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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[atomic, nuclear] The nucleus contains approximately 99.975% of the total mass of an atom and hence the energy requirements for dissociation are very high. The nuclear binding energy is the energy contained by holding the appropriate number of protons and neutrons together, and the energy released when a grouping of protons and neutrons is split off from the nucleus. The total binding energy (BE) can be derived from the mass energy equivalence: BE=[Zmp+(A−Z)mn−mzA]c2, where Z is the number of protons (the atomic number) with mp being the respective mass, A the atomic mass (with A – Z the number of neutrons, with mass mn), c the speed of light, and zmA the sum of the rest of the masses of the respective protons, neutrons, and remaining nucleus.
Nuclear Fuels, Nuclear Structure, the Mass Defect, and Radioactive Decay
Published in Robert E. Masterson, Introduction to Nuclear Reactor Physics, 2017
In Chapter 2, we also learned that the nucleus is an extremely small and dense structure that consists of protons and neutrons. Several illustrations of the atom and its nucleus are shown in Figure 6.5. On average, the higher the binding energy is per nucleon, the more stable an atomic nucleus will be. Hence a nucleus with a higher average binding energy is bound together more tightly than a nucleus with a lower one. If we take the mass defect Δm and divide it by the total number of protons Z and neutrons N in a specific isotope, then we can define the average nuclear binding energy BE that each proton or neutron possesses: BE=ΔmZ+N This equation can also be written as ΔE/c2 · (1/A), where A = Z + N is the total number of nucleons (protons and neutrons) that the nucleus possesses. Hence the nuclear binding energy is normally quoted in MeV per nucleon. When we calculate the binding energy of all of the elements in the Periodic Table, starting with the lightest element hydrogen and ending with the heaviest naturally occurring element uranium, we get the curve shown in Figure 6.6. This curve is called the nuclear binding energy curve, and it is one of the most important curves in all of nuclear science and engineering. Notice that the binding energy is different from one element to the next, and in fact, is also isotope dependent. The binding energy per nucleon varies from about 2 MeV for helium to about 10 MeV for iron. The average binding energy for an element in the Periodic Table is about 8 MeV per nucleon. Hence a nucleus with 150 nucleons will have a binding energy of about 150 × 8 MeV = 1200 MeV. Approximately 1% of the mass of the nucleus is converted into the bonds required to hold the nucleus together.
Simulation with Monte Carlo methods to find relationships between accumulated mechanical energy and atomic/nuclear radiation in piezoelectric rocks with focus on earthquakes
Published in Radiation Effects and Defects in Solids, 2022
Abouzar Bahari, Saeed Mohammadi, Mohammad Reza Benam, Zahra Sajjadi
A gamma photon with energy sufficiently large to overcome the nuclear binding energy (about 7 MeV in most nuclides) may result in the emission of nucleons ((γ, n) or (γ, p) reactions), α particles or other particles. The cross-section for photonuclear reactions exhibits the so-called giant resonances or more preciously giant dipole resonances. This vibration process has a resonance frequency at which the absorbed photon excites the nucleus, causing it to emit a neutron, a proton, etc. These resonances occur at a photon energy of about 15 MeV in 208Pb, and the resonance energy is proportional to A−1/6 MeV, where A is the nucleus mass number (31).
An evaluation of activation and radiation damage effects for the European Spallation Source Target
Published in Journal of Nuclear Science and Technology, 2018
Tomás Mora, Fernando Sordo, Adrian Aguilar, Luis Mena, Maite Mancisidor, Jorge Aguilar, Gorka Bakedano, Iñigo Herranz, Paula Luna, Miguel Magan, Octavio Gonzalez-del Moral, Raul Vivanco, Felix Jimenez-Villacorta, Kristoffer Sjogreen, Ulf Oden, José Manuel Perlado, José Luis Martinez, Fracisco Javier Bermejo
As expected, the impinging 2 GeV proton beam has an energy well above the average nuclear binding energy, ≈8 MeV and thus leads to the generation of a hadronic cascade as well as to the emission of high-energy neutrons and other particles. Such reaction products end up depositing substantial thermal energy over a large volume and trigger the generation of secondary spallation fragments which are generally radioactive and neutron deficient with respect to the valley of stability. A rough estimate of the activity that can be expected for a spallation target made of non-fissionable materials yield some 1.87 ×10 16 Bq per milliampere of proton beam.1so that the use of 2.5 mA beams as specified should yield some 4.67 × 10 16 Bq after a very long irradiation period. Apart from induced radioactivity, spallation processes lead to a significant fraction of the input proton power to be converted into nuclear heat. The expectancy on the basis of available data is that for a beam of 2 GeV, a fraction of some 0.6 will go into heat production for a non-fissionable target material, mostly resulting from spallation products and neutron capture reactions. However, the volume deposition of thermal energy during a pulse train depends on details of the hadron cascade as well as on the incident beam profile and pulse repetition frequency and pulse duration. In this respect, it is worth emphasizing that although one expects that about two-thirds of the generated inventory arise from spallation products and this can be simulated with less detailed tools, the remaining faction will surely arise from capture reactions on W and this makes mandatory to make a pretty accurate estimation of the neutron flux. Otherwise, the results may lead to a substantial underestimation of radionuclides generated by such a route. In consequence, simulations using as many fine details to represent the nuclear reactions as reasonably achievable need to be carried out to yield realistic estimates of quantities such as those above referred to.