Gone fission - where does the energy of the neutrons come from

[Andrew Mason]

I have been having an https://www.physicsforums.com/showthread.php?t=145867&page=3" with Morbius on the Nuclear Engineering board about whether the energy released in fission is from the nuclear force or the coulomb force. This quote from Feynman suggests that the energy is from the coulomb force:

" There is another question: "What holds the nucleus together?" In a nucleus there are several protons, all of which are positive. Why don't they push themselves apart? It turns out that nuclei there are, in addition to electrical forces, nonelectrical forces, called nuclear forces, which are greater than the electrical forces and which are able to hold the protons together in spite of the electrical repulsion. The nuclear forces, however, have a short range - their force falls off much more rapidly than 1/r2. And this has an important consequence. If a nucleus has too many protons in it, it gets too big, and will not stay together. An example is uranium, with 92 protons. The nuclear forces act mainly between each proton (or neutron) and its nearest neighbor, while the electrical forces act over larger distances, giving a repulsion between each proton and all of the others in the nucleus. The more protons in a nucleus, the stronger is the electrical repulsion, until, as in the case of uranium, the balance is so delicate that the nucleus is almost ready to fly apart from the repulsive electrical force. If such a nucleus is just "tapped" lightly (as can be done by sending in a slow neutron), it breaks into two pieces, each with positive charge, and these pieces fly apart by electrical reuplsion. The energy which is liberated is the energy of the atomic bomb. The energy is usually called "nuclear" energy, but it is really "electrical" energy released when electrical forces have overcome the attractive nuclear forces.

Morbius has persuaded me that Feynman overstated and oversimplified things. Also Feynman's description of the uranium nucleus is really not accurate (since U-235 or 238 are both quite stable). Morbius maintains that, while some of the energy is from the coulomb potential, most of the energy in fission comes from the nuclear energy produced when a neutron is absorbed by the nucleus.

My question is this: where do the energetic neutrons come from in fission? If the energy comes from the nuclear force yanking the neutron in and giving it such tremendous energy, how is it that this energy is sufficient to not only free more than one other neutron from the nucleus (which would have to overcome their binding energies which would be at least as great as the binding energy ofthe incoming neutron) but to also give the free neutrons more kinetic energy than the incoming neutron had?

AM

 

[Meir Achuz]

I have been having an https://www.physicsforums.com/showthread.php?t=145867&page=3" with Morbius on the Nuclear Engineering board about whether the energy released in fission is from the nuclear force or the coulomb force. This quote from Feynman suggests that the energy is from the coulomb force:


Morbius has persuaded me that Feynman overstated and oversimplified things. Also Feynman's description of the uranium nucleus is really not accurate (since U-235 or 238 are both quite stable). Morbius maintains that, while some of the energy is from the coulomb potential, most of the energy in fission comes from the nuclear energy produced when a neutron is absorbed by the nucleus.

My question is this: where do the energetic neutrons come from in fission? If the energy comes from the nuclear force yanking the neutron in and giving it such tremendous energy, how is it that this energy is sufficient to not only free more than one other neutron from the nucleus (which would have to overcome their binding energies which would be at least as great as the binding energy ofthe incoming neutron) but to also give the free neutrons more kinetic energy than the incoming neutron had?

AM

Most of the energy released in fission is from the Coulomb energy difference.
This can be verilfied either by comparing Coulomb energy for two uniformly charged spheres with R=1.2 A^{1/3} with the original sphere of uranium, or by calculating the Coulomb energy for two touching spheres. Most of the energy shows up in the nuclear mass differences. The energy carried off by neutrons is small compared to either the mass differences or the Coulomb calculation (which are comparable). The actual mechanism by which an iindividual neutron gets its escape energy may be related to the nuclear interaction,but the energy involved in that is only a small part of the destructive power.

 

[Astronuc]

It is generally accepted that the nucleus of a fissile nuclide, when excited by the absorption of a neutron, then fissions when the Coulomb repulsion of what becomes the two new nuclides (fission products) overcomes the nuclear binding forces. Approximately 168 MeV of the 198-207 MeV released during the fission process is manifest in the kinetic energy of the two radionuclides. The two or three fission neutrons share about 5 MeV. Prompt gammas account for about 7 MeV. Decay of fission prodcuts release 8, 7 and 12 MeV in the form of betas, gammas and neutrinos, respectively.

Gamma-rays from the absorption of neutrons contribute about 3-12 MeV.

The nuclear energy contributes to the strength of the Coulomb repulsion, because it is the nuclear binding that pulls the nucleons 'close' together, which means the Coulomb forces are significant.

When a neutron is absorbed by a fissile nucleus, it is generally assumed that the nucleus begins an oscillation in which two charge distributions form, i.e. it departs from a effectively spherical charge distribution. At some point the separation (distance) between the charge center is such that Coulomb repulsion exceeds the nuclear attraction and two nucleir are formed. The two or three (and rarely four) neutrons either escape from the fissioning nucleus, or they are released from either fission product (radionuclide). There are several nuclides which release 'delayed' neutrons as decay products, rather than gamma radiation, e.g. Br-87. The fission process takes about a microsecond or less.

Also it is possible that U-235 absorbs a neutron and does not fission, but rather the excited nucleus, U-236, emits a gamma ray and is stable. U-236 may absorb a neutron to form U-237, and both U-236 and U-237 decay by beta emission to from Np-236 and Np-237 respectively. Similary, Pu-239 may fission or it may decay to more stable Pu-240, and Pu-240 may absorb a neutron and decay to Pu-241, which is fissile.

Nuclides like U-238 and Pu-240 require fast neutrons to fission.

 

[Andrew Mason]

When a neutron is absorbed by a fissile nucleus, it is generally assumed that the nucleus begins an oscillation in which two charge distributions form, i.e. it departs from a effectively spherical charge distribution. At some point the separation (distance) between the charge center is such that Coulomb repulsion exceeds the nuclear attraction and two nucleir are formed. The two or three (and rarely four) neutrons either escape from the fissioning nucleus, or they are released from either fission product (radionuclide). There are several nuclides which release 'delayed' neutrons as decay products, rather than gamma radiation, e.g. Br-87. The fission process takes about a microsecond or less.

So where does the energy of the prompt neutrons come from - those produced in the fissioning process itself? It can't come from coulomb repulsion directly since the neutron has no charge. What gives them enough energy to overcome their binding energy to other nucleons and fly away alone?

AM

 

[Astronuc]

So where does the energy of the prompt neutrons come from - those produced in the fissioning process itself? It can't come from coulomb repulsion directly since the neutron has no charge. What gives them enough energy to overcome their binding energy to other nucleons and fly away alone?

That's a good question, and I'll have to look into it further. Either its from radionuclides which have excess energy, or perhaps they are the neutrons which are being 'pulled' by both fission product radionuclei, and the net force from both radionuclides slingshots the individual neutrons out from the region between the two charge/nuclear regions that will form the new nuclei. Pardon the crude description.