Nuclear threshold energy

The probability for absorption of the nuclear excitation energy is determined by the threshold energy and by the probability magnitude at en-... 

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). 

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. 

Recently new ICCs have been obtained from relativistic self-consistent-field Dirac-Fock (DF) calculations for each Zbetween 10 and 126, for K, Li, L2, and L3 atomic shells for nuclear-transition multipolarities E1-E5 and M1-M5, and for nuclear-transition energies from 1 keV above the Lj threshold to 2,000 keV (Band et al. 2002). The total ICC values were calculated from the sum of partial ICC values from all atomic shells. The calculated K and total values are, on average, about 3% lower than the theoretical relativistic Hartree-Fock-Slater values, and agree better with the most accurate experimental ICC values. A selection of total ICCs is plotted inO Figs. 11.2—11.7, for atomic numbers Z = 10, 30, 50, 70, 90, and 110. The full set of tables and graphs can be found in the original publication. 

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... 

When the separation results in two major fragments, the threshold energy for fission is given by the potential energy of the fragments at the instant of separation. If one assumes that separation yields two spherical collections of nucleons with Zi protons and of radius r,-, then the maximum value of the potential energy due to the electrostatic field is proportional to ZxZ ijx + 2) When the separation r exceeds Ti + r2, the coulomb forces predominate, and when r < ri + r2, nuclear forces predominate. A representative curve of the potential energy Ep of this system is shown in Fig. 1.2. 

In a nuclear activation reaction the following factors have to be considered besides the variables of equation (3) threshold energy, mode of decay of the product, interference by other elements present in the sample yielding the same products as the element investigated, or products with overlapping decay spectra, etc. For example in the determination of compound 6 the N(n, reaction was used . ... 

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)... 

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