3 THE NUCLEUS AND RADIOACTIVE DECAY THE STANDARD MODELThe nucleus is generally modeled as being composed of protons and neutrons“A” designates the number of nucleons (protons plus neutrons)“Z” defines the number of protons“N” specifies the number on neutrons
4 THE NUCLEUS AND RADIOACTIVE DECAY THE STANDARD MODELThe “Standard Model” assumes that quarks combine to from neutrons and protons in the nucleus. An alternative view is that they maintain separate identity in the nucleus. There are apparently experiments that suggest that both views are correct
5 THE NUCLEUS AND RADIOACTIVE DECAY THE STANDARD MODEL cont’dFermions are the basic constituents of matter and have spins of 1/2, 3/2, 5/2,... Leptons and Quarks are FermionsLeptons have spin one-half and do not undergo “strong” interactions. Neutrinos and electrons are examples of LeptonsQuarks are up, down, bottom, top, strange and charm, and they have colors of red, blue or green. Color is basically equivalent to charge of protons and electrons. They combine to form colorless combinations
6 THE NUCLEUS AND RADIOACTIVE DECAY Gluons mediate the force between quarks.Bosons carry the force between basic particles, such as Hadrons and are made up of Quarks. Photons, W-, W+, and Z0 are Bosons. They have spins of 0, 1, 2,…Hadrons undergo strong interactions and have long life times. The neutron, protons, antiproton, lambda, and omega particles are Fermionic Hadrons.The four forces: gravitational, weak, electromagnetic and strong are generally viewed to have been one before the “Big Bang.” Unification theories have apparently been successful at combining all but gravitation. Gravity is not part of the “Standard” model, but is included in the illustration since it is one of the fundamental forces.
7 THE NUCLEUS AND RADIOACTIVE DECAY BINDING ENERGYNuclear reactions can be either exothermic or endothermic, the “Q” value is the difference between “before” collision and “after” collision masses.Given the reactionwhere a is the target and b is the projectile, and c and d are the reaction products.
8 THE NUCLEUS AND RADIOACTIVE DECAY Example:The “Q” value is given by
11 THE NUCLEUS AND RADIOACTIVE DECAY Note that these are nuclear and not atomic masses. Also note that the disintegration energy is split between the kinetic energies of the reaction products. From two particle kinematics it can be shown thatwhere, m, is the mass of He and, M, is the mass of Rn. Alternatively the Q value can be calculated from the energy of the alpha particle. Radium-226 decays directly to ground state 95 % of the time and emits a 186 keV gamma 5 % of the time
12 THE NUCLEUS AND RADIOACTIVE DECAY BETA DECAYIn beta decay, the nucleus emits an electron and an antineutrino. The energy imparted to each particle varies. As example isThe Q value is the mass differences between the Co mass minus the Ni and beta masses. The average energy of the beta energy spectrum is about one-third of Q. The maximum energy is the Q value.
14 THE NUCLEUS AND RADIOACTIVE DECAY GAMMA-RAY EMISSIONNuclei that decay from an excited state with no change in the number of nucleons are called isomeric. Nuclides in the initial and final states are called isomers. Unlike betas, photons emitted from the nucleus have discrete energies. Examples are as follows:Note that Cs may decay directly to ground state (7 % of the time), but it usually (93 % of the time) decays to an excited state of Ba
15 THE NUCLEUS AND RADIOACTIVE DECAY INTERNAL CONVERSIONIn the case of internal conversion, energy is transferred directly to an orbital electron (K or L shell, most likely). A photon is not emitted which then transfers energy to the electron. This process competes with gamma emission. The energy of the ejected electron is the transferred energy minus the binding energy of the orbital electron
16 THE NUCLEUS AND RADIOACTIVE DECAY ORBITAL ELECTRON CAPTURENuclei which capture an orbital electron, usually a K shell electron, as a decay mode emit a neutrino and decrease in the number of protons by one. An example is as shown belowThe neutrino acquires all the energy associated with the decay. The Q value is given bySince the energy added to the nucleus is the electron mass minus the binding energy and since Rh has one more electron than Pd, the Q value must be greater than the binding energy of the electron
18 THE NUCLEUS AND RADIOACTIVE DECAY POSITRON DECAYNuclei that undergo positron decay emit a positively charged electron (an antielectron) and a neutrino. An example is shown belowIf Q is expressed in terms of atomic masses and binding energies are neglected, we obtainFor positron decay to be possible, the mass of the parent must be greater than that of the daughter by 2m (1.02 MeV). Note that EC competes with positron decay
20 MECHANISMS OF INTERACTION OF RADIATION WITH MATTER PHOTONS:The primary mechanisms of photon interaction with matter are: Compton effect, photoelectric, and pair production. Photons can also interact directly with the nucleus to produce photodisintegrations. Thompson and Raleigh scattering are also of interest
21 MECHANISMS OF INTERACTION OF RADIATION WITH MATTER Compton EffectCompton interactions are associated with free electrons. Even if they are not “completely free,” the binding energies are small relative to the energy transfer. For the purpose of calculating a linear absorption coefficient, two components are considered. One is associated with the energy transfer to the medium and the other is scattering out of its straight-line path. Thus,
22 MECHANISMS OF INTERACTION OF RADIATION WITH MATTER In the case of energy deposition calculations, only the energy absorption component of the Compton effect is considered. The energy of the recoil electron is given by
23 MECHANISMS OF INTERACTION OF RADIATION WITH MATTER Photoelectric EffectEinstein received the Nobel Prize for his studies on the development of the “Photoelectric Effect.” This effort involved the ejection of photoelectrons from a surface, where the energy of the ejected electron is equal to the photon energy minus the work function energy. The basic physics is the same for the “Photoelectric Effect” as used in studies of photon attenuation, but the phenomena are different. In the case of photon attenuation in matter, the phenomenon of interest refers to an interaction of the photon with the entire atom where a K, L, or M shell electron is ejected.Thus, the energy imparted to the electron is the photon energy minus the binding energy (rather than the work function in Einstein’s studies). The probability of this interaction is proportional to the fourth power of the electron density divided by the third power of the photon energy
24 MECHANISMS OF INTERACTION OF RADIATION WITH MATTER Pair ProductionIn the case of pair production, the photon is completely absorbed and an electron-positron pair is formed. Thus, the threshold for this reaction is twice the rest mass of an electronThompson Cross SectionAs photon energy approaches zero, an electron resonates at the same frequency as the electromagnetic field associated with the photon. As a result, the photon is scattered to various angles with no energy loss
25 MECHANISMS OF INTERACTION OF RADIATION WITH MATTER Raleigh (coherent) ScatteringAt low photon energies, a photon will scatter off the entire atom. Thus, the energy loss is minimal and the scattering angle is small. This phenomenon is of interest in some physics experiments, but not of much interest for dosimetry
27 NEUTRONSNeutrons undergo either absorption or scattering reactions with nuclei. If a neutron is absorbed into the nucleus, it may decay by a variety of mechanisms. It may fission, eject one or more neutrons, undergo alpha particle decay, emit a photon, decay by ejecting a proton, etc. Scattering may be elastic or inelastic
28 NEUTRONS Elastic Scattering Elastic scattering may be well defined by two particle kinematics or it may be a resonance phenomenonInelastic ScatteringInelastic scattering occurs when the neutron is absorbed and one is emitted with an isotropic angular distribution. This may or may not be a resonance phenomenon
29 NEUTRONSFissionNuclei are often classified as fissile, fertile and fissionable. Fissile nuclei fission with zero energy neutrons, fertile isotopes absorb neutrons and ultimately may decay to a fissile isotope. Fissionable nuclei will fission with neutrons of some energy. Examples of fissionable isotopes include: 235U, 233U, 239Pu, 241Pu, 238U and 232Th. Fissile isotopes include: 235U, 233U, 239Pu, and 241Pu. Examples of fertile materials are: 238U and 232Th
30 NEUTRONSFissionFission usually results in the nucleus splitting into two nuclei with masses that add to the atomic mass of the nuclei which fissions. Occasionally, three fission products are formed. Note from the bimodal mass distribution curve that the peaks on the yield curve sum to approximately It is also useful to note that low (below 60) and high (above 200) mass fission products are seldom produced. Thus, Co-60, which is common in radioactive waste, is primarily an activation product
33 ALPHA PARTICLESAlpha particles undergo continuous slowing down and consequently well defined relationships exist between range and energy. Bethe derived the following relationship for slowing down of charged particles, using relativistic quantum mechanics:wherez = atomic number of the heavy particle,e = charge on an electron,n = electron density,m = rest mass of an electron,c = speed of light,b = speed of particle relative to light, andI = mean excitation energy of medium.
34 BETA PARTICLESBeta particles do not follow a continuous slowing down model very well since electrons can lose large fractions of their energy in a single collision. However, a continuous slowing down approach does yield useful results. The range can be calculated using the formulaElectrons occasionally transfer significant energy to secondary electrons, called delta rays. This results in energy being deposited at a significant distance from the path of the initial electron
35 NATURALLY OCCURING RADIONUCLIDES COSMOGENICInteractions of cosmic rays with the atmosphere, earth, sea, etc., results in the production of several measurable radionuclides. Those of significance include: 3H, 7Be, 14C and 22Na. Others are produced by secondary neutrons and general high energy collisions. Tritium is produced primarily by the reactions 14N(n,T)12C and 16O(n,T)14N. It has a half-life of years. The reaction 14N(n,p)14C, accounts for most of carbon-14. Carbon-14 has a half-life of 5730 years. Beryllium-7 is produced by high energy interactions with nitrogen and oxygen, and has a half-life of 53.4 days. Sodium-22 results from neutron interactions with argon, and has a half-life of 2.6 years. These radionuclides contribute about 1 mrem/yr to the annual dose equivalent
36 PRIMORDIALTwo decay series, 238U and 232Th results in most of the exposure to humans. The 235U series contributes little to human exposure. These radionuclides contribute about 30 mrem/yr from direct external radiation and about 200 mrem/yr from radon
41 SERIAL RADIOACTIVE DECAY Secular equilibrium occurs when the half-lift of the parent is much greater than the daughter. In this case the activities of the parent and daughter are essentially equalTransient equilibrium occurs when the half-life of the parent is slightly greater than the daughterNo equilibrium exists when the half-life of the daughter is greater than the parentIn the case of many decay chain products, such as is in the case of U-238, U-235 and Th-232, the activities are all in equilibrium after several half-lives of the longest lived daughter, such as Ra-226 in the case of U-238
42 ARTIFICIAL SOURCES OF RADIONUCLIDES Mining and MillingConversionEnrichmentFuel FabricationPower Reactor OperationsCommercial ReprocessingProduction ReactorsDepartment of Defense ReprocessingWeapons FabricationAccelerators