A paper published in august 1995 by the Reverend Laurentin in the weekly "Famille Chretienne" (in French) describes a tentative explanation of the much controversial datation of the Shroud by J.B.Rinaudo, who is both a Catholic priest and a teacher of physics. Rinaudo surmises that simultaneous fluxes of protons and neutrons could explain at the same time the imprint on the cloth (by the protons) and the 13-century slip of time of the carbon14 nuclei (by the neutrons).
Through experimentation conducted in the CEA* laboratories, Rinaudo evaluates at 9.1012 (nine times ten to the twelfth) particles per square centimetre the necessary fluxes, and suggests that they might originate in the spontaneous disintegration of the deuterium nuclei contained in the body of the man in the shroud. Though the first part of this hypothesis is interesting, one cannot but disagree with the disintegration, since deuterium is among the most stable nuclei in universe.( but the half-life of the bare neutron is 12,5 minutes!). Thus we must resort to another origin. The first one at hand is a phenomenon of nuclear fusion, either "hot" or "cold", implying the twin nuclear reactions:
D+D® He3+n+3,27 MeV
D+D® T+p+4,03 MeV
Which provide neutrons (n), protons (p), light nuclei (He3 and T) and kinetic energy carried along by the reaction products.( 1 MeV=1 Mega electron Volt).
To irradiate a cloth of 5 square meters (order of magnitude) with a flux of 9.1012 particles/cm², one needs 9.1017 reactions (using only a few micrograms of deuterium, a tiny part of the body content ), giving off an energy of 3,.28.1018 MeV, or 525 kilojoules ( to simplify our point, we neglect in a first approximation the contribution of the highly energetic secondary reactions with reaction products He3 and T ). Translated in equivalent TNT, this energy amounts to 125 grams of high explosive. To explain the shape of imprint on the cloth, the source of radiation should be punctual rather than distributed. So, this energy is enough to cause a conspicuous "flash", but also a severe blow to a body already bruised and wounded by the flagellation and the crucifixion. As a standard of comparison, the Israeli secret services burst off terrorist Ayache with 50 grams of explosive concealed in his Motorola phone.
Moreover, nuclear fusion implies very special conditions of temperature and pressure, and eventually some catalyses such as palladium, which are not found in the body in such quantities. These are the reasons why we may think that much research work is needed still to get a convincing explanation of the shroud case, hence possibly the cautious silence of earnest scientific people about this controversed datation.
As regards the C14 datation itself, besides the 3 labs officially in charge of the analysis (Oxford, Tucson and Zurich ), a 4th lab got independently the same results (years 1260/1390). I mean the Centre d'Etudes des Faibles Radioactivites ( joint lab CEA/CNRS**), of which one can hardly question the experimental know-how and the scientific righteousness.
*CEA: Commissariat a l'Energie Atomique (French Atomic Energy Commission)
**CNRS: Centre National de la Recherche Scientifique