Training Centre / Centre de formation Fundamentals of Power Reactors Module One Science & Engineering Fundamentals Copyright Notice ©HER MAJESTY THE QUEEN IN RIGHT OF CANADA (1993) as represented by the Atomic Energy Control Board All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, electrostatic, magnetic tape, mechanical photocopying, recording or otherwise, without permission from the Atomic Energy Control Board of Canada. Training Centre / Centre de formation Training Centre / Centre de formation Basis of Nuclear Structure and Fission Training Objectives The participant will be able to describe or understand: 1 the atomic and nuclear structure, 2 the basic vocabulary of nuclear energy: typical length scales, mass and energy units, etc., 3 the atomic and nuclear phenomena, 4 the fission and energy release processes, 5 the types of radiation, 6 the concept of neutron spectrum, 7 the conecpt of cross section 8 the concept of irradiation Nuc Struc & Fission Training Centre / Centre de formation Nuc Struc & Fission Training Centre / Centre de formation Basis of Nuclear Structure and Fission Table of Contents 1 Introduction ...............................................................................................3 2 Basics of Nuclear Physics ........................................................................4 2.1 Structure of the atom and nucleus ................................................4 2.1.1 Nuclear structure ..........................................................................4 2.1.2 Isotopes ...........................................................................................5 2.1.3 Nuclear stability ............................................................................6 2.2 Binding energy and excited states of the nucleus .......................8 2.2.1 Energy and mass units .................................................................8 2.2.2 Binding energy of the nucleus .....................................................9 2.2.3 Comparison of chemical and nuclear energies .........................9 2.2.4 Excited state of the nucleus .........................................................10 2.3 Radioactivity .....................................................................................10 3 Fundamentals of Reactor Physics ...........................................................13 3.1 Fast and thermal neutrons ...............................................................13 3.1.1 Fast neutrons ..................................................................................13 3.1.2 Thermal Neutrons ..........................................................................14 3.2 Neutron-nucleus reactions ..............................................................15 3.3 Concept of nuclear cross section .....................................................15 3.3.1 Macroscopic and microscopic cross section ...............................15 3.3.2 Beam intensity ................................................................................17 3.3.3 Mean free path ................................................................................18 3.4 Rates of neutron reactions ...............................................................18 3.4.1 Reactions rates ................................................................................18 3.4.2 Neutron flux ...................................................................................19 3.4.3 Concept of the neutron current.....................................................20 3.5 Concept of irradiation ......................................................................21 3.6 Fuel burnup .......................................................................................21 Nuc Struc & Fission - Page 1 Training Centre / Centre de formation 4 Fission ..........................................................................................................21 4.1 Mechanism of nuclear fission ..........................................................21 4.2 Energy release in fission ...................................................................23 4.3 Neutron-energy considerations ......................................................24 4.4 Thermal reactors ...............................................................................26 Nuc Struc & Fission - Page 2 December 1995 Training Centre / Centre de formation 1 Introduction The nuclear energy is a powerful energy source related to the strength and stability of the atomic nucleus. It may be available in two different ways, either by fusion of light elements or by fission of heavy nuclei. The process called nucleosynthesis is taking place in stars and uses the fusion reaction to create heavy weight atomic nuclei. In this process, the fusion reaction brings together protons, neutrons and energy. They become bound by strong interactions in the nucleus. It is unlikely that the fusion reaction will be used in an industrial process of energy production in the near future. The major problem is that a tremendous amount of energy (of the order of magnitude of the temperature in stars, 100 millions degrees) is required to initiate the fusion reaction. Below is a list of various fusion reactions with their energy balance: 22→++3 1 1D + 1D 2He(0.82MeV)0 n(2.45MeV) 3.27Mev 22→++3 1 1D + 1D 1T(1.01MeV)1 p(3.02MeV) 4.03Mev 2 3→++4 1 1D + 1T 2He(3.56MeV)0 n(14.03MeV) 17.59Mev 3 3 →++4 1 1T + 1T 2He 20n 17.59Mev To date, the only macroscopic application of the fusion reaction is the H bomb (the third of the above equations). Figure 1.1 below illustrates the fusion reaction between deuterium and tritium. Fig. 1.1: Fusion reaction between deuterium and tritium Intermediate compound nucleus Deuterium Tritium 4He γ n n n n V V D T p p n p p High n Energy Collision In comparison, the fission reaction is “easier” to produce; it is the source of energy in a nuclear reactor: neutron-induced fission of uranium and plutonium nuclei. As it is the process of interest for nuclear energy production, it will be treated in greater details in this lesson. The fission reaction can liberate part of the binding energy by breaking the nuclear structure. According to the concept of equivalence of mass and energy established by Einstein, the amount of energy ∆E released is given by the following equation: ∆E = ∆m c2 where c is the speed of light and ∆m is the mass defect. The determination of Nuc Struc & Fission - Page 3 Training Centre / Centre de formation nuclear masses has shown that the mass of a heavy nucleus is higher than the sum of the individual masses of its constituent nucleons. It is called the mass defect. Figure 1.2 below illustrates the neutron-induced fission reaction of uranium. Fig. 1.2: Uranium fission reaction 235U Intermediate 92 compound nucleus n 236 95Kr 92 U 36 n 139 56 Ba γ n Reactor physics is the study of the fission chain reaction and its dependence on the materials in the reactor core and their geometrical configuration. The reactor physicist area of interest is in core neutronics: the distribution in space, time and energy of the neutron population. Reactor physics shares methods and results with thermohydraulics, safety, fuel management and operation. Fig. 1.3: Relations between reactor physics and other disciplines Operation Fuel Management Reactor Physics Safety Thermal- Hydraulics 2 Basics of Nuclear Physics 2.1 Structure of the atom and nucleus 2.1.1 Nuclear structure An atom of a chemical element consists of a small, positively charged, massive nucleus surrounded by a large, negatively charged, light electron cloud. The radius of the atom is of the order of 10-8 cm (≈1Å (ångström)), whereas the radius of the nucleus is of the order of only 10-13-10-12 cm (about 10 thousands times smaller). In spite of this, more than 99.9% of the mass (and therefore of the energy) of the atom resides in the nucleus. Nuc Struc & Fission - Page 4 December 1995 Training Centre / Centre de formation The nucleus consists of positively charged protons and uncharged neutrons. Protons and neutrons are collectively called nucleons. The mass of a proton is about 1836 times, while that of a neutron is about 1838 times, the mass of an electron. The number of protons in the nucleus - denoted by Z - (or, equivalently, the number of electrons in the neutral atom) is called the atomic number and determines the chemical element. For instance, Z = 1 (one proton) corresponds to hydrogen, Z = 8 corresponds to oxygen, Z = 92 corresponds to uranium. The number of neutrons in the nucleus is denoted by N. The total number of nucleons in the nucleus is the mass number, A ≡ Z+N. A given combination of a specific Z and a specific N is a specific “nuclide”, X. Thus any two of Z, N and A are sufficient to specify the nuclide, and it is represented by the symbol X. Figure 2.1 shows the atomic structure of various nuclides. 2.1.2 Isotopes The atomic number determines the chemical nature of an element because the chemical properties depend on the (orbital) electrons surrounding the nucleus, and their number must be equal to the number of protons, since the atom as a whole is electrically neutral. Consequently, atoms with nuclei containing the same number of protons, i.e., with the same atomic number, but with different mass numbers, are identical chemically, although they frequently exhibit marked differences in their nuclear characteristics. Such species, having the same atomic numbers but different