Decay Time Estimates by a Continuum Model for Inorganic Scintillators
Round 1
Reviewer 1 Report
The article by Fabrizio Davi entitled „Decay time estimates by a Continuum model for Inorganic Scintillators” presents a very interesting theory, in the frames of continuum mechanics, providing means to estimate the limiting terms in decay lifetime of selected scintillators. The estimated lifetimes agree very well with the reported literature data.
The experimental results concerning carrier mobilities are scarcely found in the literature resources. The presented theory also provides indirectly estimates on excitation carrier mobilities for the studied four types of scintillator crystals. Application of this theory to other scintillators would not only give insight into excitation carriers mobilities, seldom reported due to difficulties in experimental measurement, but also will be a new tool, combined with more detailed model systems, in design of faster scintillators.
Taking into account the above mentioned attributes, I recommend publishing this valuable and elegant piece of theory.
From the technical remarks, it is worth considering to make some very minor amendments. For the readers outside of the field, the readability of the article and following of thoughts of the Author would be enhanced if an appendix glossary with definition of symbols and their units were provided as well as detailed description of the two tables (in the caption). The renumeration of references (according the order in which it appear throughout in the paper) would be also required to augment readability.
Author Response
Author Response File: 
Author Response.pdf
Reviewer 2 Report
While overall English is not bad, there are few problems with it. When referring to other papers author uses expression “into [ref]” which is wrong, and should be just “in [ref]”. (Sidenote – not all uses of “into” are wrong – for example when discussing substitution of a new set of variables into eq. 7 use is correct) There are other idiosyncrasies probably from author’s native tongue, which at times lend to the lack of clarity.
While discussing relation of this paper and reference 8 it’s not really clear if author had in mind that details omitted in 8 are provided here or other way around. Quick glance leads one to believe that ref. 8 is the more detailed case.
Then while discussing notation it’s utterly unclear what author understands as capital letter (But it’s not capital letters. Probably upright?), and to add insult to injury – meaning of symbols indeed depends on case, which makes matter all the more confusing.
References are not numbered in order of appearance, which is slightly confusing. Also, while referencing things author almost never states what is referenced (equation or reference). Thing would be a lot clearer if it would be explicitly stated.
For example the sentence “It is important to remark that the Diffusive model, however, is rarely used alone; rather it is coupled with some reactive terms as in [14] and [12]; moreover, the equations proposed into [31], [17], [19] and [20] can be viewed as particular cases of (34)2.”
would be a lot clearer written like that:
“It is important to remark that the diffusive model, however, is rarely used alone; rather it is coupled with some reactive terms as in refs [14] and [12]; moreover, the equations proposed in refs [31], [17], [19] and [20] can be viewed as particular cases of eq. (34)2.”
The example sentence gives another example of problem with editing – meaningless capital letters. That is writing “Diffusive” instead of just “diffusive”. There are multiple places in which such names written with capital letter are used. This only reduces readability while giving no benefit at all.
Derivation that follows is in contrast rather clearly described. (There are some quirks, but they do not influence clarity of text too much). Author is fully aware of limited applicability of continuum models, and gives bounds of applicability to his model. This is scientifically sound description.
The paper is properly referenced, and well taught out.
Summarizing: I think that this is a good paper that needs a lot of English editing to whip it into shape. I think it’s worth publishing after necessary improvements in English editing.
Author Response
Author Response File: Author Response.pdf
Reviewer 3 Report
The present work reports a model of scintillation decay time. I think the author uses valid assumption and mathematical approximation. Importantly, the calculation results well match with experimental values. Therefore, I recommend publication after taking into account below comments.
r is not defined. What’s density?
w.r.t. is not defined. Please use an official written language in scientific paper.
How do you calculate from (4) to (5)? In (4), you have two E-related factors such as E and exp(-E), and it is impossible to solve analytically to obtain (5) without some approximations. Please explain the derivation processes.
In (9), why is e2 multiplied to n? Would you like to explain physical or mathematical reason? In addition, would you like to explain the derivation process of (9)? Without some approximations, z-related terms will remain. Do you approximate z’ = ez, as same as l and r?
How do you deduce (15)? You define ∇j = enq/e, and (∇j)2 = (enq/e)2.
In (23), would you like to explain the meaning of scintillation potential?
In the derivative version of (24), where does “c” go and what does “c” mean?
In NaI, do you mean Tl-doped NaI or undoped NaI?
In results of BaF2, the emission origins of slow and fast components are self-trapped exciton (STE) and Auger-free luminescence (AFL), respectively. To my understanding, your model does not consider the branching ratio of carriers toward STE or AFL. How do you calculate 620 and 0.26 by using the same parameter of BaF2 itself?
For table 1, please put actual (experimental) scintillation decay times.
This is just my interest. In your model, you do not distinguish the intrinsic type (BaF2) and dopant type (Ce-doped ones) scintillators. In the former type, it will be something like a condition of 100% doping (emission centers) while the latter type has 0.1~1% emission centers. The scintillation occurs at emission centers, and in the latter case, other elements will be just an obstacle for the luminescence. Does such a difference of the condition affect your model? A similar questions arises for the treatment of carrier trapping (storage phosphor-like). In scintillators, some of the carriers can recombine at emission centers, and some others are trapped, so the blanching ratio of immediate emission/trapping is important.
Author Response
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Author has significantly improved readability, which was my only qualm with this paper. Furthermore glossary is nice touch, and improves readability even further. I believe it can be published in present form.
Reviewer 3 Report
I convince all the responses from the author.
