The Underlying Physics of Nuclear Energy Systems

The Underlying Physics of Nuclear Energy Systems John William Boldeman Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee DC, NSW 2232. ABSTRACT There has been a great deal of discussion in the media of nuclear energy systems following the recent accidents at Fukushima. This paper summarises the underlying physics of the nuclear fission process and details some of the important considerations required to exploit this process in power systems. Introduction The fission process is defined as the division of a heavy excited nucleus into two fragments similar in size. Since the discovery of fission (Hahn and Strassman, 1938) there has been an extraordinary amount of research work devoted to the topic since it was quickly realised that there was the potential for commercial power systems to be based on this basic process. Essentially, the underlying physics of nuclear fission were established by the late 1970s and subsequent work has been to improve the accuracy of the experimental data and to refine the theoretical understanding of the processes involved. The development of the understanding of the fission process can be read in an extended series of conference proceedings IAEA International Conferences on the Physics and Chemistry of Fission. The Fission barrier The starting point for any discussion of the fission barrier is the application of the liquid drop model (LDM) to an understanding of the process (Bohr and Wheeler, 1939). In this model, the nucleus is assumed to be equivalent to a liquid drop in which the short range nuclear forces are idealised by the surface tension of the drop and the Coulomb repulsive forces are included by assuming the drop is uniformly charged throughout its volume. Fission occurs if sufficient excitation is given to the system to allow the internal vibrations of the nucleus to overcome the attractive surface tension of the drop. After some time it was realised that this simple model needed modification in particular to account for nuclear shell effects. As a result, the simple barrier hindering fission for a heavy nuclei near U 235, as shown in the Figure 1 as the LDM, in fact has a double humped shape with the two barrier peaks designated A and B. There is a potential well, II, in between these two peaks. Nuclei such as U 235 are deformed (essentially non-spherical) in their ground state as seen in the figure where the unperturbed nucleus sits in the potential well, I. If sufficient energy is given to the nucleus in some way so that the total energy exceeds the higher of the two barrier

peaks, then, the nucleus will fission. Of course it is possible for the nucleus to tunnel through the fission barrier and this, when it is possible, is called spontaneous fission. Figure 1 - The Fission Barrier (after Strutinski 1967) Energy Release in Fission The energy release in the fission process can be readily understood by reference to Figure 2 which shows the nuclear binding energy per nucleon as a function of atomic mass, A. Suppose, for example, that a U 236 nucleus (a U 235 nucleus after capture of a slow moving neutron) has thereby been given sufficient energy to split into the two fragments, the two most probable with atomic numbers 95 and 141. Following an analysis of the relative atomic masses, it would be seen that approximately 0.215 mass units have been lost in the process and this appears as energy according to the well known Einstein equation E = mc 2. Thus the total energy release can in this case be estimated to be 198 MeV. Figure 2 Binding Energy per nucleon as a function of Atomic Number The next question to ask is where does this energy appear. The energy produced is shared between the kinetic energies of the two fragments, because of their coulomb 2

repulsion, and the internal excitation of the two fragments. The total internal excitation has a distribution in energy but has a medium value of about 30 MeV. This internal excitation makes the fragments unstable and they lose their excess energies by emitting a number of neutrons, some gamma rays and neutrinos. It is well known that U 235 undergoes thermal neutron fission but U 238 does not. The reason for this is quite simple. The absorption of a neutron by U 235 forms a tightly bound even proton, even neutron compound nucleus with considerable internal excitation since this is a highly favoured nuclear configuration. However, the absorption of a neutron by U 238 forms an even odd compound nucleus with less excitation. Thus the excitation following neutron absorption by U 235 neutron is above the fission barrier. To achieve the same excitation for U 238 requires the neutron to bring in additional kinetic energy i.e. the neutrons have to be what are loosely termed fast neutrons, in fact, the neutron threshold for fission of U 238 is about 1 MeV. Neutron Emission As indicated previously the excited fission fragments formed in fission lose their excitation by releasing neutrons and other particles. The number of neutrons emitted in the thermal neutron fission of U 235 ranges from zero to as many as 8 neutrons per fission event. The best current value for the average number of neutrons emitted per fission, ν, is 2.432. For details of the experimental measurements of this parameter see Boldeman (1988). Since more than one neutron is emitted for each absorbed neutron it is possible to design a chain reaction provided one of these fission neutrons can cause a second fission process as illustrated in Figure 3. Figure 3 Illustration of a Chain Reaction Process 3

The vast majority of the neutrons in fission are emitted within sub-nanosecs of the fission event itself (prompt neutrons). Fortunately, there is a small proportion of the emitted neutrons, 0.016 (delayed neutrons) in the thermal neutron fission of U 235, that are emitted with lifetimes of between 0.62 secs and 80 secs. Without these delayed neutrons it would be almost impossible to construct a controlled nuclear reactor system. Another very important feature of fission neutrons is their energy spectra. The spectrum for fission of U 235 can readily be represented by a Watt spectrum but more simply by a Maxwellian Spectrum of the form N(E) E exp(e/t) with T = 1.30, giving an average energy for the neutrons of 1.952 MeV. At these energies, the probability of neutrons interacting with U 235 nuclei and, in fact, with all nuclei is relatively small. The cross section representing this probability, σ, has a value of about 1 barn at E n = 1.0 MeV. However if the neutron energy is reduced to an energy of say 0.025 ev, the neutron fission cross section becomes very much larger at σ f = 581 barns. Therefore, it should be clear that, for an operating commercial nuclear reactor power system, there would be fewer engineering problems if the average energy of the fission neutrons could be reduced to a value well below 1 ev. From the time of the first nuclear reactor constructed by Fermi in 1942, this has been achieved by reducing the fission neutron energies through a scattering process in a medium surrounding the fuel which has been termed a moderator. In essence, the energies of the neutrons are reduced through the scattering process so that they become in equilibrium with the molecular motion of atoms in the moderator. Since this process is very similar to billiard ball collision it will easily be understood that the most effective way to reduce the neutron energy is to collide them with particles of a similar size. Thus, the optimum moderator materials are the light elements such as hydrogen contained in water, deuterium in heavy water or graphite. It is notable that Fermi used a graphite moderator. There are many books developing this topic perhaps the most famous is Weinberg and Wigner (1958). Fission Products As indicated previously the fission fragments formed following fission are highly excited and lose their excitation by emitting a range of particles within a very short time period. Ultimately, they become either stable nuclei or radioactive nuclei with half lives greater than a few minutes. By convention the former fission fragments are now termed fission products. Fission product yields are determined primarily by chemical methods and a great deal of the research here was conducted in the very early years of the experimental investigation of fission. Figure 4 from A C Wahl presents a picture which is still a very accurate presentation of the fission product yields. This picture, while relatively old, has the value of showing the physics which dominate the yield of the fission products. The binary mass yield distribution is well know and the figure illustrates the role of the closed nuclear shells at N=50 and Z=50 and N=80 in causing this. The figure shows data for the fission of compound systems including thermal neutron fission of U235 (compound nucleus 236) and that of other elements. Table 1 lists several of the more important fission products which are particularly relevant to any discussion of nuclear accidents. 4

Figure 4 Fission Product Yields for several Fissioning Systems A C. Wahl (1965) The table lists the half lives, the percentage yields in thermal neutron fission of U 235, decay particles and their total energies. Of course, there are a great many other long lived radioactive fission products but their yield is relatively low and so is their significance. Table 1 Several Important Fission Products Isotope Half Life Percent U 235 Decay Energy Decay Particles Kr 85 10.76 y 0.218 687 kev β γ Sr 90 28.9 y 4.505 2.826 MeV β I 131 8.02 days 2.878 971 kev β γ Cs 137 30.23 y 6.337 1.176 MeV β γ Sm 157 90 y 0.5314 77 kev β Classification of Power Reactors Table 2 below presents a simple classification of commercial power reactor types. 5

Table 2 Classification of Power Reactors Based on the Fission Process Thermal Reactors (all existing power reactors) Fast Reactors (Experimental Systems and some Gen IV proposals) Fuel Type Natural uranium (Candu reactors, Magnox) Enriched U 235 typically 2 5% (PWR, BWR, RBMK) Mixed Fuel U 235 /Pu 239 (PWR, BWR) Moderator Light water (PWR,BWR) Heavy water (Candu) Graphite (RBMK, Magnox) Coolant Light water (PWR, BWR) Heavy Water (Candu) Gas CO 2 (Magnox) Liquid metal - Na (experimental fast reactors, some proposed Gen IV reactors) Liquid Metal Pb, PbBi eutectic (some Gen IV reactors) References N. Bohr and J. Wheeler (1939) The mechanism of nuclear fission. Physical Review 56, 426. J.W. Boldeman (1988) - The energy dependence of ν. Proc. IAEA Consultants' Meeting on the Physics of Neutron Emission in the Fission Process, Mito City, Japan, INDC(NDS)-220, p.21-45. O. Hahn and F. Strassmann (1939) Naturwissenschaften 27:11. V.M. Strutinsky (1967) Shell Effects in nuclear masses and deformation energies. Journal of Nuclear Physics A95, 420. A. C. Wahl (1965) Mass and charge distribution in low-energy fission. Physics and Chemistry of Fission, Salzburg, 1, 317. A. M. Weinberg and E. P. Wigner (1958) The Physical Theory of Neutron Chain Reactors, The University of Chicago Press. Experience John Boldeman has worked on aspects of nuclear science and technology for more than 50 years principally at the Australian Nuclear Science and Technology Organisation. He is a specialist in the nuclear fission process and has made many measurements on fission cross sections, neutron emission probabilities in fission, fission neutron spectra and neutron total and capture cross sections in general. He was also involved for many years in International Nuclear Safeguards and was the operator of the research reactor Moata. Since 1986, he has been involved in the design and construction of many major scientific facilities including the tandem accelerator, ANTARES, and the Australian Synchrotron. He was Chief of the Physics Division at Ansto from 1987 1995. His awards include Centenary Medal (2001), ANA Annual Award (2004), the ANZAAS Medal (2007) and the Clunies Ross Lifetime Achievement Award (2010). 6