Nuclear reactions: General approach An outline of the general theory and modeling of nuclear reactions can be given in many ways. A common classification is in terms of time scales: short reaction times are associated with direct reactions and long reaction times with compound nucleus processes. At intermediate time scales, pre-equilibrium processes occur. An alternative, more or less equivalent, classification can be given with the number of intranuclear collisions, which is one or two for direct reactions, a few for pre-equilibrium reactions and many for compound reactions, respectively. As a consequence, the coupling between the incident and outgoing channels decreases with the number of collisions and the statistical nature of the nuclear reaction theories increases with the number of collisions. Figs. 3.1 and 3.2 explain the role of the different reaction mechanisms during an arbitrary nucleon-induced reaction in a schematic manner. They will all be discussed in this manual. This distinction between nuclear reaction mechanisms can be obtained in a more formal way by means of a proper division of the nuclear wave functions into open and closed configurations , as detailed for example by Feshbach’s many contributions to the field. This is the subject of several textbooks and will not be repeated here. When appropriate, we will return to the most important theoretical aspects of the nuclear models in TALYS in Chapter 4.
Helium-2 (diproton) Helium-2 or 2 He , also known as a diproton, is an extremely unstable isotope of helium that consists of two protons without any neutrons . According to theoretical calculations it would have been much more stable (although still beta decaying to deuterium ) had the strong force been 2% greater. Its instability is due to spin-spin interactions in the nuclear force, and the Pauli exclusion principle , which forces the two protons to have anti-aligned spins and gives the diproton a negative binding energy . There may have been observations of 2 He . In 2000, physicists first observed a new type of radioactive decay in which a nucleus emits two protons at once—perhaps a 2 He nucleus. The team led by Alfredo Galindo-Uribarri of the Oak Ridge National Laboratory announced that the discovery will help scientists understand the strong nuclear force and provide fresh insights into the creation of elements inside stars . Galindo-Uribarri and co-workers chose an isotope of neon with an energy structure that prevents it from emitting protons one at a time. This means that the two protons are ejected simultaneously. The team fired a beam of fluorine ions at a proton-rich target to produce 18 Ne , which then decayed into oxygen and two protons. Any protons ejected from the target itself were identified by their characteristic energies. There are two ways in which the two-proton emission may proceed. The neon nucleus might eject a 'diproton'—a pair of protons bound together as a 2 He nucleus—which then decays into separate protons. Alternatively, the protons may be emitted separately but at the same time—so-called 'democratic decay'. The experiment was not sensitive enough to establish which of these two processes was taking place. More evidence of 2 He was found in 2008 at the Istituto Nazionale di Fisica Nucleare , in Italy. A beam of 20 Ne ions was directed at a target of beryllium foil. This collision converted some of the heavier neon nuclei in the beam into 18 Ne nuclei. These nuclei then collided with a foil of lead. The second collision had the effect of exciting the 18 Ne nucleus into a highly unstable condition. As in the earlier experiment at Oak Ridge, the 18 Ne nucleus decayed into an 16 O nucleus, plus two protons detected exiting from the same direction. The new experiment showed that the two protons were initially ejected together, correlated in a quasibound 1 S configuration, before decaying into separate protons much less than a billionth of a second later. Further evidence comes from RIKEN in Japan and JINR in Dubna , Russia, where beams of 6 He nuclei were directed at a cryogenic hydrogen target to produce 5 He . It was discovered that the 6 He nucleus can donate all four of its neutrons to the hydrogen. The two remaining protons could be simultaneously ejected from the target as a 2 He nucleus, which quickly decayed into two protons. A similar reaction has also been observed from 8 He nuclei colliding with hydrogen. 2 He is an intermediate in the first step of the proton-proton chain reaction . The first step of the proton-proton chain reaction is a two-stage process; first, two protons fuse to form a diproton: 1 1 H + 1 1 H → 2 2 He followed by the immediate beta-plus decay of the diproton to deuterium: 2 2 He → 2 1 D + e + + ν e with the overall formula: 1 1 H + 1 1 H → 2 1 D + e + + ν e + 0.42 MeV R. A. W. Bradford has considered the hypothetical effect of this isotope on Big Bang and stellar nucleosynthesis.
The quest for stimulated energy release Nuclear isomers provide a form of energy storage . Whereas betadecaying radioactive nuclei can also store MeV energies (per nucleus) for long periods of time, nuclear isomers usually decay electromagnetically, by g-ray emission or internal conversion. This difference may offer improved opportunities for stimulating the decay of isomers . The interaction of visible or ultraviolet photons with nuclei has long been sought. In principle, low-energy (eV) photons should be able to initiate isomer decay, either by stimulated emission to a nearby lower-energy state, or by stimulated absorption to a nearby higher-energy state. In either case, if the stimulated transition is to a short-lived energy level, a cascade of g-rays could be released, with a total energy of several MeV. If this scheme were to be realized, then it would be possible to have a type of nuclear reservoir, where the energy could be released with a photon `switch' . It would not be necessary to wait for the intrinsic half-life to release the energy and, if the isomer were in a nucleus with a stable ground state, there would be no subsequent radioactive waste. Moreover, the potential development of a g-ray laser would be brought a significant step closer52. Such an idealized scenario has not yet been realized, and low-energy photons have yet to be proven to stimulate nuclear transitions; but this does not mean that there are no possibilities. In the search for stimulated transitions, the isomers studied to date have mostly been at low energies (that is, low on a nuclear energy scale). The 45-hour isomer in 229Th, at an excitation energy of 3.5 eV, has received special attention51,53,54 because the nuclear excitation is on a similar energy scale to atomic valence electrons. Although the stimulation of the 3.5-eV transition would release no additional energy, it is of fundamental interest for investigating photon±nucleus interactions . But the MeV isomers discussed here have the potential to release significant quantities of energy. A recent encouraging advance was the de-excitation55, using ,100-keV photons, of the 2.4-MeV, 31-year isomer in 178Hf , although this is still a long way from de-excitation with eV photons. At face value, the use of eV photons to stimulate nuclear transitions requires one or more states to lie within a few eV of the isomer. For low-lying isomers, this presents a general problem. A chance near-degeneracy is needed, such as that found exceptionally in 229Th. For highly excited isomers, however, with energies of several MeV, the isomers become embedded in a high statistical density of excited states. For example, at 5MeV in a nucleus such as 178Hf, there is on average about one state per eV, so the `chance' of a near-degeneracy becomes certain. Notwithstanding this certainty, the isomer would probably have very different spin quantum numbers from the background of statistical states (otherwise it would not be an isomer in the first place). To stimulate isomer de-excitation, additional processes may therefore be required; one such example is the assisted electronbridge mechanism51, in which excitation of atomic electrons can eliminate energy and spin mismatching between the isomeric state of a nucleus and the state to which it decays. There is, therefore, room for chance to play an important role in providing the right conditions for isomer formation , and for allowing transitions to be stimulated by low-energy photons . Many new isomers are predicted to exist in nuclei with about 180 nucleons. The insights already gained into the nucleus, together with the development of experimental facilities, suggest the possibility of wide technological benefits in the future.
Figure 1： Excitation energy as a function of various nuclear variables. The secondary energy minima are responsible for the different kinds of isomers: a, shape isomers; b, spin traps; c, K-traps. In each case, the relevant nuclear shapes are illustrated; where appropriate, angular momentum vectors are shown as arrows. For both the spin trap and the K-trap, the angular momentum comes from a small number of orbiting nucleons (two are illustrated in red in each case).
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