B. Rouben McMaster University Course EP 4D03/6D03 Nuclear Reactor Analysis (Reactor Physics) 2015 Sept.-Dec.

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1 2: Fission and Other Neutron Reactions B. Rouben McMaster University Course EP 4D03/6D03 Nuclear Reactor Analysis (Reactor Physics) 2015 Sept.-Dec September 1

2 Contents Concepts: Fission and other neutron reactions Beam Intensity Cross Sections Reaction rates 2015 September 2

3 Go Forth and Multiply! Nuclear reactors exploit the neutron-induced fission chain reaction to release heat energy. Neutrons are the agents of the reaction. We need to know what neutrons can do and what they re doing September 3

4 Neutron Interactions with Matter Inelastic Scattering: elec tron Scattered neutron, E 2 neutron Incident neutron, E 1 p roton E 1 = E + E 2 Gamma Photon, E Elastic Scattering: elec tron Scattered neutron, E 2 neutron Incident neutron, E 1 p roton a E A E 1 = E A + E 2 Neutron Absorption: Gamma Photon, E E ~ 7 MeV elec tron neutron p roton 2015 September Incident thermal neutron, E 4

5 Neutron Interactions with Matter Scattering The neutron bounces off, with or without the same energy (elastic or inelastic scattering) Absorption Following absorption these outcomes can happen: Activation: the neutron is captured, & the resulting nuclide is radioactive, e.g. 10 B(n, ) 7 Li [n in, followed by alpha decay] 16 O(n,p) 16 N [n in, followed by proton emission] Special Case, Radiative Capture - decay by gamma emission: e.g., 238 U(n, ) 239 U or 40 Ar(n, ) 41 Ar Fission (happens only with some heavy nuclides) The nuclide splits into 2 lighter nuclides and releases energy Neutrons are also released which continue the chain reaction 2015 September 5

6 (neutron-induced) A neutron splits a uranium nucleus, releasing energy (quickly turned to heat) and more neutrons, which can repeat the process. The energy appears mostly in the kinetic energy of the fission products and in the beta and gamma radiation September 6

7 Spontaneous and Neutron-Induced Fission Question: Does spontaneous human combustion exist? Answer: I doubt it, but I don t really know. Question: Does spontaneous fission exist? Answer: Yes. Nuclei of uranium sometimes split spontaneously, releasing energy. However, this happens with very low frequency: The half-lives of U-235 and U-238 are 7.038*10 8 years and 4.68*10 9 years respectively, and most of their decay is by alpha emission, so spontaneous fission is not a practical source of energy. But fission can be made into a practical source of energy when induced by a neutron collision with a nucleus of uranium (or a nucleus of a few other heavy elements) September 7

8 Multiplying Medium Multiplying medium: A material or environment in which fissionable nuclides are present, i.e., where neutrons can induce fission, and thereby be multiplied September 8

9 Outcome of Neutron-Induced Fission Reaction Energy is released (a small part of the nuclear mass is turned into energy). One neutron enters the reaction, 2 or 3 (on the average) emerge, and can induce more fissions. The process has the potential of being a chain reaction; this can be self-perpetuating ( critical ) under certain conditions. By judicious design, research and power reactors can be designed for criticality; controllability is also important. The energy release is open to control by controlling the number of fissions. This is the operating principle of fission reactors September 9

10 Outcome of Neutron-Induced Fission Reaction ~200 MeV of energy is eventually released per fission There is only a small variation in this quantity, depending on which nuclide is fissioning. Discussion: A fundamental law of physics is that energy is always conserved. How can energy be released in fission? 2015 September 10

11 Fission Process The fission process occurs when the nucleus which absorbs the neutron is excited into an elongated (barbell) shape, with roughly half the nucleons in each part. This excitation works against the strong force between the nucleons, which tends to bring the nucleus back to a spherical shape there is a fission barrier, ~ 6 MeV If the energy of excitation is larger than the fission barrier, the two parts of the barbell have the potential to completely separate: binary fission! 2015 September 11

12 Radiative Capture and Fission If the neutron is absorbed by a very heavy nuclide (as opposed to being scattered), the two most important outcomes are: 1) (radiative) capture, where the neutron remains in the nucleus and a gamma ray is emitted, and 2) fission Whether there is a real potential for a selfsustained fission chain reaction to take place depends on the relative probabilities of these outcomes ( cross sections ), and on the number of neutrons emerging September 12

13 Concepts of Cross Sections To understand the concepts of macroscopic and microscopic cross sections, let us first start by considering neutron beams interacting with targets September 13

14 Intensity of a Monoenergetic Beam Consider a monoenergetic beam of neutrons: All have the same speed and all are moving in the same direction. Density of neutrons in monoenergetic beam = n cm -3 Unit Area of Target Speed of neutrons = [cm/s] The Beam Intensity I is defined as the number of neutrons crossing a unit area of the target per unit time. All neutrons within a distance ( *1 s) will cross the target within 1 s, I = n [units = n.cm -2.s -1 - or cm -2.s -1 ] 2015 September 14

15 Neutron Beam Impinging on a Slice of Target The monoenergetic beam of intensity I is impinging on a target. Let be the effective area of interaction presented by a single nucleus to a neutron (not necessarily the geometric area of the nucleus!). is called the miscroscopic cross section; it has units of area, e.g. cm 2. Consider a thin slice of target of unit area and infinitesimal thickness dx ( of volume V = 1*dx=dx). = area presented to neutron by 1 nucleus Neutron Beam (area 1 cm 2 ) Thin (dx) slice of target Density of atoms (nuclei) in target = N cm September 15

16 Neutron Beam Impinging on a Slice of Target Atomic density in target = N Microscopic cross section of nucleus Area of beam and of target = 1 Differential thickness of target = dx Volume of target = 1 * dx = dx Bull s Eye Area in slice = N dx Beam intensity = I Reaction Rate (per unit volume of target per s) = I*N dx/dx = IN = I where = N is called the macroscopic cross section; it has units cm -1. can be identified as the probability of a beam of unit intensity interacting with the target per unit distance of beam travel. Area = 1 cm September 16

17 Cross Sections and Reaction Rate, and, varies with: the nuclide the type of interaction i (scattering, absorption, fission, etc.) the neutron speed If there are several types of nuclei, the s add: i = N 1 1,i + N 2 2,i + N 3 3,i + For each type of interaction, Reaction Rate i = I i (1) This is an all-important equation! 2015 September 17

18 Cross-Section Databases The s are obtained by experiment. They must be measured (by aiming neutrons of various speeds at various targets). They cannot be calculated from first principles. Therefore experimental databases of cross-section values have been, and continue to be, developed by international teams of experimenters. Evaluated Data Sets (such as ENDF/B-VI) are sets of cross-section values established over the ranges of neutron energy important in reactor applications. They are of crucial importance to reactor-physics calculations September 18

19 Energy Instead of Speed It is important to remember that neutron energy E can be used instead of the neutron speed, since these two quantities are directly related to one another by 1 E m 2 2 (in reactors neutron energies are not relativistic) 2015 September 19

20 Macroscopic & Microscopic Cross Sections Again: i = N i (1), where N = atomic density = number of atoms of the material per cm 3 N can be obtained from the material s density and atomic or molecular weight. Remember or rederive the expression: N0 24 N, where N0 Avogadro' s number *10, A material density, and A atomic weight of material (use judiciously when the material is a composite or a solution!) Note: When the material is composed of several types of nuclides, denoted say by a subscript k, the macroscopic cross section must be calculated taking all nuclides into account, i.e. i N k ik (1)' k therefore the relative abundances of the nuclides, and all microscopic cross sections, must be known September 20

21 Macroscopic & Microscopic Cross Sections Both and depend on the material, the neutron energy (or speed), and the type of reaction. The cross sections for scattering, absorption, fission and radiative capture are often denoted by subscript s, a, f,, e.g., s, a, f and respectively. The total cross section tot measures the total number of all types of reaction per unit distance: tot = s + a For nuclear fuels, only radiative capture and fission are significant. Neglecting other reactions, then: a = f + (2) 2015 September 21

22 Important Quantities in Neutron Production Neutrons are produced in fission, but not all absorptions result in fission. The probability of radiative capture relative to fission is given by the parameter = / f (3) Important quantities which can be quoted when we consider neutron production are: = Average number of neutrons per fission (4) & = Average number of neutrons per absorption (5) and can be related using the various cross sections and the relative probability α. Show that September 22

23 Fission Chain Reaction The chain reaction of neutrons in one generation giving rise to neutrons in a next generation can be self-perpetuating ( critical ) under certain conditions. By judicious design, research and power reactors can be designed for criticality; controllability is very important. The energy release is open to control by controlling the number of fissions September 23

24 Fissionable and Fissile Nuclides Only a few nuclides can fission. Fissionable nuclides are nuclides which can be induced to fission, e.g., 238 U, 235 U, 239 Pu, and 240 Pu. In some cases, e.g., 238 U, the nuclide is fissionable only by neutrons of energy higher than a certain threshold A fissionable nuclide which can be induced to fission by an incoming neutron of any energy is called fissile. There is only one naturally occurring fissile nuclide: 235 U. Other fissile nuclides are 233 U, isotopes 239 Pu and 241 Pu of plutonium, and some isotopes of elements with still higher atomic number. None of these is present in nature to any appreciable extent September 24

25 Plutonium There is no appreciable amount of plutonium in nature, but plutonium is produced in the reactor by absorption of neutrons in U-238. Some of these absorptions result in U-239 betadecaying to Np-239, which then beta-decays to Pu- 239 Some Pu-240 is produced by neutron absorption in Pu-239, and some Pu-241 is produced by neutron absorption in Pu-240 Pu-239 and Pu-241 are very important because they are fissile and therefore contribute to the chain reaction Pu-240 is not fissile, therefore it is mostly an absorber of neutrons 2015 September 25

26 Fission Products The two large fission fragments in the sketch of fission represent fission products, i.e., elements with roughly half the mass of uranium. Most of these elements are radioactive, and decay with various half-lives (some very long). Irradiated nuclear fuel must therefore be handled and disposed of very carefully. Fission products absorb neutrons and therefore represent a negative load on the chain reaction. Also, the decay of fission products is a source of heat in the fuel. Decay heat represents ~7% of the energy released in the reactor, a not-insignificant fraction. Nuclear fuel must continue to be cooled even when the reactor is shut down and also when fuel is discharged September 26

27 Discussion: Fission-Product Decay There are hundreds of fission products (different nuclides). Why are most of them radioactive? Hints: What is the ratio of neutrons to protons in light nuclei (e.g., 12 C or 16 O). What is it in heavy nuclei (U)? Why? What is this ratio in the fission fragments? Why? You would say that the fission fragments are neutron- ***. Can this ratio be sustained? What are ways in which most fission products can decay? 2015 September 27

28 END 2015 September 28

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