Nuclear reactions Coulomb barrier

The energy of the y-rays is indicative of the isotope present, and the intensity of the y-rays is a measure of the concentration of the isotope in the sample. The limitation of this method is that, in order to have a nuclear reaction, the repulsive Coulomb barrier has to be overcome. For incident particles of energy up to 3 MeV, the only accessible elements are the light elements with Z< 15 the cross-sections of the remaining elements become rapidly negligible. 

NRA is a powerful method of obtaining concentration versus depth profiles of labelled polymer chains in films up to several microns thick with a spatial resolution of down to a few nanometres. This involves the detection of gamma rays produced by irradiation by energetic ions to induce a resonant nuclear reaction at various depths in the sample. In order to avoid permanent radioactivity in the specimen, the energy of the projectile is maintained at a relatively low value. Due to the large coulomb barrier around heavy nuclei, only light nuclei may be easily identified (atomic mass < 30). 

For slow neutron-induced reactions that do not involve resonances, we know (Chapter 10) that ct ( ) °c 1 /vn so that (ctv) is a constant. For charged particle reactions, one must overcome the repulsive Coulomb force between the positively charged nuclei. For the simplest reaction, p + p, the Coulomb barrier is 550 keV. But, in a typical star such as the sun, kT is 1.3 keV, that is, the nuclear reactions that occur are subbarrier, and the resulting reactions are the result of barrier penetration. (At a proton-proton center-of-mass energy of 1 keV, the barrier penetration probability is 2 x 10-10). At these extreme subbarrier energies, the barrier penetration factor can be approximated as ... 

As the temperature and density continue to increase, the 0(a,y) Ne and 0(a,p) F reactions lead to break out from the CNO cycle to a process of rapid proton capture (rp-process) which involves sequential proton captures out to the proton drip line or until the Coulomb barrier becomes too large. Each of these transitions to higher-temperature reactions lead to orders-of-magnitude increases in the rates of energy production. Thus, in addition to effects on nucleosynthesis, the dynamics of the various high temperature environments are intimately coupled to the cross sections for proton and alpha-particle capture reactions on unstable nuclei. In a few cases [WAL81] even the question of whether the next proton or aphha capture leads to a bound nuclear state can have a dramatic effect on the evolution of the environment. 

The primordial nuclear reactor is short-lived, quickly encountering an energy crisis. Because of the falling temperatures and the coulomb barriers, nuclear reactions cease rather abruptly when the temperature drops below roughly 30 keV, when the universe is about 20 minutes old. As a result there is nuclear freeze-out since no already existing nuclides are destroyed (except for those that are unstable and decay) and no new nuclides are created. In 1000 seconds BBN has run its course. 

The nuclide gCf emits neutrons through spontaneous fission in 3% of all decays, the rest being a-decays. All the other neutron sources listed involve a radioactive nuclide whose decay causes a nuclear reaction in a secondary substance which produces neutrons. For example, ffSb produces neutrons in beryllium powder or metal as a result of the initial emission of 7-rays, in which case there is no coulomb barrier to penetrate. Radium, polonium, plutonium, and americium produce neutrons by nuclear reactions induced in beryllium by the a-particles from their radioactive decay. For the neutrons produced either by spontaneous fission in californium or by the a-particle reaction with beryllium, the... 

In order to induce nuclear reactions with positively charged projectiles such as protons, deuterons, or-particles, oxygra ions, or uranium ions, it is necessary that the projectile particles have sufficient kinetic energy to overcome the Coulomb barrier created by the repulsion betwem the positive charges of the projectile and the nucleus. While there is some probability that a positive projectile can tunnel through the Coulomb barrier at kinetic ergies lower than the maximum value of the barrier, this probability is quite small until the kinetic energy is close to the barrier maximum. 

Experimentally, it is found that nuclear reactions sometimes occur at energies less than that required by the Coulomb barrier. This behavior is related to the wave mechanical nature of the particles involved in a nuclear reaction. 

As a projectile approaches a target nucleus in a nuclear reaction, the probability that there will be overlap and hence interaction in their wave functions increases. This concept was used in 11.7.3 to explain the emission of a-particles with energies less than that required by the Coulomb barrier height. Such timneling may also occur for projectiles approaching the nucleus from the outside. An example is provided by the reaction of protons with lithium (Fig. 14.3). 

A common method of making N-13 is the (d,n) nuclear reaction on carbon-12. This reaction has a Q value of —0.28 MeV and a coulomb barrier of 1.8 MeV, and so it will occur with deuterons of energy greater... 

Thus it is clear that some form of direct interaction must occur in the photo-nuclear process and it is very probable, especially in heavy elements, that compound nuclei are also formed. What is not so clear is the mechanism of the direct interaction, the extent to which direct interaction and compound nucleus formation occur, and the relationship between them. It is quite reasonable to suppose that direct interaction is an essential preliminary to all photonuclear reactions, in the same sense as direct interaction for heavy particles is the preliminary to compound nucleus formation, because there is a high probability that the nucleon acted upon is absorbed in the process of ejection. In the heavy elements, where proton emission is hindered by the Coulomb barrier, it is clear that direct interaction on the proton must nearly always lead to compound nucleus formation, for the retention of the proton must produce a general excitation of the nucleus. 

The kinetic energy that the charged particle has lost through the Coulomb barrier is released again when a nuclear reaction occurs. Consequently, the Coulomb barrier does not influence the energetics... 

No general statement can be made about the elements that can be determined and the samples that can be analyzed, because these depend on the nuclear characteristics of the target nuclide (isotopic abundance), the nuclear reaction (cross-section and related parameters such as threshold energy and Coulomb barrier), and the radionuclide induced (half-life, radiation emitted, energy, and its intensity) for the analyte element, the possible interfering elements and the major components of the sample. CPAA can solve a number of important analytical problems in material science (e.g., determination of boron, carbon, nitrogen, and oxygen impurities in very pure materials such as copper or silicon) and environmental science (e.g., determination of the toxic elements cadmium, thallium, and lead in solid environmental samples). As these problems cannot be solved by NAA, CPAA and NAA are complementary to each other. 

Radionuclides are produced by nuclear reactions. These nuclear reactions can take place between highly accelerated atomic nuclei or between nuclei and nucleons (e.g., protons). To overcome the Coulomb barrier the charged nuclei or nucleons have to be provided with high kinetic energies. This is achieved by the use of accelerator systems such as cyclotrons, synchrotrons, and linear accelerators. Frequently nuclear reactors are used for radionuclide production because the uncharged neutrons... 

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