Part A - Basic Nuclear Physics

Slide 1 This section will be a review of basic nuclear physics.

Slide 2 We will start our discussion with a neutral atom in the ground state. The atom consists of a small nucleus surrounded by a number of electrons. The electrons orbit around the nucleus in very well defined energy levels. The lowest energy level is called the K shell, and can contain a maximum of two electrons. The second energy level is called the L shell, and can contain a maximum of eight electrons. The third shell is the M shell, the fourth the N shell, and so forth. The diameter of a typical atom is about 10-8 centimeters. The diameter of a typical nucleus is about 10-12 centimeters, for a factor of ten thousand. This means that the volume of the atom is about 1012 times larger than the volume of the nucleus. Thus an atom consists of a very, very small nucleus surrounded by a few electrons, much like the solar system consists of the sun surrounded by a few planets. The atom, like the solar system consists of mostly nothing but empty space. Thus it is possible that radiation, such as photons or even electrons, can pass through an atom without having any interactions.

Slide 3 The nucleus consists of neutrons and protons, both of which are called nucleons. The nucleons are about two thousand times heavier than the mass of an electron. The nuclear forces between the nucleons are the same; that is the force between neutrons and neutrons, protons and protons, neutrons and protons are all the same. Nature would like to have an equal number of neutrons and protons in the nucleus. However, if one gets too many protons in such a small volume the Coulomb force tends to make the nucleus unstable, that is, the protons want to repel each other. For Z greater than twenty, the Coulomb forces cause the nucleus to become unstable or radioactive. If one wants a stable nucleus above Z equal twenty or more than twenty protons, one must add more nuclear glue. In this case, one must add more neutrons to the nucleus. Stable nuclei can be found for all elements up to Z equal eighty-three, with one exception, Technetium. Above Z equal eighty-three all of the known nuclei are unstable or radioactive. In the same way, nuclei with too many neutrons, or too many protons, may also be unstable or radioactive.

Slide 4 The notations we will use are the following: “Z” will be the number of protons in a nucleus, this is also the atomic number of the element, and is also the number of electrons in a neutral atom. Examples are hydrogen which has Z equal one, Z equal twenty-six is iron, Z equal eighty-two is lead, Z equal ninety-two is uranium. “N” will be the number of neutrons in the nucleus. “A” will be the total number of nucleons, that is the total number of protons and neutrons, in the nucleus. The notation is as follows: In this example X represents the element and would be

1 given as the abbreviation for the element. The superscript on the left is A, the total number of nucleons. The subscript on the left is Z the total number of protons. The subscript on the right, N, is the total number of neutrons. An example is Co-60 which has a total of 60 nucleon consisting of 27 protons and 33 neutrons.

Slide 5 Isotopes are nuclides with the same number of protons or the same Z but a different number of neutrons. Examples: Hydrogen can have three forms, which are listed here: Hydrogen – 1, 2, and 3. Hydrogen - 1 has only a single proton in the nucleus. Hydrogen - 2 which is commonly called Deuterium, has one proton and one neutron in the nucleus. Hydrogen 3, or Tritium, has one proton and two neutrons. Another example of isotopes would be Uranium - 235 and Uranium - 238. In this case, Uranium - 235 has 143 neutrons and Uranium - 238 has 146 neutrons.

Slide 6 If one makes a plot of all the known nuclides, one has a chart first proposed by Segré and more commonly called the chart of the nuclides. Here all of the nuclides are plotted as a function of Z and N. In this case, the black dots represent the 256 known stable nuclides. The other dots represent some of the more than 1200 known radioactive nuclides.

Slide 7 Radioactive Decay In this section we will discuss two forms of radioactive decay, Alpha and Beta decay, together with the three types of radiation, alpha, beta, and gamma radiation.

Slide 8 The first type of radioactive decay that we will consider is beta (β) decay. There are three types of beta decay. The first we will consider is beta minus. If the nucleus has too many neutrons, it will undergo a radioactive decay by emitting an electron or a β- particle and an anti-neutrino (ν ). In this situation, a neutron in the nucleus is converted to a proton. In the process, the number of protons in the nucleus increases by one and so the nucleus or atom changes to a new element or a daughter element. On the other hand, if the nucleus has too many protons, then it can either capture one of the atomic electrons (usually from the inner most or K - electron shell) or if there is enough energy available, it can emit a positron (β+) particle. In the case of a proton capturing an electron, the proton is converted to a neutron and in the process emits a neutrino (ν ). In the case of a proton emitting a positron or β+ particle, the proton is converted to a neutron, β+, and a neutrino. In both cases, the charge of the nucleus decreases by one, and again, the atom is changed.

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Slide 9 Electrons and positrons are the anti-particles of each other. If they interact, they will annihilate each other, as we will discuss later. In the same way, neutrinos and anti-neutrinos are also anti-particles of each other. However, in this case, the probability of an interaction is very, very small. Neutrinos and anti-neutrinos are small neutral particles with nearly zero rest mass that travel at nearly the speed of light. They have a very, very small probability of interacting. In fact, neutrinos from the Sun have a high probability of passing through the Earth without an interaction.

Slide 10 THE ENERGY DISTRIBUTION OF BETA PARTICLES. Since beta plus and beta minus radioactive decays are both three body decays, that is, the end products are the daughter nucleus, a beta particle, and a neutrino, one cannot predict how the energy of the reaction will be shared by the three daughter products. However, since the nucleus is massive compared to the beta particle and the neutrino, almost all the energy will show up as kinetic energy in the beta and neutrino. The energy of the beta particles will then range from zero to the full energy of the decay. In the same way a neutrino may also have energies ranging from zero to the full energy of the decay. A typical spectrum from a beta minus decay is shown in the next slide.

Slide 11 In this slide, To represents the full energy of the decay. It also represents the maximum energy that the beta particle can have. Thus, the beta particle can have an energy ranging from zero up to To. The beta spectrum has a peak at approximately one-third To. In the beta plus spectrum the peak will occur at about two-thirds To.

Slide 12 Another mode of radioactive decay is alpha decay. For radioactive nuclei with Z > 82, alpha decay has a very high probability. There are a few nuclei with Z < 82 that will also undergo alpha decay. However, these few radioactive nuclei are seldom encountered. Alpha particles are heavy charged particles consisting of two neutrons and two protons, or the nucleus of the helium-4 atom. As the alpha particle has a charge of 2, this means that nuclei undergoing an alpha decay will lose two protons, and the charge of the nucleus decreases by two. Alpha decay is frequently followed by one or more beta minus decays. Since the number of products of alpha decay is only two, the daughter nucleus and the alpha particle, the full energy of the decay is shared between two daughter products and the energy of each can be calculated exactly. Thus the alpha particles are monoenergetic. However, because the decay is usually to an excited level of the daughter nucleus, there

3 may be several groups of monoenergetic alphas in the spectrum. This is shown in the next slide.

Slide 13 Here we see a typical alpha particle spectrum. Note that the highest energy group is a relatively small group. This would represent the alpha decay to the ground state for the daughter nucleus. In this example, the most probable alpha particle energy is the second highest energy group. This represents a decay to one of the excited levels of the daughter nucleus.

Slide 14 If one goes back to the chart of nuclides, one can identify the regions on the chart corresponding to the different types of radioactive decay. If the nucleus has too many neutrons, then it will undergo a beta minus decay. This is the region below and to the right of the line of stability. If the nucleus has too many protons, electron capture or beta plus decay is possible. This is identified as the region above and to the left of the line of stability. For Z > 83, one has the possibility of alpha decay followed by beta minus decay.

Slide 15 Most radioactive decay is not to the ground state of the daughter nucleus. Instead the daughter nucleus is usually left in an excited state and then de- excites or moves to a lower energy level by emitting photons (called gamma rays) until it reaches the ground state.

Slide 16 Photons are the particles associated with electromagnetic waves. They have zero rest mass and no charge. In a vacuum they travel at the speed of light. There are many types of photons, and they received their names based on the physical process generating them. Some examples that you may be familiar with are visible light, radio waves or infrared radiation. The four types of photons that we are interested in, for this course, are X rays, gamma rays, Bremsstrahlung radiation, and annihilation photons. X rays are photons that are emitted from the atom when atomic electrons move from one energy level to a lower energy level. As the atomic electrons exist at well-defined energy levels, the difference between the energy levels is also well-defined. Therefore, the x rays are mono- energetic. Gamma rays are the photons that are emitted when an excited nucleus moves from one energy level to another, lower energy level. Again, the nucleus exists only at very well defined energy levels, and so the difference between the energy levels is also well defined, and the gamma rays are also mono-energetic.

Slide 17 On the other hand, Bremsstrahlung radiation which are the photons emitted when charged particles, usually electrons interact with the electric field of a

4 nucleus have a continuous energy distribution. In this case the trajectory of the electron is changed and in the process the electron may radiate a photon. The photons that are emitted are called Bremsstrahlung radiation and can have any energy, from zero to the full kinetic energy of the charged particle. Therefore Bremsstrahlung radiation will have a continuous energy distribution ranging from zero energy to the full energy of the electron. The fourth type of photon that we will be addressing here are the annihilation photons. These are the photons emitted when an electron interacts with its anti-particle, the positron. When they interact, they annihilate each other and disappear. The energy then appears as two annihilation photons, each containing one rest mass energy or 0.511 MeV. However, since the electron and positron may have small amounts of kinetic energy before they annihilate each other, this additional energy must also be carried off by the two annihilation photons, so their energies will vary slightly from 0.511 MeV.

Slide 18 On the next three slides we will be looking at some examples of radioactive decay. On this slide, we have an example of a beta minus decay. Cobalt 60 has a halflife of about 5.3 years. It undergoes a beta minus decay to an excited level of nickel 60. The excited level is about 2.50 MeV above the ground state of nickel 60. It promptly decays to the 1.33 MeV excited level by emitting a 1.17 MeV gamma ray. The 1.33 MeV excited level has a half life of about 10-9 seconds and then decays to the ground state of Nickel by emitting a 1.33 MeV gamma ray.

Slide 19 An example of a beta plus decay is the decay of sodium 22. Here, the sodium 22 emits a positron, going to a 1.27 MeV excited level of neon 22. The excited neon 22 de-excites by emitting a 1.27 MeV gamma ray, moving to the ground state.

Slide 20 An example of an alpha decay is uranium 238. Here the uranium 238 emits an alpha particle, moving to an excited level of thorium 234. The alpha decay is shown by a double line representing a change of two units of charge. The daughter nucleus, thorium de-excites by emitting a gamma ray, and then undergoes a β- decay to an excited level of protactinium 234. After the protactinium decays to its ground state, it will undergo a β- decay to an excited level of uranium 234.

Slide 21 It is worth repeating the information on the energy distributions of photons. Remember that gamma rays originate when a nucleus moves from one energy level to a lower energy level. All of the energy levels in the nucleus are very well defined. Therefore, all of the gamma rays from similar decays will all have the same energy, or are monoenergetic. In the same way, X rays from the transition

5 of atomic electrons from one energy level to a lower energy state are also monoenergetic. Annihilation photons from the interaction of positrons and electrons are also monoenergetic except that the electrons and positrons may have some kinetic energy that must also be carried off by the two annihilation photons. This will cause a small variation in their energy. Bremsstrahlung photons can have any energy from zero to the full kinetic energy of the charged particle producing the Bremsstrahlung interaction.

Slide 22 Sometimes excited nuclei will de-excite by transferring their energy to one of the atomic electrons rather than emitting a gamma ray. This process is called internal conversion and the electrons will carry off the excess energy. The energy of the internal conversion electrons will be the energy difference between the two energy levels of the nucleus minus the binding energy of the atomic electron. This process results in a monoenergetic electron being emitted by the nucleus.

Slide 23 The activity, or number of radioactive nuclei decaying per unit time, is given by the symbol A, where A is equal to λ times N. Here N is the number of radioactive nuclei and λ is the decay constant, or probability per unit time that a nucleus will decay. The units of activity are Becquerel (Bq) or Curie (Ci). One Bq is defined as one disintegration or decay per second while a Curie (which is the older unit) is defined as 3.7 x 1010 disintegrations per second. Activity should not be confused with the number of radiations being emitted by the source per unit time. For example, referring back to our example of Co-60 radioactive decay, in one disintegration, Co-60 emits one beta particle and two gamma rays. Therefore, a 1000 Becquerel source of cobalt 60 would be producing (or emitting) 1000 beta particles per second and 2000 gamma rays per second.

Slide 24 The number of radioactive nuclei left after a period of time, t, is given as

-λt N = No * e . where No is the number of radioactive nuclei at time t equal to zero. Because this is an exponential relationship, the concept of half-life has been introduced. The half life is defined as the period of time that it takes for one half of the radioactive nuclei to decay and is given as t1/2 = 0.693 / λ.

For example, if one starts off with 1 million radioactive nuclei, after one half life, one would have 500,000 radioactive nuclei left. After a second half life, one would have 250,000 radioactive nuclei left. After a third half life, one-half of the 250,000 would decay, and one would have 125,000 radioactive nuclei left. After

6 ten half lives, the number of radioactive nuclei has be reduced by a factor of 1000.

Slide 25 This ends Part A, A Review of Nuclear Physics

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