Nitrogen vs. Carbon re: Production of 14c

Dr. Paul Giem, carbon-14 researcher and former assistant professor of ermergency medicne at Loma Linda University, had originally published this statement: "nitrogen-14 captures neutrons 110,000 times more easily than does carbon-13..." (Giem, P. 2001. Carbon-14 content of fossil carbon. Origins 51:6–30). He has now corrected it to: "nitrogen creates carbon-14 from neutrons 110,000 times more easily than does carbon..."

Here is an explanation from Dr. Giem via his private communication to Real Science Radio, June 11, 2013:
 

Supposing that one has a given material that is mostly carbon but has a small amount of nitrogen in it, and it is irradiated with neutrons. The question is, what percentage of nitrogen would cause the production of carbon-14 from nitrogen to equal that from carbon? This will be weight percent rather than molar percent. Or a related question is, if we start with equal weights of carbon and nitrogen, which produces more carbon-14 from neutrons, and how much? The second question will give us the number 110,000. and this is how.

The production of carbon-14 from a given isotope is given by 
 
phi * sigma * n,
 
where phi is the neutron flux, sigma is the cross-section of the nuclide in barns, and n is the number of atoms being irradiated. Notice that by hypothesis, phi is the same for both carbon and nitrogen, which is true for small or mixed samples. So (using ( ) for subscripts).
 
14C(N)     phi   sigma(14N) * n(14N)         sigma(14N) * n(14N)
______ =  ___  ___________________ =  ___________________
14C(C)     phi   sigma(13C) * n(13C)         sigma(13C) * n(13C)
 
Nitrogen is 99.636% 14N, which has a cross section for the production of carbon-14 of around 1.8 barns (the smallest number I have seen is 1.74 barns, and we will use it). Carbon is 1.07% 13C, which has a cross-section for the production of carbon-14 of 1.22 millibarns or 0.00122 barns.

For 12.011 grams of either carbon or nitrogen (chosen to equal 1 mole of carbon), the number of carbon atoms is 6.02 x 10^23, and the number of nitrogen atoms is [12.011/14.0 (the molecular weight of nitrogen which is mostly 14N)] * 6.02 x 10^23. Since Avogadro's number is on both sides of the fraction, we can cancel it out, and obtain
 
                  1.74 barnes   *  (12.011 / 14.0) moles * 0.99636
             =  __________________________________________  =  114,000
                  0.00122 barns            *  1 mole             * 0.0107
 
Since we probably are not justified in more than two significant figures here, I rounded it out (down) to 110,000.
 
One may argue about the precise percentage, but I have it within 10 percent, and the estimate is low. The point remains. A specimen with 1/100,000 nitrogen content by weight (or 0.001%) should have just over double the amount of carbon-14 than a pure carbon specimen, if they are both irradiated by the same neutron source. A specimen with 1% nitrogen (not unheard of for coal) should have 1,100 times as much carbon-14 as a pure carbon specimen, with equivalent neutron irradiation. Thus my point about, in theory, the carbon-14 content of coal varying wildly with the nitrogen content, is a valid one. If it does not happen in practice, it strongly suggests that the neutron theory is defective.
 
During our RSR interview (rsr.org/giem) Dr. Giem criticized his own quote on this topic. As originally published, it stated that,"nitrogen-14 captures neutrons 110,000 times more easily than does carbon-13..." which he indicated is slightly inaccurate. As stated on air, and again here via private communication, Dr. Giem wrote:

That phrase should read, 
"since nitrogen creates carbon-14 from neutrons 110,000 times more easily than does carbon..."
 
This is a mistake that illustrates the deficiencies of peer review. The article did go through peer review, but it was mostly friendly, so when I said things that were mostly believable, the work was not sufficiently checked. Once it was publsihed, it was then (peer) reviewed by people who were unfriendly and disinclined to take my word for it, and they found that obvious error. But they stopped there, not asking if I might have a point, and instead attempted to use the error to discard the entire argument. So in one case the peer review was too lenient, and in the other case too harsh.
 
Thanks Dr. Giem!
-Bob Enyart
Real Science Radio