the following comments:

1. The author mentioned several advantages of the new method. Is it possible to describe the CPU time reduction comparing to the traditional approaches to show its advantages? 

2. I wonder if there are any restrictions in using the program, if yes, the author should point it out in the paper. Or, is there anything could be improved in future work on this topic?

3. There many equations in the paper. To be honest, it is difficult to check them carefully during the limited time. 

Author Response

Dear Reviewer,

Thank you very much for your valuable comments. I have taken all of them into account and am sending a revised version of the article. All modifications are marked in red.

Best wishes,

Gediminas