Applications of Nuclear Physics: Nuclear Reactions & Transmutation of Elements

1. Applications of Nuclear Physics 1. Nuclear Reactions and the Transmutation of Elements A nuclear reaction takes place when a nucleus is struck by another nucleus or particle. If the original nucleus is transformed into another, this is called transmutation. Example: Generic reaction: • Laws of conservation: • the total number of nucleons • the total charge • the energy • the momentum • must be conserved in nuclear reactions.

2. Conservation of energy For reaction: • The reaction energy, or Q-value, is the sum of the initial masses less the sum of the final masses, multiplied by c2 • If Q is positive, the reaction is exothermic, and will occur no matter how small the initial kinetic energy is • If Q is negative, there is a minimum initial kinetic energy that must be available before the reaction can take place

3. Artificial transmutation. Transuranic elements Neutrons are very effective in nuclear reactions, as they have no charge and therefore are not repelled by the nucleus.

4. 2. Nuclear Fission. Nuclear Reactors After absorbing a neutron, a uranium-235 nucleus will split into two roughly equal parts. One way to visualize this is to view the nucleus as a kind of liquid drop. The mass distribution of the fragments shows that the two pieces are large, but usually unequal. The energy release in a fission reaction is quite large.

5. The chain reaction Since smaller nuclei are stable with fewer neutrons, several neutrons emerge from each fission as well. These neutrons can be used to induce fission in other nuclei, causing a chain reaction. Neutrons that escape from the uranium do not contribute to fission. There is a critical mass below which a chain reaction will not occur because too many neutrons escape. A moderator is needed to slow the neutrons; otherwise their probability of interacting is too small. Common moderators are heavy water and graphite. Unless the moderator is heavy water, the fraction of fissionable nuclei in natural uranium is too small to sustain a chain reaction, about 0.7%. It needs to be enriched to about 2-3%.

6. Nuclear Reactors Control rods, usually cadmium or boron, that absorb neutrons can be used for fine control of the reaction, to keep it critical but just barely. An atomic bomb also uses fission, but the core is deliberately designed to undergo a massive uncontrolled chain reaction when the uranium is formed into a critical mass during the detonation process.

7. 3. Nuclear Fusion The lightest nuclei fuse to form heavier nuclei, releasing energy in the process. Example1: the sequence of fusion processes that change hydrogen into helium in the Sun. The net effect is to transform four protons into a helium nucleus plus two positrons, two neutrinos, and two gamma rays. More massive stars can fuse heavier elements in their cores, all the way up to iron, the most stable nucleus.

8. Example2: There are three fusion reactions that are being considered for power reactors: • These reactions use very common fuels – deuterium or tritium – and release much more energy per nucleon than fission does. • A successful fusion reactor has not yet been achieved, but fusion, or thermonuclear, bombs have been built. • Several geometries for the containment of the incredibly hot plasma that must exist in a fusion reactor have been developed – the tokamak, which is a torus; or inertial confinement, which is tiny pellets of deuterium ignited by powerful lasers.

9. http://news.yahoo.com/s/nm/20060420/sc_nm/energy_nuclear_usa_dchttp://news.yahoo.com/s/nm/20060420/sc_nm/energy_nuclear_usa_dc Three Mile Island shows US nuclear risks, rewards By Jon Hurdle Thu Apr 20, 6:35 AM ET Pennsylvania (Reuters) - Four giant cooling towers loom over the Three Mile Island nuclear plant, reminders of the fears and hopes surrounding an industry that may help cut U.S. dependence on foreign oil. Two towers stand quiet, idle since a partial meltdown in a reactor almost 30 years ago in the nation's worst nuclear accident. Two others belch steam from an active reactor, providing cheap electricity to 400,000 homes. Unlike the Chernobyl disaster in Ukraine (April 26, 1986) no one died at Three Mile Island. But critics of atomic power raise concerns over potential terrorist threats to plants and say science has yet to provide an adequate solution for highly toxic nuclear waste.

10. Nuclear Fission:Nuclear Power Plants A controlled chain reaction can be used to generate electrical power. The United States uses 103 nuclear power plants to produce ~20% of our electricity. Worldwide about 400 nuclear power plants produce about 1/6 of the world’s electricity needs. The nuclear reaction is used to create heat; the heat is converted to mechanical energy and used to create electricity.

11. Elementary Particles 1. High Energy Particles and Accelerators • We need accelerators because: • As the momentum of a particle increases, its wavelength decreases (λ = h/p), providing details of smaller and smaller structures • If an incoming particle in a nuclear reaction has enough energy, new particles can be produced • This effect was first observed in cosmic rays; later particle accelerators were built to provide the necessary energy. • With additional kinetic energy more massive particles can be produced • Cyclotron: • Charged particles are maintained in near-circular paths by magnets • An electric field accelerates them repeatedly. The voltage is alternated so that the particles are accelerated each time they traverse the gap • The frequency of the applied voltage must equal cyclotron frequency (frequency of circulations)

12. Synchrotron: • Here, the magnetic field is increased as the particles accelerate, so that the radius of the path stays constant. This allows the construction of a narrow circular tunnel to house a ring of magnets. • Synchrotrons can be very large, up to several miles in diameter. • Synchrotron radiation (radiation due to the centripetal acceleration) • Accelerating particles radiate; this causes them to lose energy. • Particles in a circular path radiate due to the centripetal acceleration. • For protons this is usually not a problem, but the much lighter electrons can lose substantial amounts. • One solution is to construct a linear accelerator for electrons Linear accelerator: E = eV. The largest is about 3 km long. Collider: Two beams of accelerated particles collide head-on.

13. Example: What is the wavelength, and hence the expected resolution, for the beam of 1.3 GeV electrons? Note! Comments:

14. 2. Beginnings of Elementary Particle Physics – Particle Exchange The today's model views quarks and leptons as basic constituents of ordinary mater. • The electromagnetic force acts over a distance – direct contact is not • necessary. How does that work? • Because of wave-particle duality, we can regard the electromagnetic force • between charged particles as due to: • an electromagnetic field, or • an exchange of photons Feynman diagram for photon exchange by electrons The photon is emitted by one electron and absorbed by the other. It is never visible and is called a virtual photon. The photon carries the electromagnetic force. Feynman diagram for meson exchange by nucleons

15. This is a crude analogy for how particle exchange would work to transfer energy and momentum. The force can either be attractive or repulsive.

16. Mesons Originally, the strong force was thought to be carried by mesons. The mesons have nonzero mass, which is what limits the range of the force, as conservation of energy can only be violated for a short time. The mass of the meson can be calculated, assuming the range, d, is limited by the uncertainty principle: This meson was soon discovered, and is called the pi meson, or pion, symbol π. Pions are created in interactions in particle accelerators; here are two examples:

17. This table details the four known forces, their relative strength for two protons in a nucleus, and their field particle. • The weak nuclear force is also carried by particles; they are called the W+, W-, and Z0. They have been directly observed in interactions. • A carrier for the gravitational force, called the graviton, has been proposed, but there is as yet no theory that will accommodate it. • Every type of particle has its own antiparticle, with the same mass but most quantum numbers being opposite. • A few particles, such as the photon and the π0, are their own antiparticles, as all the relevant quantum numbers are zero for them.

18. Particle Classification • As work continued, more and more particles of all kinds were discovered. They have now been classified into different categories. • Gauge bosons are the particles that mediate the forces • Leptons interact weakly and (if charged) electromagnetically, but not strongly • Hadrons interact strongly; there are two types of hadrons, baryons (B = 1) and mesons (B = 0). Almost all of the particles that have been discovered are unstable If they decay weakly, their lifetimes are around 10-13 s If they decay electromagnetically, around 10-16 s; and if strongly, around 10-23 s Strongly decaying particles do not travel far enough to be observed; their existence is inferred from their decay products.

19. Quarks Due to the regularities seen in the particle tables, as well as electron scattering results that showed internal structure in the proton and neutron, a theory of quarks was developed. There are six different “flavors” of quarks; each has baryon number B = ⅓. Hadrons are made of three quarks; mesons are a quark-antiquark pair. Here are the quark compositions for some baryons and mesons: