1. The Nuclear, Plasma and Radiation Universe

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Unformatted text preview: THE NUCLEAR, PLASMA, AND RADIATION UNIVERSE © M. Ragheb 2/4/2009 INTRODUCTION The study of Nuclear, Plasma and Radiation phenomena is a reflection of the nature of, and an attempt at understanding and describing the universe that we belong to. Sustainable human development depends upon such an understanding, and upon using our knowledge in tackling the present and future global challenges of hunger, disease, management of natural resources, environmental pollution and global climate change. In the long term, this would help humanity spread life within and beyond the confines of our Solar System. As the world is becoming more reliant on its scientific advancements, its leaders as scientists and engineers, as well as members of the public in general, need to be aware the role of these fundamental processes and their applications in modern society. These applications can be found in every field of Science and Engineering, at every economical and social level, and every place on Earth. Since human progress goes hand in hand with the dissemination of knowledge, improvement of human well being and increasing the potential for human development depends on the spread of such knowledge about their potential to both decision makers and the people that it touches. For the present's perspective, people around the world are genuinely concerned about the dangers posed by nuclear weapons, are skeptical about the safety of nuclear power generation and are apprehensive about the radiological effects of natural as well as man-made radiation sources. These negative perceptions are neutralizing the potential positive contributions of Nuclear, Plasma and Radiation science to everyday life. THE FORCES OF NATURE It is convenient to consider four fundamental physical interactions that govern our universe. It is suggested that a general law part of the ”Theory of Everything” described these forces at the time of the Big Bang when extremely large energy densities existed. These laws separated at the time of creation of our universe about 13.8 billion years ago, in the Big Bang postulated event. Scientists are still attempting at combining the description of these forces within the framework of the “General Theory.” These are: THE GRAVITATIONAL FORCE GENERAL RELATIVITY FORMULATION The theory of General Relativity describes the behavior of gravitation in the Universe. This theory describes gravitation as a warping of space in the presence of matter: the more matter, the more acutely the curving of space. Relativistic models are based on a 4 dimensional space-time continuum. A special case of it that we are familiar with on Earth is Newtonian space. This kind of space is flat, and is the 3 dimensional equivalent of a 2 dimensional plane. The theory of General Relativity does away with any need for a force of gravity, depicting the planets as following paths of least resistance or geodesics through curved space, and indicates that cosmic space can be mapped by going to 4 dimensions. The trajectory of any object describes a world line, which is a course through space and time. If an apple is falling from a tree, it is falling because space in the vicinity of the Earth is curved, it is moving downhill in the space time continuum. The moon orbiting the Earth is rolling around an inner wall of a well occupied by Earth in space-time. In General Relativity, objects respond to the contours of space in their immediate vicinity, while in classical physics gravitation involves action at a distance. General Relativity interprets gravity, not as a force, but as an effect of hyper dimensionality on the 3 dimensional world that we are used to, and accordingly gravitation is just a consequence of geometry. Which theory should be used in favor to another is determined by the ratio: u= 2GM c2r (1) where c is the speed of light, G is the constant of gravitation, M is the mass of the object of interest, and r is the distance from the mass M. NEWTONIAN APPROXIMATION If u is less than 10-3, Newtonian theory can be used. If u is around unity, General Relativity must be used. At intermediate values, the post Newtonian approximation is to be used. For the effect of the sun's gravity on Earth, u=10-8, and Newtonian law is adequate. For the universe, u = 10-2 to 1, and General Relativity must be used. Newton postulated the existence of a force of gravity described by the laws of Newtonian Mechanics. On an earthly scale, it determines the mechanical interactions on our planet Earth, affects the tides, the seasons, and the weather. It is the realm of our mechanical technology in transportation: cars, trains, ships, planes and rockets. In 1665, a year where the great plague epidemic spread in Europe, Isaac Newton is surmised to have come out with the idea of the inverse square law. Supposedly, he came out with it at his home in Woolsthorpe, England, when he saw an apple drop from a tree. He describes in his book: “Philosophiae Naturalis Principia Mathematica” published in 1687, 22 years after his supposed discovery, and after correspondence with Robert Hooke, the inverse law of gravitation: F= Gm1 m2 r2 (2) This law describes the fact that the force F between two bodies or particles of masses m1 and m2 is proportional to the masses, but inversely proportional to the square of the distance r between them. The constant of gravitation G is very small. For instance, the gravitational energy between the electron and the proton is of the order of 10-40 times less than the electrical attracting force between them. Thus the effect of this law is negligible when we consider atomic or nuclear phenomena. If we consider the Earth’s gravitational pull on objects on it, this law becomes important. If we set: m1 = mass of the Earth, and: m2 = the mass of an object that it exerts a gravitational pull on, then F becomes the “weight” of m2, or the gravitational pull of the Earth on it. FIRST LAW OF DYNAMICS This law is the basis of science of motion or “Dynamics”. Galileo introduced its initial framework with the first law of motion, which for the first time states that a force is necessary, not for motion, but for a change of motion: “A body continues to move in a straight line with uniform speed if no force acts on it.” SECOND LAW OF MOTION: NEWTON’S LAW The first law is qualitative, the second law of motion by Newton, quantifies how much force is needed to change motion: F = ma (3) This states that the vector force F is equal to the mass m multiplied by the acceleration a . The mass m is a measure of the quantity of matter in the body. It is also a measure of the inertia of the body, or its ability to resist the effect of the force as an external agent applied on it, trying to change its state of motion. The change of the state of motion for a given force is the acceleration. The acceleration is the rate of change of velocity. Velocity is a vector quantity, containing information about both the speed and the direction of motion of an object. A change in either one or in both, leads to acceleration. THIRD LAW OF MOTION, ACTION AND REACTION Newton’s third law of motion states that: “Action and reaction are of equal magnitude and in opposite directions”. Treating the Earth as a sphere of mass M, and considering R as the distance to its center, the force exercised on a body of mass m on the surface of the Earth is: F= GMm R2 (4) We can define the acceleration on a body m due to the Earth’s gravitation as: g= Force F GM = = 2 m m R (5) Since G, M and R are constants, g is designated as the Earth’s gravitational constant. A body at a height h above Earth has a potential energy equal to: E potential = m.g.h (6) A body possessing a velocity of v has a kinetic energy equal to: E kinetic = ½ m.v2 (7) The equation of conservation of energy states that: E potential + E kinetic = Constant (8) 1 mgh + mv 2 = Constant 2 (9) Or: If we consider the dissipative forces such as friction to be important, work has to be done to surmount them. This work normally appears as heat. If we care to include heat in our consideration, the law of conservation of energy becomes the first law of Thermodynamics. Force fields like the Earth’s gravity, electric fields and magnetic fields are conservative fields, in the sense that the work done against them is converted into the form of potential energy. This potential energy is fully recoverable as kinetic energy if needed. In nature, the controlling forces place limitations on motion in the form of potential barriers. The Earth’s gravity presents a potential barrier to a rocket trying to escape its pull. The escape velocity of a rocket of mass m can be estimated by equating its potential energy to its kinetic energy: 1 2 GMm mv = 2 R (10) From which we get the rocket’s escape velocity at which it must be fired to escape the Earth as: vescape ⎛ 2GM ⎞ =⎜ ⎟ ⎝ R ⎠ 1 2 (11) This escape velocity for different celestial bodies is shown in Table 1. Table 1: The Escape Velocities of different bodies. Celestial Body Earth Moon Sun White Dwarfs Neutron Stars Escape Velocity (miles/sec) 7 1.5 400 3,000 100,000 THE ELECTROMAGNETIC INTERACTION FORCE CONCEPT OF RADIATIVE INTERACTION The laws of Electromagnetics in the form of Maxwell's Equations describe this force. They describe an important part of human civilization, in that these laws govern biological and chemical processes. They form the basis of electrical production systems, and communications in radio, microwave, television, and other electrical and electronic technologies. They are also the basis of Plasma interactions describing processes occurring in interstellar gas, the solar corona, the Earth’s ionosphere, arc discharges and in thermonuclear plasmas. Consider two particles to possess an electrical charge. The motion of each particle will be affected by the presence of the other charged particle, and the two particles will interact. This is described in terms of the concept of radiation traveling from the path of the first particle to affect the other charged particle in its path. If one particle oscillates in one spatial dimension with frequency ν, the radiative interaction causes the second particle to oscillate with the same frequency ν, if we assume that the second particle has no motion other than that that arises from the influence of the first particle. The first particle is designated as the source particle, and the other particle as the detector particle. Depending on the frequency ν of oscillation, the radiation falls in one or another category depending on the application involved. For electromagnetic radiation, moving at the speed of light c, the wavelength λ is related to the frequency ν by: λ= c ν Radiation's wavelengths are measured in units of the Angstrom, where: (12) 1 Angstrom (Ao) = 10-8 cm = 10-10 m. Table 2 displays the range of the Electromagnetic Spectrum. It can be noticed that the visible spectrum is only a minor part of it. Table 2: The Electromagnetic Spectrum and Areas of Applications Wavelength 10-4 A 10-3 A 10-2 A 10-1 A 1A 101 A 102 A 103 A 104 A 105 A 106 A 10-3 m 10-2 m 10-1m 1m 101 m 102 m 103 m 104 m 105 m 106 m 107 m 108 m Applications Cosmic waves. Betatron. Gamma rays emitted by radioactive substances. Gamma ray used in medical therapy. Industrial Radiography. Medical Radiography. x rays. Crystallography. x rays. Soft x rays. Very soft x rays. Ultraviolet radiation. Visible light. Near Infrared. Mid Infrared radiation. Far Infrared. Millimeter waves. Microwave radiation, radar. Television. Communications. Communications. Electric waves. 60 cycle (Hz) Alternating Current (AC). Nuclear, plasma and atomic phenomena cover a much larger portion of the electromagnetic spectrum than does the visible part. X rays are primarily results of atomic phenomena, but they can result from nuclear processes such as the electron capture process. Gamma rays are primarily results of nuclear interactions in the nucleus, including the process of radioactive decay. Gamma rays can result from atomic phenomena such as those produced in thunderstorms from runaway electrons accelerated in the strong electric fields losing their energy through the bremstrahlung process. Radio waves derive from synchrotron radiation in magnetic plasmas. MAXWELL’S EQUATIONS Electromagnetic phenomena are described by Maxwell’s equations. For the description of Electromagnetic phenomena we consider Coulomb’s law in the conventional or centimeter-gram-second (cgs) unit system, describing the inverse square force F arising between two charges e1 and e2 with a separation distance r as: F= e1e2 r2 (13) Newton’s law from Eqn. 3 allows us to define the unit of force, the dyne, in terms of centimeters, grams, and seconds (cgs). The dyne is that force which, acting upon a mass of 1 gm, produces an acceleration of 1 [cm/s2], or: 1 dyne = 1 [gm.cm/s2]. The unit of charge, called the electrostatic unit (esu) of charge or statcoulomb, using Coulomb’s law, is defined as that charge e which placed 1 cm from a similar charge e, experiences a force of 1 dyne. Thus we can write that: F= e2 r2 (14) Consequently: 1 esu = 1 [cm.dyne1/2]. The unit of potential V: V = e r becomes: 1 statvolt = 1 [esu/cm]. From the definition of the Electric Field Intensity E: (15) E= e V = r2 r (16) It follows that its unit is the [statvolt/cm]. Current is defined as the rate of change of charge and consequently has the unit: 1 statamp = 1 [statcoul/sec]. The electromagnetic unit (emu) unit of current or abamp was originally defined as that current which, flowing in a long straight wire placed 1 cm from a parallel wire carrying the same current, results in a force per unit length of 2 dynes/ cm between the wires: F 2I1 I 2 = l r (17) where I1 and I2 are in abamp units. In the Gaussian cgs units Ampère’s law is expressed as: F 2I1 I 2 = 2 l c r (18) where I1 and I2 are in statamp units, and where the constant c is such that: I [abamp] = I [statamp] / c. (19) From Ampère’s law, 1 abamp = 1 dyne1/2, and thus c has the dimensions of a velocity. The magnetic induction B at a distance r from a long straight wire carrying a current I is written in emu units as: B= 2I , I in abamp, r (20) In the Gaussian cgs system of units it is written as: B= 2I , I in statamp. cr Thus we can write for the Gauss unit of magnetic induction: 1 Gauss = 1 [statcoul/cm2]. The magnetic vector potential is given by: (21) B = curl A = ∇xA (22) where B is the magnetic field and A is the magnetic vector potential. With these units for charge, current, electric field, and magnetic induction, Maxwell’s equations encompassing four laws, including two divergence and two curl vectorial operations on the electric and magnetic fields, take the form: 1 ∂B c ∂t Faraday’s Law: ∇xE = curl E = − Ampère’s Law: ∇xB = curl B = Coulomb’s Law: ∇.E = div E = 4π q (25) Gauss’s Law: ∇.B = div B = 0 (26) 1 ∂E 4π j + c ∂t c (23) (24) where q in Coulomb’s Law Eqn. 25 is the charge in [statcoul/cm2], and j is the current density in units of statamp/cm2. This form of Maxwell’s equations is the appropriate form for microscopic phenomena, and is the form used in plasma calculations, where q and j , represent the total charge and current densities respectively. In a vacuum, where q = j = 0, and Maxwell’s equations can be combined to yield the wave equations: ⎛ 2 1 ∂2 ⎞ ⎜∇ − 2 2 ⎟ E = 0 c ∂t ⎠ ⎝ (27) ⎛ 2 1 ∂2 ⎞ ⎜∇ − 2 2 ⎟ B = 0 c ∂t ⎠ ⎝ (28) from which c can be identified as the speed of light, c = 3 x 1010 [cm/sec]. LORENTZ EQUATION If the radiative effects can be neglected, the equation of motion for a charged particle of mass m and of charge q moving in a magnetic field B , and an electric field E , is given by the Lorentz equation, for non-relativistic velocities: q F = ma = eE + ( vxB ) c (29) where v and a are the velocity and acceleration of the particle, respectively. In the absence of an electric field, this equation shows that charged particles will rotate around the magnetic field lines. The gyro radii will depend on the masses of the particles, e.g. electrons and protons, as well as their charge. If confined by a magnetic field, the electrons in this case will have smaller radii than the protons, and will move in the opposite direction to the protons because of their opposing charge. This effect plays an important role in the magnetic confinement of plasmas in controlled thermonuclear fusion devices, as well as separation of the uranium in the electromagnetic enrichment process or Calutron. THE WEAK INTERACTION FORCE RADIOACTIVE DECAY The transformations in the weak interaction force occur slowly, even though high values of energy are involved. This force of nature expresses itself the process of radioactivity, where isotopes of different elements, either naturally occurring, or artificially created transform into other isotopes. It is the dream of the ancient alchemists come true. Radioisotopes can have deleterious effects if mishandled, but have beneficial applications in medicine, pharmacology, biology and as power sources in space exploration. In Germany, Wilhelm C. Röntgen produced x rays in 1896. These x rays were observed to produce Fluorescence in the glass walls of x ray tubes and in some other materials. An incorrect idea held by scientist at this time, was they are being produced by ordinary light interacting with atoms. In France a few months later, Henri Becquerel, in investigating fluorescence, exposed a material containing uranium to light: Potassium Uranyl Sulfate, K2UO2(SO4).2H2O. He noted its fluorescence when exposed to ultra violet light. He placed it then under a photographic plate wrapped in black paper with a thin sheet of silver in between. His idea was that only the x rays would be capable of penetrating the silver. After a time period, the photographic plate was developed. It was found to be exposed. So, the conclusion is that, indeed, shining light on materials causes them to emit x rays. Right? Not quite. Becquerel had the genius and good scientific sense to check the appropriateness of his conclusion. He repeated the experiment without shining light on his uranium material, and still the photographic plate became fogged. He obtained more puzzling results: the effect was as strong with weak as with strong light, it happened in complete darkness, and for crystals always kept in the dark, and it was emitted by other uranyl and uranous salts, by solutions of uranium salts, and even by metallic uranium. He observed that the rays from uranium would discharge an electroscope. Becquerel concluded that the uranium itself was doing something to fog the photographic plate, and not the light. Pierre and Marie Sklodowska Curie found that only thorium and uranium materials possessed that property of fogging photographic plates. This property is what came to be called Radioactivity. Both Mr. and Mme. Curie concentrated from large quantities of uranium ores, substances that possessed a high level of activity. These were later determined to be the elements radium and polonium. Since uranium has an atomic number of 92, whereas radium has an atomic number of 88, it became clear that uranium was transforming into radium. The Curies wife and husband team found radium in the barium fraction chemically separated from pichblende, a dark ore of uranium containing about 75 percent U3O8. With concentrated radium samples, the Curies made measurements of the heating effect, and found it to be in the range of 100 calories per hour per gram of radium. J. J. Thomson and others, in their studies of x rays, were then developing an understanding of the ionization of air molecules. In the Curie laboratory ionization currents were measured with an electrometer. Ernest Rutherford made measurements of the absorption of the rays emitted by radioactive materials in metal foils. He found one component of the radiation absorbed in the first few thousands of a centimeter of aluminum, and it was called: α radiation. Another component of the radiation was absorbed in 100 times the previous thickness of aluminum, and was named β radiation or beta rays. For the beta rays, Rutherford found that the ionization effect decreased exponentially by a factor of: I = e − μd I0 (30) when d centimeters of absorber were present. The attenuation coefficient μ, was about 15 [cm-1] for aluminum and increased with the increased atomic weight of other metallic foils. W. H. Bragg in 1904 discovered that the α radiation did not follow the same behavior as the β radiation, but rather that it had a definite range in materials. Magnetic and electrostatic deflection experiments lead to the recognition of the alpha and beta rays as being in fact particles. The beta rays were found to be electrons moving close to the velocity of light. The alpha rays were found to be helium ions traveling at one tenth the velocity of light. An even more penetrating radiation that is not deviated by magnetic nor electrostatic field was detected and given the name: γ rays. It was later realized that it was electromagnetic waves, of lower frequency than x rays. From the large amounts of lead found in uranium ores shown in Table 3, it was also realized that Pb was the ultimate product. Rutherford and Frederick Soddy, realized that the activity of radioactive substances diminished in intensity with a characteristic time specific to different substances. They also realized that the radioactivity process was accompanied with a change of the chemical properties of the substances at hand. By 1903, they worked out the transformation schemes of radioactive substances in the form of the radioactive decay schemes. It was later found by N. R. Campbell that radioactivity can occur in elements lighter than lead, in potassium and rubidium. The idea of the atomic nucleus did not come out until eight years later. Table 3: Uranium and thorium ores. Ore Chemical Composition Uranium Thorium Autunite Carnotite Monazite Pilbarite Thorianite Thorite or Organite Uraninite or Pitchblende Calcium Uranyl Phosphate, Ca(UO2)2(PO4)2.8H2O, Greenish yellow, rhombic Potassium Uranyl Vanadate, K(UO2)VO4.nH2O, Yellow, hexagonal, rhombic. Phosphates of Cerium Earths and Thorium, CePO4 + Th3(PO4)4, Red, brown, yellowish brown, monoclinic Thorium Lead Uranate and Silicate, Yellow Thorium and Uranium Oxides, ThO2, UO2, with Rare Earths Oxides, Gray, greenish or brownish black, cubic, amorphous. Thorium Ortho-Silicate, ThSiO4, Brown or black, Orange-yellow, tetragonal. Uranium Oxide UO2 to U3O8, with rare earth and other oxides, Grayish, greenish, brownish black, cubic, amorphous. [percent] 50 [percent] 45 16 25 25 4-40 30-82 70 68-80 0-10 THE STRONG INTERACTION FORCE FUSION PROCESS This force governs the processes occurring within the nucleus of the atom such as nuclear reactions in general. The processes of fission and of fusion are nuclear phenomena. Thus, reactions occurring in current fission reactors, as well as those that will occur in future fusion reactors are governed by its laws. Nuclear reactions induced by neutrons for the creation of radioactive isotopes fall within that description. Nuclear fusion reactions in the stars, the process of nucleo-synthesis and cosmic rays creation are within the realm of this force. Radioactivity could not be construed to be the source of energy in stellar atmospheres since their abundance there is so low. J. Perrin in 1920, considered the light nuclei that are more abundant. He suggested that the hydrogen nuclei in the sun could fuse together with a release of energy Q according to the equation: 4 H → He4 + Q. (31) Since protons are held together in the nucleus, it was postulated that they are being held by the nuclear force, which is active only for particles that are close together. NEUTRON AND NEUTRINO James Chadwick in 1932 discovered the neutron as a constituent of nuclei, and it was considered as a constituent of the atomic nucleus, with the entire particle in the nucleus, protons and neutrons, being able to attract each other by the strong nuclear interaction force. Wolfang Pauli suggested another particle, the antineutrino to conserve energy and parity in nuclear reactions. This was promptly followed by the discovery of the positron or positive electron in 1932 by C. D. Anderson, P. M. Blackett, and G. P. S. Occhialini. It is interesting to notice that the strong and weak interaction forces both coexist inside the atomic nucleus, as exemplified by the following weak transformations that can be undergone by the proton and the neutrons which are themselves held together by the strong interaction force inside the nuclei: 0 n1 → 1 p1 + −1 e0 + ν * (32) 0 n1 + ν → 1 p1 + −1 e0 (33) 1 p + −1 e → 0 n + ν (34) 1 p → 0 n + ν + +1 e (35) 1 1 0 1 1 0 where n is neutron, p is proton, ν is neutrino, and ν∗ is the antineutrino. THE NUCLEAR ORIGIN OF OUR UNIVERSE STANDARD MODEL OF COSMOLOGY, THE BIG BANG According to the Standard Model of Cosmology, all the matter and energy in the cosmos were concentrated into a space smaller than a dime. From that infinitely dense and hot speck, an explosion that is referred to as the Big Bang, occurred about 13.8 billion years ago. The early universe would have initially expanded at faster than the speed of light. Since then the universe has been expanding and cooling. The Big Bang is the accepted mainstream theory of cosmology, has a Biblical Old testament origin in the Book of Genesis, and has a large following of physicists who emphasize the role of gravitational forces in shaping the universe. There exists a minority alternate cosmological theory followed by cosmologist Alvén and primarily electrical engineers of an Evolutionary Universe where a major role is given to electric and magnetic fields acting over long distances on a cosmological scale. In the first moments after the postulated Big Bang cataclysmic event, the universe would have been a single hot dense entity in which all the forces of nature that we know today: the strong or nuclear force, the weak interaction, the gravitational, and the electromagnetic forces, were unified. In the first hundred billionth of a second after the Big Bang, the four forces of nature separated one by one in a series of rapidly occurring phase transitions. The most elementary particles would have been the quarks and gluons floated freely for a while. In the final phase transition of the early universe at about a hundred thousands of a second after the Big Bang, they became bound together to form the protons and neutrons that make ordinary matter. Three minutes after the Big Bang protons and neutrons bound together to form nuclei of hydrogen and helium in the process of nucleo synthesis. At the age of 300,000 years electrons and nuclei joined to form the first neutral nuclei. The heavier elements such as nitrogen, oxygen, iron and copper were created much later in the stars. Stars started developing when the universe was 100 million to 1 billion years old. When the electrons and nuclei combined, the temperature of the universe was about 3,000 degrees Kelvin. Since then, the universe expanded and cooled such that its present day temperature is just 3 degrees Kelvin, corresponding to the microwave radiation background that permeates the universe since the separation of radiation and matter. The concept that expansion started from a small egg of matter needs to be modified. The Big Bang would have had no center, since it would have occurred everywhere at once. Recent evidence shows that the universe today is not slowing down its expansion as was thought for a while. It is in fact accelerating. This suggests that empty space is filled with a background energy density that exists everywhere. It creates gravitational repulsion rather than attraction, causing the universe to expand faster and faster, rather than slowing the universe down, which is the way we know gravity to work. An appropriate description of the situation is something that we do not know about on Earth, and tantamount to the existence of the opposite of gravity or antigravity. The concepts of “dark matter” and “dark energy” are suggested to explain the situation. It is assumed that in the early stages of the universe a hot mixture of radiation in the form of photons, electrons, positrons, protons, neutrinos and antineutrinos, existed in thermal equilibrium. Table 4: Evolution of matter in the early stages of the known universe. Age [sec], [yrs] 10-44 s 10-37 s Dimension [cm] Temperature [oK] 1032 1028 Energy [GeV] 1019 1015 Predominant particles photon γ γ tau t, t* quarks q, q* gluon g, neutrinos ν, ν* electrons e, e* muons μ, μ* bosons W-, Z, Physical Phenomena Postulated Big Bang Quantum gravity era Probable era of inflation 10-10 s 1015 102 10-5 s 1012 10-1 10-2 s 10-1 s 1s 1.5x108 1.5x109 1.5x1010 3.0x1010 1.0x1011 1.0x1010 13.8 s 102 s 2.1x1011 3.0x109 109 160 s (3 m) 2x103 s (35 m) 300,000 y 3x105 y 2.2x1013 s (7x105 y) 100x106 y 3.0x1013 3x10-10 3.0x103 Formation of protons and neutrons from quarks γ neutrinos ν, ν* electrons e, e* ion γ neutrinos ν, ν* atoms Synthesis of hydrogen and helium nuclei 4 1 2He / 1H = 0.22-0.28 e/p=1 First atoms form Cosmic microwave radiation visible Neutral atoms form 109 y 15 10-12 12x109 y 2.7 2.3x10-13 13.7 billion y Possible dark matter relics. Strong, weak, electromagnetic and gravitational forces appear n/p = 1 n/p =0.61 Neutrinos escape n/p = 0.32 2 4 1D , 2He formation 3.0x108 3,000 3.3x1023 10-4 γ tau t, t* quarks q, q* gluon g, neutrinos ν, ν* electrons e, e* muons μ, μ* γ neutrinos ν, ν* electrons e, e* meson qq* baryons qqq, q*q*q* First stars, galaxies and quasars appear γ neutrinos ν, ν* stars galaxies γ neutrinos ν, ν* black holes Modern galaxies appear Present day The term “radiation” is used since particles with large random speeds close to the speed of light would behave more like radiation than like particles. This stage corresponds to an age of about 10-2 second after the postulated Big Bang, where the temperature would be around 1011 degrees K and the neutron to protons ratio would be 1. At this stage the density of matter was so high as to hold the neutrinos within the characteristic size of the early universe. Under present circumstances, neutrinos have minimal interaction with matter and can travel without interaction through several light years of Pb thickness. The characteristic size of the universe is expressed in terms of the Hubble constant H at that time as: L= c H (36) where H = 530 [km/(second. mpc)], and: c is the speed of light: 3x1010 [cm/sec]. Here 1 parsec (pc) corresponds to 3.26 light years, and 1 mpc is 1 million parsecs. One parsec is the distance at which the radius of the Earth's orbit around the sun subtends an angle of 1 second of an arc. A star at a distance of 1 parsec would undergo an oscillation through an angle of 2 arc seconds in its position on the celestial sphere due to the yearly motion of the Earth around the sun. For the early universe, H= 2 t (37) where: t is the age of the universe. Eliminating the Hubble constant from the last two equations, we get; L= 1 ct 2 (38) Thus at t = 10-2 sec, the size of the Universe was of the order of: L = ½ x 3 x 1010 x 10-2 = 1.5 x 108 cm = 1.5 x 106 m = 1.5 x 103 km. At that initial time, the light particles such as photons, electrons or neutrinos predominated over protons or neutrons by a ratio of about 109. As shown in Table 4, the predominance of antineutrinos and positrons produced rapid changes of protons to neutrons, and vice versa: ν∗ + 1p1 ↔ +1e0 + on1 (39) Similar inverse reactions were caused by the predominance of neutrinos and electrons: ν + on1 ↔ -1e0 + 1p1 (40) At time 10-1 second, the universe would have cooled to about 3x1010 degrees K, and expanded to L = 1.5x104 km, with a subsequent reduction in density. The lower mass of the proton compared with the neutron at this lowered temperature favors its abundance to a neutron to proton ratio of about 0.61. At about 1 sec, the cooling had proceeded to about 1010 degrees K and the universe has expanded to L= 1.5x105 km, allowing the neutrinos and antineutrinos to escape due to the lower density. The positrons and electrons are disappearing through the annihilation process: 0 0 +1e + -1e →2γ (41) where matter transforms into electromagnetic radiation. At higher temperature, this disappearance rate was balanced by a larger rate of electron-positron pair production from photons: γ + γ → +1e0+ -1e0 (42) which is the inverse reaction to the annihilation one in Eqn. 41. The neutron to proton ratio is further reduced to 0.32, but the neutrons and protons still remain separate due to their high energies. At around 13.8 seconds, the temperature would have dropped to 3x109 degrees K, and the universe expanded to 2.1x106 km. At this lower temperature deuterium is formed according to Gamow’s cosmological scenario through the reaction: 1 on + 1p1 → 1D2 (43) These deuterons would be transformed through interaction with neutrons and protons to tritium and 2He3: 1 on 1 1p + 1D2 → 1T3 + 1D2 → 2He3 (44) (45) The addition of a proton to the tritium produced would produce 2He4: 1 1p + 1T3 → 2He4 (46) The addition of a neutron to 2He3 would have also produced 2He4: 1 on + 2He3 → 2He4 (47) Combining the last equations, two at a time, yields the following result: 1 on + 1D2 + 1p1 + 1T3 → 1T3 + 2He4 (48) 1 1p + 1D2 + on1 + 2He3 → 2He3 + 2He4 (49) Tritium and the He3 isotope act here as catalysts and cancel out from both sides of the equations, yielding: 1 on + 1D2 + 1p1 → 2He4 (50) 1 1p + 1D2 + on1 → 2He4 (51) Here 2He4 is formed from neutrons, proton and deuterons through a process where tritium and 2He3 act as catalysts. According to the Einstein-deSitter model, a helium production amounting to about 22-28 percent of the primeval mass would result. At 2,000 seconds, the temperature would have decreased to about 3x108 degrees K, and the universe characteristic size increased to 3x108 km. The nuclear processes now stop and the helium to free protons ratio is frozen. The electron to protons ratio is now about unity. The free electrons still block radiation and the universe is still opaque. When the temperature dropped to around 3,000 degrees K, after about 2.2x1013 seconds, or 7x105 years, the characteristic size of the universe is now 3.3x1023 cm, or 3.3x108 km. The electrons can be held to the nuclei through chemical binding into neutral atoms. Radiation can travel now unimpeded by free electron absorption. The universe changed from a radiation dominant phase to a matter dominant phase. At this stage the proportion of deuterons has stabilized around a mass fraction of 1/5,000. This mass fraction for deuterons is found on the Earth, sun and in meteorites. It is far too high to be explained on the basis of the process of nucleo synthesis in the stars. Processes at the surfaces of the stars involving high speed particles can explain the creation of some deuterium and other nuclei such as 2He3, 3Li6 and 3Li7, as shown in Table 5. Deuterium, as an isotope of hydrogen, is however unique, and has such a large mass fraction that it may have been only been created through primeval nucleo synthesis. Table 5: Mass fraction and cosmic abundance of some light nuclei thought to have originated from primeval nucleo synthesis Nuclei 1 1H 2 1D 3 2He 6 3Li 7 3Li Mass Fraction 2x10-4 6x10-5 1x10-9 1x10-8 Cosmic Abundance (Si = 1) 3.18x104 5.20x10-1 3.70x10-1 3.67x10-6 4.58x10-5 FORMATION OF THE SOLAR SYSTEM AND EARTH The original subatomic particles came together to make nuclei of the two lightest elements: hydrogen, and helium. Although the universe was, and is still expanding, hydrogen and helium gases gather as giant clouds, which eventually became the galaxies. The first stars formed within these galaxies. Hydrogen and helium were combined through the process of nucleo synthesis into a large variety of chemical elements in the super dense, super hot cores of dying stars. Fig. 1: Solar flare showing its plasma eruptions. Fig. 2: Hubble space telescope of Mars showing ice at its south pole. Fig. 3: Spirit rover arm using an alpha particle x ray spectrometer to determine the elemental composition of the Mars surface’s rocks, 2004. Many stars were born and died before the genesis of our sun. The nuclear energy release in the stars primarily converts hydrogen into helium. Roughly 4.6 billion years ago, near our solar nebula, which was the cloud of matter that was to become our solar system, a star several times more massive than the sun ran out of hydrogen in its core. Without energy to hold pressure in the core, it collapsed inwards. This collapse generated another form of energy: gravitational potential energy. This is the energy of objects moving under the effect of the force of gravity. The liberation of enormous amounts of gravitational potential energy made the star so hot that helium in its core ignited into a fusion reaction. This process led to the nucleo synthesis of intermediate elements, from lithium to iron. Over time the helium fuel was exhausted, and its core experienced another collapse sending a strong shock wave through the Milky Way Galaxy. This is the process denoted as a Supernova. From the light and medium elements, the heavier elements such as gold, lead and uranium were formed in this process. The explosion burst the star apart, shooting its newly formed elements in the Nebula beyond. The shock wave that accompanied it fragmented and compressed the gases composing the Nebula into large gas clouds. In one of the clouds, the passage of the shock wave caused large turbulence, liberating different types of energy in matter which would become our solar system. Gravity pulled the moving matter inwards, with the release of gravitational potential energy. Kinetic energy was released from the collision of small particles of dust and gas together, forming larger ones. Gravity continued to pull matter to the cloud’s center, which increased the core’s gravity. The angular momentum, which is the rotational momentum of a spinning object, caused the cloud to spin slowly. The remaining gas that was not pulled to the center formed a large disk that spiraled outwards. In this disk were simple organic molecules, the initial hydrogen from the Big Bang, as well as the elements created in supernova explosions. Within about 50 million years, the continuous collapse of the center created so much temperature that the material in the center, primarily hydrogen and helium, started undergoing a fusion reaction, and the sun was created. As the internal pressure in the sun built up, the gravitational collapse ceased. Temperature extremes of 20 degrees C in the center, to –270 degrees C at the outer reach existed. This low temperature still exists at the outer reaches of the solar system, and necessitates the use of radioisotope power generators to heat up the equipment and generate electricity in space probes sent to explore the outer planets. In a model of the formation of the planets, the matter in the cooling disk condensed about 4.6 billion years ago, with gravity attracting the heaviest elements to the center. Light gaseous elements near the sun, or the volatiles, vaporized. They bound together in the colder regions of the disk forming methane, ammonia and water. Molecules collided and coalesced into specks, pebbles, rocks and boulders. In ten million years, planetesimals with tens of kilometers in diameter formed. Larger bodies were formed eventually through accretion forming the planets. The metallic sulfides and rocky silicates compounds became the solid matter inner planets: Mars, Earth, Venus and Mercury. The hydrogen primarily found in methane, ammonia, hydrogen sulfide and water, formed the outer gaseous planets: Jupiter, Saturn, Uranus, Neptune. Pluto. no longer classified as a planet, is an icy object much like a comet, as part of the Kuiper belt. It took about 100 million years for the planetary accretion process to occur. The Earth grew from cosmic dust to its present size in about 70 million years. Other objects reside in our solar system. Asteroids have the same composition as the inner planets, primarily rock and metal. Most of them exist in the asteroid belt between Mars and Jupiter, and could have the remnants of a failed planet, that never formed because of a gravitational disruption by Jupiter. Comets exist in the far reaches of the solar system beyond Neptune. They are composed of rock and frozen water, methane, ammonia and hydrogen sulfide. Moons of planets in the solar system have varied compositions. Titan is a frozen world of hydrocarbons that evaporate and condense and form lakes and shores on its surface. Fig. 4: The Cassini space mission to Saturn and its Huygens probe revealed that the moon Titan is formed of solid, liquid and gaseous methane (left). Surface and boulders on the surface of Titan (right). Source: NASA. Fig. 5: Cassini’s space probe picture of Saturn’s moon Enceladius reveals jets of evaporated hydrocarbons, 2006. Source: NASA. The initial Earth incorporated all material it found in its path. A process of homogenization followed by differentiation layered it in its present core, mantle and crust structure. The accretion process provided heat energy from collisions and the release of kinetic energy, and the further compression of the planet masses toward their core provided gravitational energy. Many elements in the early solar system were radioactive, and nuclear energy was also released through radioactive decay. Early forms of life on Earth date back to 4 billion years with the appearance of self replicating molecules. It is thought that Homo Sapiens originated in Africa around 100,000 years ago, a very small fraction of the age of the universe. THE MILKY WAY GALAXY The galactic center of the Milky Way galaxy has been imaged by the NASA’s Chandra x ray observatory, launched in 1999. It shows in Fig. 6 hundreds of white dwarf stars, neutron stars and black holes in a fog of 100 million degrees hot gas. In the super hot gas new stars are being born. Old stars are exploding into supernovae explosions. Black holes are swallowing in clouds of matter. A dense screen of dust, gas and the glare of millions of stars obscure the center. The solar system, including the sun and Earth is halfway out of the galaxy’s spiral arms at about 25,000 light years from the center. Ordinary telescopes are unable to obtain a clear picture of the center. However x rays generated at the center do penetrate the dust. The Chandra telescope picture covers an area 400 light years high and 900 light years long, with a light year about 6 trillion miles. The galactic center contains hundreds of white stars, which are hot dwarf stars. Neutron stars, the remnants of medium sized stars also exist. Stellar black holes, which are massive stars that have collapsed into a point of such high density that not even light can escape from it, exist there. Most notable is a massive black hole that exists at the center of the galaxy. The hot gases at the center of the galaxy circulate outward, cooling the edges of the galaxy, and then stream back into the center. This gas could be distributing throughout the galaxy many of the heavier elements such as carbon that were synthesized in stars explosions. Fig. 6: An image of the Milky Way galactic center. The super massive black hole at the center of the galaxy is located inside the bright white patch near the center of the image. Source: NASA. THE COSMIC SCALE The cosmic scale covers a large range, from the size of nuclei up to the stars and galaxies. The focus of nuclear, plasma and radiological science lies primarily at the level of the atomic nucleus at 10-14 m, and, to a lesser extent, at the level of the overall atom at 10-10 m. From this perspective, it can be noticed that the nucleus possesses a characteristic length of 10-12 cm. This is only 1/10,000 of the characteristic length of the atom at 10-8 cm. To measure nuclear areas or cross sections, the convention is to use the square of the characteristic length of the nucleus, and call it as the barn unit: 1 barn = 10-24 cm2 Workers in the field of cross sections measurements, in a humorous mood, in called such a small object as the atomic nucleus by the name of such a large object as a barn Neutron scattering experiment suggest that the nucleus is a sphere with a radius given by: R = 1.25 x 10-13 A1/3 [cm], (52) where A is the atomic mass number. On the other end of the scale, the Earth has a radius of 6,400 km or 6.5 X 108 cm. The distance from the Earth to the sun is about 1.5 x 1013 cm, or about 23,500 times its radius. The outermost known large icy object in the solar system is Pluto at 106 times the radius of the Earth at a distance that is 40 times away from the sun than the Earth. Our Milky Way galaxy contains about 1011 stars distributed over a large distance. The appropriate unit of distance here is the light year unit, which is the distance traveled by light in a year: 1 light year = 9.46 x 1017 cm. The distance of our solar system to the center of the galaxy is approximately 30,000 light-years. Another useful unit to measure such large distances is the parsec (pc), defined as: 1 parsec = 3.26 light-years. The parsec is the distance at which the radius of the Earth’s orbit subtends an angle of one second of an arc. The distance between other galaxies in our universe and between clusters of galaxies is expressed in terms of the million parsecs (mpc) unit. Some large clusters have diameters of 5 mpc, and some super clusters, which are groups of clusters have diameters of about 50 mpc. Our telescopes can access region at about 3,000 mpc, which is at about 10 billion light years. Since we are looking at light that originated at the initial time of the creation of our universe, we are in fact looking into the past, and this distance of 10 billion light years constitutes the characteristic scale of our universe. To get a feel of the place of atoms and nuclei in the cosmic scale, Table 7 shows the dimensions in meters of cosmic objects. The scope of Nuclear Science is the very short distances on the cosmic scale, covering nuclear sizes and gamma rays, from the 10-10 to the 10-15 meter scale. Table 6: Dimensions in meters of cosmological objects Dimension (m) 10-15 10-14 Cosmic Object Neutrons, protons Atomic nucleus 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 101 102 103 104 105 106 107 108 109 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 Wave length of 1 MeV γ-ray Atom Sugar molecule Large molecules Bacterial virus Animal virus Blood cell Bacteria Wave length of visible light Grain of sand Flea Cherry fruit Mouse Humans Dinosaur House Skyscraper Neutron Star Earth Sun Size of Earth’s orbit Pluto’s orbit Distance to nearest star Size of Milky Way Galaxy Distance to nearest galaxy Distance to distant galaxies Distance to edge of visible universe HIGGS BOSON, THE GOD PARTICLE Small armies of physicists and engineers are dedicated to the discovery of an elementary particle central to the modern conception of nature. The particle is called the Higgs boson, after Peter Higgs, an English physicist who conceived its concept in 1964. It is said to be responsible for endowing the other elementary particles in the universe with mass. Leon M. Lederman, the former director of the Fermi National Accelerator Laboratory, or Fermilab near Chicago, Illinois, USA, referred to the Higgs as “the God particle” in the book of the same name he published with the science writer Dick Teresi in 1993. It made metaphorical sense, because the Higgs mechanism made it possible to simplify the universe, resolving many different seeming forces into one, like tearing down the Tower of Babel. The Higgs has lived up to its name. Several Nobel Prizes have been awarded for work on the Standard Model, of which the Higgs is the central cog. Billions of dollars are being spent on particle accelerators and experiments to find it and figure out how it really works. With modesty and humility, we must admit that our present state of scientific knowledge about the universe is just the 5 percent that we can detect, see and understand. LARGE HADRON COLLIDER, LHC INTRODUCTION The Large Hadron Collider (LHC) will search for the Higgs Boson, the theoretical particle described by Peter Higgs in 1964. It could explain how matter possesses mass. Given the energies involved in the experiments, scientists are confident they will find something, whether or not it is Higgs boson. Built underground near Geneva, Switzerland, it is 27 kilometers in circumference and uses powerful superconducting magnets kept at a cryogenic temperature of minus 271 degrees Celsius, to accelerate protons to 99.9999991 percent of the speed of light, before colliding them into each other. It cost €6.4 billion or $9.2 billion, most of it contributed by the European countries. The data collected by its detectors will be analyzed by 60,000 computers throughout the world. Many physicists are hoping that the LHC will provide proof of the veracity of string theory, a theoretical construct meant to smooth out inconsistencies between the General Theory of Relativity and Quantum Mechanics. Fig. 7: Schematic of the detectors part of the Large Hadron Collider (LDC). Source: CERN, Switzerland. MINI BLACK HOLES Some fear that the LHC could create a mini-black hole that could continue growing and swallow the Earth in the process. CERN insists the LHC is safe, however A scientist at the University of Tübingen, Dr. Otto E. Rössler, has lent academic weight to the possibility of the creation of mini black holes that would be just one billionth of a billionth of a gram in weight and would be extremely unstable. According to a theory developed by the physicist Stephen Hawking, they would vanish almost instantaneously: a phenomenon known as Hawking radiation. Some physicists are hoping the Large Hadron Collider will allow them to observe, however briefly, the creation of these, so far theoretical, tiny black holes. Fig. 8: The Large Hadron Collider (LHC), CERN Laboratory, Switzerland. STRING THEORY One of the goals of the project is to create conditions very much like those in the first milliseconds of the universe's existence, right at the beginning of the Big Bang. By doing so, those who ascribe to string theory, a mathematical construct seen by many as a possible means of unifying quantum mechanics with general relativity or the “Theory of Everything,” hope to find physical proof of an idea which has until now been little more than an exercise in theoretical physics. String theory predicts the existence of a number of dimensions beyond the four we are aware of, as well as a number of ultra-tiny particles and anti-particles that have not yet been observed. Because the Large Hadron Collider is so much larger than any particle accelerator ever built, some see it as the best chance yet to find those particles or those dimensions. STRANGELETS CREATION Other than mini black holes, "strangelets;" a potential by product predicted by some physics theories could transform the Earth into a lump of uninhabitable "strange matter." Some scientists contend that even if the chance of things going wrong is infinitesimally small, the potential disaster is unimaginably large. The question of “’How improbable does a catastrophe have to be to justify proceeding with an experiment?’ seems never to have been seriously examined," wrote University of Cambridge physicist Adrian Kent in a 2003 paper. CERN asserts that: “It is impossible for microscopic black holes to be produced at the LHC. Were they created, they would disappear immediately.” Strangelets too were discounted: “According to most theoretical work, strangelets should change to ordinary matter within a thousand-millionth of a second.” FILAMENTS OF DARK MATTER Using the ultraviolet light from distant quasars, astronomers have found about 40 percent of the missing “normal” matter in the cosmos in hot gas clustered around filaments of dark matter crisscrossing the space between the galaxies. Much of the missing "normal" matter in the cosmos has been found clustered around wispy ropes or filaments of invisible matter spanning the space between the galaxies. These filaments form part of the weblike superstructure of the universe, within which galaxies are embedded. Fig. 9: Computer simulation of “normal” matter congregating around filaments of “dark” matter criss crossing the space between the galaxies over a region of space spanning 1.5 light years on the side. Source: University of Colorado at Boulder. Yet, with billions of visible galaxies, astronomers have not been able to account for the majority of normal, or baryonic matter believed to have been created by the Big Bang. There was a suspicion that the missing normal matter is hidden in the intergalactic medium or the space between the galaxies, but they could not prove it. The ultraviolet light emitted by distant galaxies with radiation spewing black holes at their centers or quasars, act like lighthouses piercing a fog, revealing gases that are too hot to be detected by optical scans but too cool to be seen by x ray probes. Using this observation, scientists found evidence that about 40 percent of the missing baryonic matter is concentrated around filaments that crisscross the intergalactic medium. BARYONIC MATTER Regular visible matter is made up of protons, neutrons, and other subatomic particles collectively called baryons. Baryonic matter only accounts for about 5 percent of the universe, and galaxies, stars, planets, and all life forms are thought to represent about just 1/10 of that 5 percent. The rest of the universe is in the form of a mysterious invisible substance called dark matter and an unknown force that is causing the universe's expansion to accelerate called dark energy. Using NASA's Hubble and FUSE space observatories, Shull and Danforth from the University of Colorado at Boulder examined light from 28 distant quasars scattered across the night sky. As some of the quasars' light travels through space, it pierces filaments of dark matter and gas. Atoms of neutral hydrogen and charged oxygen clustered around the filaments absorb portions of the quasar's ultraviolet light, creating dark bands in the spectrum that reaches Earth. By analyzing this altered light, scientists can determine the position of a filament and the amount of normal matter gathered around it. BRAIN MODEL OF THE UNIVERSE Scientists think dark matter filaments are part of a larger cosmic web connecting vast dark matter islands. Together the filaments and islands form a hidden support structure for galaxies that could be likened to a dense cluster of brain cells connected by gangly appendages. Normal matter is drawn toward this dark cosmic web by gravity and flows within and around it like electric impulses coursing through neurons. Wherever normal matter concentrates within the web, the galaxies and galaxy clusters have formed. Recent observations confirm that much of the universe's baryons flow through the filaments. But even with these new discoveries, more than half of the universe's baryonic matter is still unaccounted for. Scientists think the remaining missing matter most likely exists in the form of extremely hot gas that also floats between the galaxies. This gas is heated to millions of degrees and will require future x ray telescopes to detect it. POSTULATED FATE OF THE UNIVERSE The universe has been expanding since its beginning albeit at a changing rate. During the inflationary period over the few first hundred million years the expansion rate was faster than it 9 is now. The present rate of expansion is estimated at 1 part per 14x10 per year. Several theories exist about the future of cosmic evolution. Cyclic universe theory At larger than a critical density, it is thought that the universe would continue expanding for another 10 billion years at a decreasing rate of expansion until the gravitational forces would predominate leading to a collapse of the universe upon itself. After another 25 billion years it would become again a small hot dense spot starting another cycle of expansion and collapse or reincarnation with a period of 35 billion years. Steady state universe theory At below the postulated critical density, the expansion would slow down and eventually stop. There may still be a process of solar systems and stars death and rebirth and the universe may not initially change much. However, a heat death would occur with an evolution toward an eternal constant temperature. Runaway inflationary universe theory This would consist of continuous expansion and cooling of space where eventually the rate of expansion exceeds the speed of light. In this sobering scenario, the stars would ultimately die and an Earth observer would not be capable of detecting their dark and cold remnants. Unfortunately, the latest cosmic radiation data point to a universe that is currently expanding at an ever expanding rate. The possible explanation offered by scientists is that the universe is filled with dark energy as an anti gravitational repulsive force. Moreover, they postulate that this repulsive force is getting stronger. The observational evidence for the runaway expansion suggests a composition of the universe as given in Table 7. Table 7: Postulated composition of the universe. Universe components Normal matter as protons, planets, stars and galaxies. Dark matter as stars that have collapsed into super dense black holes. Dark energy as poorly understood invisible property of space Percentage 5 25 70 EXERCISE 1. The energy of a photon is expressed as: E = hν, where h is Planck's constant and ν is the electromagnetic radiation's frequency. Compare the energy carried by photons in units of electron-volts (eV) in different parts of the electromagnetic spectrum: a. The visible region. b. The x-ray region. c. The gamma ray region, which is of particular interest for nuclear phenomena. Note: h = 4.136x10-15 [eV.sec] REFERENCES 1. Fred Hoyle, Jayant Narlikar, and John Faulkner, "The Physics-Astronomy Frontier," W. H. Freeman and Company, San Fransisco, 1980. 2. 3. 4. Gerhart Friedlander, Joseph W. Kennedy and Julian Malcolm Miller, "Nuclear and Radiochemistry," John Wiley and Sons, Inc., New York, 1966. S. Nadis, "Hunting the Invisible," Popular Science, April, 2001. G. P Collins, “Setback for Super-K,” Scientific American, p.26, Feb. 2002. ...
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This note was uploaded on 06/16/2010 for the course NPRE 402 taught by Professor Ragheb during the Spring '08 term at University of Illinois at Urbana–Champaign.

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