RAR, 1/4/00, revised 9/25/00
Energy Production Reactions
Transuranic Element Fission
Neutron-induced fission of Uranium-235 has a positive Q value of approximately 200 MeV. This Q value results from harvesting approximately 1 MeV/nucleon of binding energy from a compound nucleus of mass 236, since the fission products are each more tightly bound than uranium. In order for fission to occur, the compound nucleus must receive about 1/2 MeV of excitation, causing it to vibrate until "magic" causes the fission fragments to separate. This is called the "liquid drop" model.
Uranium-235 is an odd-A nucleus that fissions with thermal neutrons having essentially zero kinetic energy. The required 1/2 MeV of excitation of the compound nucleus is supplied by the positive l/2 MeV pairing energy of the last neutron, which makes the compound nucleus even-even.
Uranium-238, on the other hand, is an even-A nucleus, which loses the l/2 MeV pairing energy when the compound nucleus becomes even-odd. Hence, this is a fission threshold reaction which only proceeds for neutrons having a kinetic energy > 1 MeV. Half of this amount is needed to supply the pairing energy, and the other half supplies the liquid-drop excitation. The total energy of Q + KE (of the incoming neutron) is shared by the fission fragments inversely proportional to their masses. The incoming KE is essentially negligible compared to the Q-value of 200 MeV.
Fusion is typified by the D-T reaction, where deuterium and tritium ions fuse to form a neutron and an alpha particle. Because the alpha particle is doubly magic, it is extremely tightly bound, causing the Q-value of this reaction to be a positive 17.5 MeV.
Fusion does not occur at low energy because Coulomb repulsion prevents the deuterium and tritium ions from forming a compound nucleus. The reaction cross section is essentially zero. In a star, heating is caused by gravitational compression. As the plasma is heated to an effective temperature of several KeV, the cross section increases because some of the particles strike each other head-on and penetrate the Coulomb barrier. As the temperature is increased further, the cross section increases rapidly as more and more collisions at other incidence angles allow barrier penetration. Once the compound nucleus is formed, fusion takes place and a 14 MeV neutron having 4/5 of the Q + KE (of the incoming particles) is produced. Again, the incoming KE is essentially negligible relative to the Q-value.
Normal anti-neutrino reactions with protons involve the valance up quark, causing it to become a down quark and changing the proton to a neutron, emitting a positron. Likewise, neutrino reactions with the valance down quark in a neutron cause it to become an up quark, changing the neutron to a proton, emitting a negatron. These are the reactions used in large underground neutrino and antineutrino detectors. Cross sections are of the order of 10-42 cm2/neutrino, but it should be noted that the cross sections have a threshold and increase rapidly with energy. Hence, low energy neutrinos would not be detected at all, and the detection efficiency for high energy neutrinos would depend upon their production spectra. The evaluation of the detector efficiency for any particular neutrino source would be highly uncertain and subject to large error because none of these factors are known to high precision.
Fredricksson has proposed a pair of diquark reactions whereby an incident neutrino or antineutrino of sufficient energy is able to create a virtual W particle, which turns one of the quarks in the diquark to its opposite kind. This leads to an unstable final state, which then fissions.
Let us carry the above analogies to the Fredricksson model of neutrino-induced fission of a proton. From the cloud chamber photograph appearing in Gamow's book, it appears that an incident cosmic ray proton (at least the diquark part) is fissioned completely into neutrinos, mesons, electrons and gamma rays. Hence, the Q-value for a proton of mass 1 AMU is a positive 931 MeV. If the reaction can be triggered, it will go to completion.
The excitation energy for any reaction is the total excitation in the Center-of-Mass system. This energy can be supplied by the projectile, the target, or both. For normal neutrino detection reactions, the neutrino has an energy of several MeV and the target is essentially at rest. In the Brookhaven Supercollider, both particles will be accelerated to several GeV and will hit head-on to add the sum of their energies to an essentially zero-energy Center-of-Mass.
For our postulated supercritical neutrino-induced fission of protons in the iron core of supernova SN1987a, we propose that the excitation is supplied to surface protons on the iron nuclei by the gravitational collapse of the atom when the Chandrasekhar limit is passed. Hence, neutrinos with only a few MeV of energy can combine with protons excited to several hundred MeV by gravitational pumping. Like the liquid-drop model of neutron-induced uranium fission, we propose that only a small fraction of the Q-value of the final reaction is needed to cause the reaction to go. Like neutron reactions, the cross section should be related to the "size" of the reacting particles. Hence, we believe that once the threshold energy is reached, the neutrino cross section will be of the order of 10-42 cm2. For each proton fissioned, the energy released would be 931 MeV plus a few hundred MeV of gravitational collapse excitation. Calculations show that plentiful gravitational collapse excitation is available to make the reaction work.
Since there are only two surface protons in an iron nucleus of 56 nucleons, and only one of these would fission, the maximum efficiency of the process would be ~2%. To the extent that all atoms would not participate, the overall efficiency of energy conversion in a star would be less than 1%. Nevertheless, instant total conversion of 1% of the mass of any star to energy would represent a gigantic nuclear explosion, which is exactly what a supernova is!
In the Fredricksson model, the attack is on the odd quark in the diquark core of the nucleon, which, by the way, contains most of the binding energy of the baryon. Clearly, it takes considerable excitation to break into the diquark, and the real questions are how much excitation is needed and where does it come from? If our speculation is correct, then the amount of energy needed to attack the up quark in the diquark is considerably greater than that needed to attack the down quark. The reaction cross section is smaller in the case of neutrons than protons.
To carry this speculation further, we propose that a hyper-nova gamma burst may be the result of two colliding neutron stars that undergo supercritical antineutrino-induced neutron fission before they can combine fully to collapse and form a black hole. In this case, the excitation energy is supplied by the kinetic energy of collision of the two massive neutron stars as gravity causes them to collide head on. If a small asteroid striking the Earth has enough kinetic energy to potentially destroy all life on the planet, then think of how much energy is involved in the collision of two neutron stars!
All that is needed is for the threshold energy of antineutrino-induced neutron fission to be exceeded, and potentially 100% of the mass of the two neutron stars plus all of the kinetic energy of their collision can be released. In principle, this can be 100 to 1000 times as much energy as is released in an ordinary supernova, and approaches the measured energy released by the largest hyper-nova that has ever been observed.
Think about it. What other process can release so much energy so quickly without converting mass to energy?