In reply to Eric Walker's message of Sat, 6 Jul 2013 18:08:52 -0700: Hi, [snip]
>This point reminds me of some related questions that I've had: > > - In a system with lots of energy available, are endothermic reactions > just as likely as exothermic reactions, all else being equal, provided the > energy to be consumed in the reaction in question is sufficiently small > (e.g., 0-1 MeV)? Or are exothermic reactions greatly preferred? I think it's pretty safe to say that any reaction that is energetically possible has some chance of happening. Relative chances (i.e. branching ratios) get harder to predict. However faster processes generally win out. >It seems > like nothing but the cross sections would be relevant here, and you could > easily have an equilibrium set up between an endothermic and an exothermic > reaction if there was enough energy in the system. > - Is the cross section of a fusion reaction proportional to the release > in energy? All else being equal (and it rarely is ;), that seems to be so. I look at it from this point of view: Larger energy release => Larger spatial energy gradient, i.e. stronger force => greater acceleration => likely to happen sooner => Larger cross section. I was just looking at some n(x,alpha)y reactions, and I noticed that the point where the neutron capture cross section roughly equals the cross section for alpha emission is roughly when x = sulphur (though this varies considerably from one isotope to the next), so I suspect that this would likely also be roughly the upper limit for H(x,alpha)y reactions, where the H is an electron shielded proton. Farther toward the middle of the table, capture reactions tend to rule over fission reactions, e.g. The radiative capture cross section for thermal neutrons for 43Ca is 11.6 barns, whereas the alpha emission cross section for thermal neutrons is only 25 milli-barns (i.e. more than 400 times smaller). Clearly by the time one gets to Calcium, fission is essentially no longer a serious contender. This is despite the fact that the capture reaction depends on gamma emission, while the p->alpha reaction produces a fast particle according to:- n+43Ca => 40Ar + 4He + 2.278 MeV Note however that the radiative capture cross section for 26Al is already much larger than either the n->p reaction or the n->alpha reaction. The cross section of the particle reactions seems to be strongly enhanced when the final nucleus is exceptionally stable. Not coincidentally, these are also the reactions that release the most energy. Also capture reactions tend to get preference when the speed of the initiating particle is low, while fission reactions tend to prevail at high initial particle energies. I think the take away lesson from all this is that for shielded proton reactions, capture reactions are most likely (because the initiating particles are very slow), and the cross section is considerably enhanced when another particle is available to carry away the energy. Regards, Robin van Spaandonk http://rvanspaa.freehostia.com/project.html
