Display MoreTHH Huxley " These two equations are inconsistent"
They appear inconsistent to you because they refer to different things
My interpretation is that Equation 6 yields the unscreened reactivities (UR)
which are graphed in Fig 1.
Equation 14,15 multiplies these UR by the screening factor to give the screened reactivities (SR) as shown in Fig 2.
I do not think that 3 research physicists working collaboratively on a research paper for one year
are going to make an error that can be 'debugged' up in 1hour by a pharmacist like me or any other layman scientist.
Perhaps not unless you pay attention to the equations. I agree they refer to different things.
(6) is the unscreened reactivity - I'm sure we both agree.
(15) is stated to be the reactivity enhancement factor fR(kT). There is no ambiguity. It is a scalar (no units) as expected for an enhancement factor. It is clearly inconsistent as explained below.
(14) Unremarkably gives the screened reactivity as the unscreened value from (6) multiplied by fR(kT) from (15). But then the T dependence from fR(kT) is completely inconsistent, because fR(kT) dependence on T is not compatible with screening being (roughly) equivalent to a decrease in Eg by roughly U0. (Nor an increase in average projectile energy kT by a factor of roughly U0).
The intuitive argument here is that whatever the screening, at low projectile energies (low T) increasing the projectile energy kT must increase, not decrease, the cross-section. That is obviously not true in (14) as derived from (6) and (15), on a cursory comparison of the exponents. And Figure 2 underscores this obvious inconsistency - although it is not so obvious because the horizontal axis of Fig 2 is obscure - is this under conditions of varying T, fixed U0 or varying U0, fixed T? From context I believe the former. This error is so large a physicist with math background would be unlikely to miss it on grounds of both physics and maths. However, anyone can make mistakes.
What I've said follows. If you'd like to make your criticism above more precise I could reply more precisely, but you are a bit vague so I'm not entirely sure what is your point - (14) and (15) are different as above, and I'd guess you agree with my definitions since they come from the paper.
I do not agree with your "don't ask, just accept authority" judgement that you propose here. We do not know that these authors are an authority. My own background in Math is not necessarily worse than that of 3 random experimental research physicists. In any case that is not the point. Science is judged based on merit, not the credentials of the authors. The error here is obvious and clear. The paper is inconsistent. I've e-mailed the corresponding author.