Seth I am going to get you one day for sending me a bunch of comments even more detailed than Albert's at the 11th hour, but until that day... **************************************************************************** * Seth's email **************************************************************************** Gentlemen, I hope the following is helpful. I haven't thought about these issues in a long time.... General comments: First, sorry for the delay and absolute last minute e-mail. Even though systematic errors are discussed in the original paper, I think a cursory sentence in this paper to our understanding of the potential systematic errors is important for future readers who may only glance at the scintillator paper. For instance, I think it would be nice to add a sentence about the chamber background and our background subtraction method and another sentence about the grids and our secondary electron production suppression methods. At the very least I would say that we have thought about these issues and they are addressed in our previous paper. >>>>>>>>>>>>>>>>>>>>>>Added the following sentence: ``Effects due to backgrounds from X-rays, and multiply backscattered electrons were also discussed in detail in our previous work, resulted in systematic uncertainties at the 3-5\% level at $q=0.2$ for the highest beam energy considered, and were considerably smaller in every other case.'' And in the current mode section made significant changes based on some of your comments below which I think address this issue. Second, to interpret the scale factors in the monte-carlo comparisons we need a systematic error specific for the double-differential normalization. Table 1 lists all the systematic errors for the NIBF measurement with the silicon detector, but, isn't that an over-estimate for the double-differential distribution? >>>>>>>>>>>>>>>>>>>>>>12% is on average correct for all the double-differential distributions. Removed explanation attempted in figure caption and replaced with: Aside from target deterioration, which is specific to the case of scintillator, these systematic uncertainties were described in detail in our previous work~\cite{bib:prcme}. The effects listed in the upper portion of Table~\ref{tab:simode} refer to results for the observable $\frac{1}{N_e}\frac{dN}{d\Omega dq}$, and average 12\%. The effects in the lower portion refer to extrapolation uncertainties encountered when integrating these data over $q$ and/or $\theta$, and these must be added in quadrature to those above when considering our results for $d\eta/d\Omega$ and $\eta$ from silicon detector mode. For extrapolation over $q$, the uncertainty is larger for lower beam energy, as the finite detection threshold becomes more important; hence the 20\% value refers to beryllium at 43.5~keV incident energy, since the beryllium data is more peaked at lower $q$, while the 6\% value refers to data taken with 124~keV incident energy. Considering the range given for the total systematic uncertainty, the lower bound (12\%) refers to all observations of $\frac{1}{N_e}\frac{dN}{d\Omega dq}$, while the upper bound (23\%) refers specifically to the extraction of $\eta$ from beryllium at 43.5~keV, where extrapolation uncertainties dominate. More detailed comments: Abstract: Sentence reads "and those challenges were addressed in detail." Change to "and those challenges are addressed in detail." to maintain consistent tense. First paragraph section II: change "Two modes of running were used where backscattering data were acquired." to "Two modes of acquiring backscatter data were used." Clearer sentence structure. I would change "sensed" in the fourth sentence in that paragraph to "measured." >>>>>>>>>>>>>>>>>>>>>>>>>>fixed those three Third paragraph section II: The second sentence beginning "The range for 43.5keV electrons ..." is not clear to me. The effect of the aluminum is actually a very tricky problem. I absolutely agree that the aluminum over-layer is not going to influence the silicon detector backscatter measurements. However, it may very well influence the current integration measurements. In either case I think a path length argument may be weak. As the electron beam penetrates the target some of the particles will backscatter, from both multiple scatter and single ruther-ford like events. But, the cross section for elastic scattering grows as the energy falls, so, the backscatter "rate", so-to-say, is not uniform across the penetration depth of the particle. Very few electrons will return from the "entrance" layer of the target, and very few will return from the "end" layer of the target. Most will come from somewhere in the middle, and how this relates to the electron "range" (which, to my understanding, is an undefined concept for electron transport is unclear. An even bigger problem: Most of the secondary electrons which are not suppressed by the grid (i.e. energies above 50eV and below 1keV) are liberated in a very thin layer on the surface of the material. But, it is an even worse situation because the cross section for liberating secondaries in low z materials is FAR greater than the cross section for rutherford like scatter. In other words, for thin targets, a current integration like measurement of NIBF will be dominated by the secondary electron flux, by potentially several orders of magnitude, for sufficiently thin foils. And to make life even more complicated, the secondary electron cross section falls far slower with energy than the rutherford cross section. A path length argument does not really address these issues. But it's not clear in my mind yet how to think about them. However, since this paper is only about scintillator, and since the aluminum over coat is what makes it possible, it is probably worth thinking about some more. Here are a few points we could make. First, we would expect the electron beam to loose 80eV by passage through 500\AA\ of aluminum (ESTAR) so the aluminum can not by any stretch of the imagination change the backscatter from the scintillator itself by changing the incident energy. Second, we expect the single-collision elastic scatter from the aluminum layer to add 0.0004 to the scintillator NIBF @50keV. (I can provide details to this calculation later, but, I thoroughly believe it and it is based on the numerical calculations of the elastic cross section, interestingly enough it is also 3 orders of magnitude smaller than what we see from scintillator .. maybe the path length is not so bad... :) ) Based on some PENELOPE simulations I did a very long time ago I would expect the secondary yield from the aluminum layer for electrons with energy above 100volts to be about 0.004. That's 10% of the scintillator NIBF! I propose two options. First, increase the systematic error budget for the current integration technique to incorporate this additional uncertainty. Second, perform some additional monte-carlo studies which incorporate this thin aluminum layer and can model the secondary production from it. Since we know these secondaries are not interesting from the ultimate monte-carlo point of view (which from my point of view is the ultimate point of the paper) I would argue for the first course. But, I could revive my penelope simulations after I return from Mongolia at the end of August. >>>>>>>>>>>>>>>>>>>>>>>>>>>The 0.0004 number is <1%, in agreement with statement currently in there. The 0.004 (10%) number agrees with 2 * 5%, which is applied to the silicon detector mode data when extrapolating from 10 keV to 50 eV. My counter-proposal is therefore to include an additional systematic uncertainty on the current-mode data in the amount of (10%-4%) = 6% to account for possible _differences_ for yields in the current-mode measurements with or without the Al layer. The 10% is the 50 eV to 10 keV Penelope estimate for Be or Scint. The 4% is the Penelope estimate for Si. The following statements were modified/added to reflect this: ``The effect of the aluminum layer can be estimated by comparing the thickness of the Al layer to the mean range of the electrons. The range for 43.5~keV electrons in plastic scintillator is 30~$\mu$m \cite{bib:estar}, which is three orders of magnitude smaller than the mean range. Backscattering from the Al itself, or rescattering from the Al, is therefore suppressed at a level below 1\%, even for the lowest energy incident electrons reported in this work. This was confirmed in Monte Carlo studies of backscattering from thin layers \cite{bib:seth}.'' The above quote was moved into the ``silicon detector systematics'' section from the ``intro'' section. ``An additional systematic effect due to the Al coating on the target arises, due to differences arising from the coating in our unmeasured region (50 eV to 10 keV) which cannot be accessed via altering voltages on components, nor via the silicon detector mode data. From similar considerations to the extrapolation uncertainty for silicon detector mode, we limit possible differences to the 6\% level.'' Added 6\% to table. Deleted comments I could find relating to the total syst. being 7\%. It is now back up to 9\%. Please let me know if you see any old 7\%'s hanging around! >>>>>>>>>>>>>>>>>>>>>>>>>>>>end long comment Back to detailed comments. Section II fourth paragraph: "using an 25 mm^2" should that be "using a 25 mm^2" >>>>>>>>>>>>>>>>>>>>>>>>>>>>fixed Section III, after first paragraph. I would add a description of the chamber, clearly mentioning the secondary electron mitigation techniques. >>>>>>>>>>>>>>>>>>>>>>>>>>>>This was difficult, but likely worthwhile. Also I put it in a different spot: ``In order to characterize and control the effects of low-energy secondary electrons (for our work, defined to be below 50 eV in energy), a wire mesh grid was inserted into the chamber and held at a negative potential. This prevented secondaries from traveling from the chamber walls to the target and vice versa. As with the previous work, a residual correction due to a piece of conducting target rod penetrating the top of the grid must be applied to make the results independent of target voltage (due to secondary electrons created on that piece of the rod). This correction gave rise to a 7\% contribution to the systematic uncertainty in the previous work, and was the dominant uncertainty. For this work, the contribution was reduced to 3\% by reducing the solid angle subtended by the relevant portion of the target rod. This reduced the size of the correction, and hence the systematic uncertainty. Detailed analytical calculations of the effect of the solid angle and its variation with e.g. distance of the beam spot from the top of the target close to the target rod gave additional confidence in this uncertainty. As before, secondaries created on the grid were characterized by monitoring the grid current, and contributed at the 1\% level. '' Section III A second paragraph. Perhaps a simpler sentence: "To ensure the reliability of our current measurements, we compared the measurements of two identical, carefully calibrated current integrators for identical experimental conditions. Our current measurements are consistent at the 3\% level. >>>>>>>>>>>>>>>>>>>>>>>>>>>>Changed somewhat - we had four possible devices: ``To ensure the reliability of our current measurements, we compared the measurements of two different, carefully calibrated current integrators against one another for identical experimental conditions, and in turn cross-compared those measurements against two calibrated picoammeters. Our current measurements are consistent at the 3\% level.'' Section III B: second paragraph: "Detailed analytical calculations of the effect..." I am not sure what this sentence means. :) >>>>>>>>>>>>>>>>>>>>>>>>>>>Mike made an analytical model of the fractional NIBF sensed by the target rod, and hence, how the measured NIBF should vary when you move the beam around. This worked at some level, and it worked very well in a relative sense, giving us additional confidence in the uncertainty we assigned for this ``target rod'' thing (7\% -> 3\%). Section III B: third paragraph: " This would increase the carbon content and hence..." should be "This would increase the relative carbon content and hence ..." Actually this is subtle. If the target is thin enough, liberating hydrogen would reduce the backscatter fraction by reducing the number density of scatterers. The argument only works if the target is greater than saturation thickness (which of course it is). >>>>>>>>>>>>>>>>>>>>>>>>>>>fixed Section III B: fourth paragraph: "This resulted in a contribution..." This what? It's not clear to me. How do the other things in this paragraph generate a systematic uncertainty? >>>>>>>>>>>>>>>>>>>>>>>>>>>>``This limited the contribution to the systematic uncertainty to 1\%.'' Section III B: fifth paragraph: change "level 3%" to "3% level" change "on the chamber" to "in the chamber" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>changed Section III B: sixth paragraph: change "dominant systematic uncertainties are listed" to "dominant systematic uncertainties for current integration mode are listed..." >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>changed Section IV A: second paragraph: here is the first place you start talking about the simulations. I would add a sentence or two describing what we simulated. I.e., we included the silicon detector response, and we included backscatter from the silicon detector itself. You might also want to add a reference for each code. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>added Fig. 1: The GEANT graph (at least in the version I downloaded from the web) is not right. The data and monte-carlo don't agree at the 7/% level. I would take "rebinded" out of the figure caption. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>removed ``rebinned''. What isn't right about the figure? Basically Geant4 sucks. If you're saying the Fig looks bad, it does, and it's because we did a chi2 fit under certain assumptions for the point-to-point uncertainty. A factor of more like 0.95 makes it look ``good''. Section IV B: I would comment on the funny behavior of the NIBF measured with the silicon detector method. Why does it go up at higher energies? That can't be physical. It's within the statistical errors so in some sense it's okay. But still... >>>>>>>>>>>>>>>>>>>>>>>>>>>>>Don't want to go there. Energies below 120 keV are from the turn of the century, renormalized based on a ``Mike factor'' from our summer 2004 data, and we know there were certain funny looking things about those old data. My only statement, if pressed in private conversation or conference talk, would be: yes it's funny, it's likely due to some point-to-point uncertainty which is small compared to the overall normalization uncertainty. I don't think it is worth including a sentence on it in the paper, since it's probably due to a small glitch. I also don't find such an approach too dishonest. The data is there for all to see. Table II: I would make all the scale factors have 2 decimal places. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>made Cheers! Seth