Nuclear reactions threshold

Table 2. Exponent of the temperature dependence of the Maxwellian averaged nuclear cross section (middle column) for four different nuclear reactions, evaluated at a temperature of 1.5 107 K. The last column gives the Coulomb threshold energy.

This particular reaction is of interest for several reasons. It was the first nuclear reaction that was produced in a laboratory by means of artificially accelerated particles (Cockcroft and Walton 1932 cf. 13.3). Reaction (b) is still used for the production of y-radiation (17 MeV), while reaction (c) is used as a source of mono-energetic neutrons. The energy of the neutrons from reaction (c) is a function of the proton energy and the angle betwe the neutron and the incident proton beam. A necessary requirement, however, is that the threshold energy (1.64 X (8/7) = 1.88 MeV) must be exceeded, the g-value for reaction (c) being —1.64 MeV. 

Probably the most common method for making N for labeled compound s)mthesis is now the (p, ) nuclear reaction on 0, usually in the form of water. Several groups have used this reaction to produce NHs (13-16). This reaction has a Q value of —5.2 MeV, a threshold energy of 5.52 MeV, and a peak cross section of about 200 mb at 8 MeV. A yield of 25 mCi//LLA at saturation can be achieved with 14.5-MeV protons (17). 

The fission neutrons produced in nuclear reactors have a continuous kinetic-energy spectrum, mostly in the range of 1-10 MeV. Since (n, y) reactions are of more widespread analytical use, fission neutrons must be slowed to thermal energies by passing them through HjO, D2O, or graphite, which act as moderators. Depending on the type of nuclear reactor and the irradiation position in the reactor, the neutron spectrum may vary widely. Therefore, both (n, y) and threshold reactions can occur in samples placed in nuclear reactors. Threshold reactions may produce interferences, of which the experimenter should be aware. 

Herb et al. have measured the threshold for the Li ( n) Be reaction as 1.882 MeV with an accuracy of 0.1%, and similar measurements for a number of resonant reactions establish a high voltage scale for the measurement and inter-comparison of nuclear reaction energies. 

The starting point for muon experiments is the production of pions (it) in a nuclear reaction initiated by energetic protons (e.g., Be + p — l Be + ir ). Threshold energies for pion production are > 150 MeV but the cross sections peak in the "intermedi-... 

The F-factor can be calculated according to eqn [15] if (1) the stopping power of sample (Sx) and standard (Ss) and (2) the nuclear reaction cross-section (cr) are known, both as a function of energy in the energy interval between the threshold energy (Ej)... 

These two approximative methods are equivalent and yield accurate results if one or more of the following conditions are fulfilled (1) the atomic number of (the elemental components of) sample and standard are comparable (2) the threshold energy of the nuclear reaction used is high or (3) the incident energy is high as compared with the threshold energy. 

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. 

Barrier number one is the fuel element cladding, which contains and confines the nuclear reaction products, and whose leak tightness is continually monitored. In the event fuel cladding failures occur, radioactivity thresholds are exceeded, the installation is shut down, and the damaged elements are removed and replaced. 

R. J. HOWERTON, Thresholds of Nuclear Reactions Induced by Neutrons, Photons, Protons, Deuterons, Tritons, and Alpha Particles, UCRL-S0400, Vol. 9. 

The nuclear reaction (b) is chiefly induced by thermal neutrons and shows a cross section of 6 10 cm (Maxwell spectrum, T=575 K). Reaction (c) on the other hand is induced by fast neutrons with an effective threshold energy of 2.4 MeV the cross section averaged over the flux of neutrons with energies beyond this threshold value amounts to 8.5 10 cm . Using this data and assuming a lithium concentration of 2 ppm (99.99% Li), which is held constant... 

Nuclear reactions used to determine carbon, nitrogen and oxygen are shown in Table II-IO, which also gives the threshold energies and the half lives of the radioisotopes produced. 

Element determined Nuclear reaction used Threshold energy (MeV) Half life of radioisotope produced (min)... 

Element determined Competing nuclear reactions Approximate threshold energy (MeV)... 

Furthermore, by comparing the threshold values given in Tables II-IO and II-ll, it is clear that it is in all cases possible to eliminate totally the effect of competing nuclear reactions, by the appropriate choice of the maximum energy of the gamma photon beam. 

Table IV-1 gives nuclear reactions that can be used for the determination of boron, along with the nuclear interferences. For some reactions the sensitivity is also given. The half lives of the radionuclides produced are 9.97 min ( N), 20.4 min ( C) and 53.3 d ( Be). N and C are positron emitters, Be emits 478 keV 7-rays. For the B(d,n) C and B(o,n) N reactions, energies below the thresholds of the interfering reactions (resp. 5.9 and 13.6 MeV) can be used, so that no nuclear interferences occur.

Table IV-1 Nuclear reactions for the determination of boron and nuclear interferences (threshold energies in MeV)...

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