13 April 2010

NUCLEAR PHYSICS

The Structure of Matter

Introduction

The Structure of Matter

The Greeks were the first to speculate that matter was discrete, in the form of particles. The word atom derives from the Greek (ατομοζ) for indivisible. Democretus, argued that matter on the large scale is composed of atoms and that different substances were composed of different atoms or combinations of atoms. Furthermore, one could substance could be converted into another simply be re-arranging the atoms. The atomic theory was roundly rejected by Aristotle, and, thus, by almost everybody else for the next two millennia.
The modern definition of an element was made in 1661 by Robert Boyle. An element is a substance that can not be broken down into simpler substances but can form compounds with other elements. There are 88 naturally occurring elements (not the much reported 92 natural elements - The elements Tc, Pm, At and Fr have no stable isotopes, and none of long half-life, so they are not naturally present.) Including man-made elements, at the time of writting (Dec, 2006) there are 117 elements. The existance of these more massive elements is fleeting with elements lasting from a few microseconds to about 30 seconds.
For the Greeks, atoms were as far as the indivisibility of matter went. However, in 1906 J. J. Thompson discovered a negatively charged particle which eventually became known as an electron. Early models the atom considered 'atom as a nice hard fellows, red or gray in color, according to taste', in which the charged particles were distributed much like the plums in a Plum pudding. However, this model of the atoms was shown to be wrong by Rutherford's experiment, in which a high energy beam of alpha particles was fired at a very thin gold foil.
rutherford's alpha particle experiment
Ruferford's alpha particle experiment.
If the plum pudding model of the atom was correct then the alpha particles would pass through the foil with little deflection. As shown in the figure.
scattering
Expected results and actual results of experiment.
Most of the alpha particle passed through the foil with very little deflection. However, about 1 in every 8000 was scattered through an angle of more than 90 degrees. To Rutherford this was incredible. “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you had fired a 15-inch shell at a piece of tissue-paper and it came back and hit you.” For the alpha particles to be scattered through such large angles and even coming back on themselves, they had to encounter a massive concentration of charged particles of very small size. The back scattering of alpha particles showed that most of the mass of the atom was concentrated at the nucleus.
Rutherford's model of atom
The Ruferford Model of the atom.

Atomic and Nuclei Radii

The size of an atomic radius is difficult to guage since the orbits of the electrons are not in general, circular and the electron cannot be said to orbit but exists as a cloud of probability. However, taking the average distance from the nucleus as a measure of 'radius'. With the exception of the lightest elements, most atoms have radii of the order of 10-11 m. As for the nucleus, it is some 10,000 times smaller at 10-15 m. If an atom had the same diameter as the length of a football pitch (120m) then the nucleus would be about the size of a marble (1.2cm). The structure of matter is mostly empty space.

The Bohr Model of the Atom

One problem with the classical theory of the atom was that with the electrons travelling around a positively charged nucleus, the electrons would be accelerating. Accelerating charges produce radiation. This radiation takes energy from the electron orbiting the nucleus and therefore the electron would spiral into the nucleus bringing about the end of atoms and the end of the universe.
Bohr model of the atom
The Bohr model of the atom.
Neils Bohr considered the Hydrogen atom, as it is the simplest atom, having one electron oribiting the nucleus. The Bohr model atom propossed that the electron has certain orbits, called stationary states, which are allowed without losing energy. If the electron were to lose energy by emission or gain energy by absorption it would move to another stationary state.
To overcome this problem, Niels Bohr proposed that using Planck's quantum theory, the electron could only lose energy in fixed quantities, or quanta. The electron could only lose energy if it was one of the fixed quantities allowed by the quantum mechanics.
Bohr used his theory to explain emission spectra of Hydrogen. When heated, object emit light which when diffracted into a prism the light would be separated into discrette lines which were characteristic to each type of element. He realised that the frequency of the lines was the result of the discrette changes in energy as electron changed from one stationary state to another, in the process radiating a small quantity of energy.
ParticleLocationChargeMass
NeutronNucleusNone1.008665 amu
ProtonNucleus+11.007277 amu
ElectronShells around the nucleus-10.0005486 amu


Nomenclature

Now we move on to a few definitions that are used in Nuclear physics. Nuclide - a combination of protons and netrons. Not all nuclides are possible but about 2500 unique combinations have been identified
atomic nomenclature for Nuclides
In this graphic, X is a generic chemical element symbol. A represents the sum of the protons plus the neutrons making up the nucleus. It is called the nucleon number or mass number. The lower number, Z is known as the atomic number and is the number of protons in the nucleus.

Isotopes

The number of protons determines what the element the atom is. However, it is possible for an element to exist in more than one form by having greater or fewer neutrons in the nucleus. The different forms of the same element are known as isotopes of an element. Most elements have a few stable isotopes and a few unstable isotopes. For example: Carbon exists in 15 isotopes with the most common forms being the stable C-12,C-13 and the unstable or radioactive C-14.

Probing Matter

There are many techniques for investigating the structure of materials. The basic concept is to direct a beam of particles at a sample and the structure can be determined by the pattern of diffraction. The physical properties of the particle beam such as charge, mass, determine what properties of the sample can be investigated.

X-ray diffraction

To probe the internal arrangement of the atoms in a matterial we can use electromagnetic radiation but the wavelength must be of the same order as the spacing between planes in the material. X-rays have a wavelength that is similar to the spacing in the crystal planes.
To determine the structure of a crystal, a single crystal or powdered material is placed as a target for a columated beam of X-rays. The X-rays penetrate the crystal and some of the energy is reflected back from the different planes. The spacing of the atoms causes the X-rays to diffract. In some regions the X-rays will interfere constuctively and the combined amplitude will be must greater. In other regions, the X-rays will interfere in a destructive way and the sum of their amplitudes will be zero. Using a suitable means such as a photographic film the strength of the diffracted and reflected X-rays will shown and it is possible to calculate the structure of the material.
For amorphous substances, the arrangement of the atoms does not possess a long range order of symmetry, the X-ray diffraction pattern will be diffuse.
In crystals, the ordered position of individual atoms in a molecule will lead to a rather mysterious pattern of dark spots from which the structure can be calculated.
Quasi-crystals - materials which show some symmetry over relatively short distances, X-ray diffraction shows patterns of spots with impossible rotational orders of symmetry such as 5, 7, 13, etc.

Neutron Scattering

A similar technique is that of Neutron Scattering. Neutrons carry no charge but they also have a wavelength. It might seem strange that a particle can also have a wavelength. However, this is one of the percularities of the quantum world. This idea was postulated by Prince Louis De-Broglie. Light which was thought to behave like a wave can act like a particle, maybe particles can act like waves sometimes and this is indeed the case. When the size of the particle is small then wave effects begin to become apparent. By small in this case we mean nanometer scale.
The wavelength λ of a particle is given by: λ= h/p where h is Planck's constant ~ 6.6x10-33 and p is the momentum of the particle.

Electron Beam Diffraction

Calculating nuclear diameter electron scattering
The nuclear diameter d can be calculated from the electron scattering data.
Electron beam energy = 100 MeV = 100 106=1.6x10-19 J = 1.6 x 10-11 J
Momentum p = E/c = 1.6 x 10-11/3.0 x108 = 5.3 x 10-20 kg m s-1
De Broglie relationship λ = h/p = 6.6 x 10-34/5.3 x 10-20 = 1.2 x 10-14 m
The first diffraction minimum occurs at about 22°, so using the single slit diffraction equation sinθ = λ/d we have d = λ/sin θ = 1.2 x 10-14 m /sin (22°) = 3.3 x 10-14 m
Electron beams can provide information about the surface of matterials. RHEED - Reflection High-Energy Electron Diffraction is a common tool to study the surface of growing semiconductor crystals. A high-energy electron beam is directed toward the semiconductors material. The electrons cannot penetrate the surface of the sample because of the electromagnetic force. The electrons are diffracted and form a pattern of bright and dark spots on a phorescent screen. This information can tell you about the surface quality of the material.
Radioactivity

Introduction

In 1896, Bequerel, a French physicist discovered that crystals of Uranium salts emitted penetrating rays similar to X-rays which could fog photographic plates. Two years after this Pierre and Marie Currie discovered other elements: Polonium and Radium which had this property. The emission was known as Radioactivity.

The Stability of Nuclei

Protons and Netrons are held together in the nucleus of an atom by the strong-force. This force acts over a very short distance of about ~1 fm, (10-15m) and over this short distance it can overcome the electromagnetic repulsion between the positively charged protons. Nuclei with radii that are within the range of the Strong force are stable. As atomic number increases the radius of the nucleus also increases and the element becomes unstable. This instablity manifests itself as the emission of particles or energy from the nucleus. The elements with atomic number greater than 82 are radioactive.

The Decay Constant

The decay constant is a measure of how quickly on average a radioactive nuclei will take to decay. Since radioactive decay is a random process, the decay of a single nucleus may happen at any time but for many undecayed nuclei, the average decay rate is given by the decay constant, λ and it has the unit of [s-1] or [h-1] or [year-1].
Activity
The activity of a radioactive material is defined by two factors:
1. the number of undecayed atoms, N
2. the decay constant, λ
The activity, A is measured in Becquerels [Bq] or [s-1].
AN
The corrected activity is the activity taking into account the background radiation.
Radioactive Decay
Consider a block of radioactive material, initially the number of undecayed nuclei is, N0. On the basis of our reasoning above we can say that the number which will decay will depend on overall number of nuclei, N, and also on the length of the brief period of time. In other words the more nuclei there are the more will decay and the longer the time period the more nuclei will decay. Let us denote the number which will have decayed as dN and the small time interval as dt. So we have reasoned that the number of radioactive nuclei which will decay during the time interval
from t to t+dt must be proportional to N and to dt. In symbols therefore: -dNNdt.Turning the proportionality in this equation into an equality we can write: -dN=Ndt
Dividing across by N we can rewrite this equation as: eqn.3


So this equation describes the situation for any brief time interval, dt. To find out what happens for all periods of time we simply add up what happens in each brief time interval. In other words we integrate the above equation. Expressing this more formally we can say that for the period of time from t = 0 to any later time t, the number of radioactive nuclei will decrease from N0 to Nt, so that:
eqn.4

eqn.5

eqn.6
The final expression is known as the radioactive decay law. It has the form of an exponential decay curve like the one we saw in the discharge of a capacitor.
decay curves with different decay rates

Radioactive Decay Law with Sweets

You can simulate the decay process the next time you have a bag of M&Ms. Take the packet of M&Ms and empty them on a flat surface. The M&Ms which land such that you can see the 'M' represent the nuclei that have decayed. Since you can see the M or not the decay constant is 0.5 Record the number that of decays and you can eat the them. Repeat the process with the remaining M&Ms until there are no more remaining.
Starting with 50 M&Ms, the decay sequence is
ThrowTheoryActual
15050
22525
312.512
46.258
53.1253
61.56122
700


Half-Life

The decay law leads to an exponential decay which reaches zero in an infinite amount of time. A useful measure of rate at which the material decays is given by the half-life. This is the time taken for the number of undecayed nuclei to decrease by half the initial amount.
half-life
Half-life of a radioactive decay curve
Successive half-lifes decreases the number of undecayed nuclei by N0/4, N0/8, etc. As shown in Figure X.
half-life
Successive half-lives decrease the number of undecayed nuclei by half each time
Mathematically, the half-life can be calculated by seting Nt=N0/2 in the radioactive decay equation. Therefore, N0/2=N exp(-λt1/2). Taking logs and re-arranging for t1/2 leads to t1/2 = ln(2)/λ

Modes of Radioactive Decay

There are broadly three types of radioactive emissions. These are:

α radiation

Alpha radiation is the emission of two protons and two neutron from the nucleus, which is the same as a Helium nucleus. Due to the heavy mass and charge, α radiation the least penetrating, being stopped by a sheet of paper. However it also is the most ionising form of radiation, knocking electrons from their shells in nearby atoms. The dangers of alpha-radiation come from being ingested into the body. When an alpha particle is emitted, the proton number decreases by 2 and and mass number decreases by 4.
AZX → A-4Z-2(X-2) + 42α

β radiation

β radiation is the emission of an electron from the nucleus. Since the nucleus does not contain any electrons, either a proton or a neutron transforms. Depending on which transforms leads to one of two kinds of beta radiation.
Beta radiation occurs in two forms. β+ and β-
  • β+ a positive electron called a positron is created by the transformation of a proton into a neutron. AZX → AZ-1(X+1) + 0+1e+ + 00ν
  • β- the electron is created by the transformation of a proton into a neutron. AZX → AZ+1(X-1) + 0-1e- + 00ν;
The emission of the positron or electron is accompanied by the emission of a ghostly particle called a neutrino ν or antineutrino ν, respectively. Particle tracks photographed in a cloud chamber showed that the energy of emitted particles that showed up in the cloud chamber was not conserved. Rather than abandon the principle of the conservation of energy a new particle was postulated by W. Pauli in 1930. The lack of interaction between matter and neutrinos ment that it was 26 years latter the neutrino was discovered by Reines and Cowan with the anti-neutrino being found in
Beta radiation is more penetrating then α radiation but it can be stopped by a few mm of aluminium. Once again, the main danger of β radiation comes from when it is ingested in the body.

γ radiation

After the emission of an α particle or β decay, the nucleus is left in an excited state and it releases its excess energy in the form of a γ-ray photon. γ-rays are high-energy electromagnetic waves. They are also highly penetrating and are not stopped but the probability of absorption is proportional to the thickness of the absorbing medium, leading to an exponential decrease in the number of γ-ray photons passing through.

Transmutation

transmutation of elements with radiation


Mass-Energy Conservation

Introduction

When a nucleus breaks apart or undergoes a nuclear reation the mass of the products is less than the mass of the initial nucleus. What happens to the missing mass? The answer is that it is converted into energy. The energy contained within the nucleus is far greater than the energy released when the atoms undergo chemical change.

Atomic Mass and Energy Units

Because the unit of the kilogram is so large for sub-atomic particles and the unit of the Joule is so small, new units based on the mass proton and neutron. In actual fact, since 1961, by definition the unified atomic mass unit, (amu) is equal to one-twelfth of the mass of the nucleus of a carbon-12 atom. This is because Carbon 12 has 6 electrons, 6 neutrons, and 6 protons. Therefore, the amu represents an average value for the mass of a proton and neutron.
1 amu is equal to 1 u = 1.6605 10-27 kg.
The energy of atomic processes is measured using the Electron volt eV. This is defined as 1.602 x 10-19 J. The table below lists the energies for common atomic processes.
Energy for the dissociation of an NaCl molecule into Na+ and Cl- ions.


ProcessEnergy
Room temperature thermal energy of a molecule0.04 eV
Visible light photons1.5-3.5 eV
4.2 eV
Ionization energy of atomic hydrogen13.6 eV
Approximate energy of an electron striking a color television screen20,000 eV
High energy diagnostic medical x-ray photons200,000 eV (=0.2 MeV)
γ0-3 MeV
β0-3 MeV
α2-10 MeV
Cosmic ray energies1 MeV - 1000 TeV


Table: Energies of various atomic processes

Mass Defect

When a nuclear process takes place such as a spontaneous fission, the mass of the products is slightly less than the initial nucleus. This mass is converted into energy. The energy liberated in the reaction is given by Einstein's famous equation E=mc2. In this equation the mass is actually the change in mass, ie the difference between the initial mass and the sum of the product masses. c is the speed of light in a vacuum. (3 x 108 ms-1. The difference between the masses is very small, in-fact one must take care to use the full precision of measured masses, but because the value of the speed of light squared is such a large value, the energy liberated is quite substantial.

Nuclear Fission

Introduction

Nuclear Fission is the breakup of a large nucleus into two smaller nuclear fragments. Accompanying the break-up of the large nucleus is the release of energy determined by the mass defect.
spontaneous fission

Liquid-Drop Model of the Nucleus

A model of how the nucleus breaks apart is called the 'liquid-drop' model of the nucleus. An incoming neutron collides with a large nucleus and causes it to become unstable, the large nucleus vibrates like a large water drop and can cause the nucleus to split into two smaller fragments
a nuclear fission event

Chain Reactions

a series fission events
A nuclear chain reaction.

Critical Mass

Even though an incoming neutron can initiate the emission of more than one outgoing neutron, the outgoing neutrons may completely miss other nuclei, therefore, to create a chain reaction, one must increase the probability of hitting other nuclei. To insure that the probability of a neutron colliding with a nuclei, the number of nuclei must be increased, or the density of nuclei must be increased. When there are so many fissile nuclei that chance of initiating a chain reaction is equal to one, we speak of a critical mass

Nuclear Power

controled fission

Nuclear Fusion

Introduction

Nuclear fusion is the process of binding nuclei together to form heavier nuclei with the release of energy. It is the process that powers the stars and of course our own Sun. Research into producing nuclear fusion on Earth began in the early 1950s with the development of the Hydrogen bomb. Research into nuclear fusion to generate electricity is ongoing despite the huge technical challenges. To put thing in perspective, to operate for a whole year generating about seven billion kilowatt hours of electricity, a fusion plant would use just 100 kg of deuterium and three tonnes of lithium - releasing no greenhouse gases in the process. A typical coal-fired power station, in contrast, devours three million tonnes of fuel and produces some 11 million tonnes of carbon dioxide to yield the same annual output.

Making Nuclei Stick

Atomic nuclei do not stick together easily. Protons have a positive electrical charge which prevents them combining with other protons. The repulsion is caused by the electromagnetic force between the two nuclei. However, at distances of 1015 m there is an attractive force which acts on the nuclei to keep them together and it is much stronger than the electromagnetic force. Appropriately, this force is called the Strong force. Over such short distances the strong force wins over the electromagnetic force and so the nuclei stay together. To create a situation where the nuclei have sufficient energy to overcome the electromagnetic force requires the nuclei to have extremely high kinetic energy and therefore, a high temperature.
We can estimate the temperature required to initiate fusion by calculating the Coulomb barrier which opposes the protons coming together. The magnitude of the force between protons is given by:
F= (k q1 q2)/r2
where k=1/(4πε0) is the Coulomb constant = 8.988×109 m F-1.
The work done, U in moving the two protons together until they are attracted by the strong force is given by:
U=F.dr= (k q1 q2)/r0.
The limits on the integration are -∞ and r0.
The Coulomb barrier increases with increasing atomic number.
U=(k Z1 Z2 q2)/r0.
Where Z1 and Z2 are the proton numbers of the nuclei being fused. Using figures for 2 Deuterium nuclei, for which Z1,2=1, we obtain: U= (8.988 x 109 x 1 x 1 x (1.6 x 10-19)2)/(1 x 10-15) = 2.298 x 10-13 J
The kinetic energy of the nuclei is related to the temperature by:
(1/2) mv2 = (3/2) kBT
By equating the average thermal energy to the Coulomb barrier height and solving for T, gives a value for the temperature of around 1.1 x 1010 K.
In practice, this simple calculation overestimates the temperature. The temperature of critical ignition should be lower because there will be some nuclei with higher energies than average, however the temperature requirement is still to high for even these high energy nuclei. This treatment using classic physics does not take into consideration the effect of tunneling, which predicts there will be a small probability that the potential barrier will be overcome by nuclei 'leaking' through it.

Tunneling

Tunneling is a consequence of the Heisenberg Uncertainty Priciple which states that, the greater certainty we know the velocity of a particle the less we know about its position in space and vice versa
The uncertainty in the position is such, that when a proton collides with another proton, it may find itself on the other side of the Coulomb barrier and in the attractive potential well of the strong force. The probability of such an event happening decreases exponentially as the ratio of the classical turning point r0, to the de Broglie wavelength (λ=h/p).
P(tunneling) ∝ exp(-r0/λ)
We can now estimate the temperature for fusion to occur taking into account the tunnelling probability.
Rewritting the kinetic energy, in terms of the momentum p.
KE= (1/2) mv2 = p2 / (2m) = (h/λ)2 / (2m)
If we require that the nuclei must be closer than the de-Broglie wavelength for tunneling to take over and the nuclei to fuse.
Z1Z2q2/λ = (h/λ)2/(2m).
λ = (1/2) h2/(Z1Z2q2m)
If we use this wavelength as the distance of closest approach to calculate the temperature, we obtain
(3/2)kBT = Z1 Z2q2/(r)
The temperature is T = (4/3) (Z12Z22q4 m)/(h2kB).
For two protons this gives a temperature of 107 K.

Nuclear Fusion in the Stars

Before the process of nuclear fusion was known about, how the Sun and stars produced energy was a big problem in cosmology.
In 1848, J.R. Mayer examined the then-popular theory of the Sun being composed of burning coal. He stated that if the Sun began burning 5000 years ago, corresponding to the Biblical age of the Earth, then by his calculations, it already would have burned out.
The eminent physicist, Lord Kelvin, proposed several explanations on how the Sun might generate its energy including: mass contraction, which could allow the Sun to shine for up to 45 million years. At around the same time, Charles Darwin was looking at the erosion of rocks and concluded that the Earth had to be at least 300 million years old. The Sun had to be at least as old as the Earth so clearly the solution had not been found.
It was discovered that the when nuclei of hydrogen combine to form Helium, the resulting mass of was less than the sum of the mass entering the sum of the initial masses. The missing mass was converted into energy with an exchange rate of Emc2 where Δm is the difference in the mass of the nuclear reaction and c is the speed of light (3 x 108 m s-1). The conversion of a relatively small amount of mass into energy would allow the Sun to shine for billions of years.
The fusion of Hydrogen into Helium in stars occurs in three stages. First, two ordinary Hydrogen (Hydrogen-1) nuclei, which are actually just single protons, fuse to form an isotope of Hydrogen called Deuterium (Hydrogen-2), which contains one proton and one neutron. A positron (a positively charged electron) and a neutrino (a neutral particle which travels nearly at the speed of light and has, perhaps, almost no mass) are also produced. The positron is very quickly annihilated in the collision with an electron and the neutrino travels right out of the Sun.
11H +11H = 21H+ 00e+ +00ν
The newly-formed Deuterium fuses with another regular Hydrogen to form an isotope of Helium, Helium-3 containing two protons and one neutron.
21H+ 11H = 31H
Next, two of the Helium-3 nuclei fuse to form a Helium-4 nucleus and two hydrogen-1 nuclei. Energy as gamma rays are produced in each step.
31H+31H = 42He + 210H
The resulting reaction cycle generates around 25 MeV of energy. Another series of reactions may occur in stars hotter than the Sun. such as the Carbon-Nitrogen cycle, in which a Carbon nucleus is involved in the first step. Here again, the overall result is to combine four Hydrogen nuclei to form one Helium nucleus. Other cycles, involving Nitrogen and Oxygen, have been proposed for explaining the fusion process in even hotter stars. The high density of the Sun allow the temperature for fusion to occur to be around 1.5 x 107 K

Nuclear Fusion on Earth

Man-made nuclear fusion uses a different reaction to that which occurs in the stars. In stellar Hydrogen burning, the reaction of two Helium-1 nuclei requires a proton to change into a neutron. Fusion on Earth starts by fusing Deuterium and Tritium. (Tritium is an isotope of Hydrogren which contains 1 proton and 2 neutrons.) The reaction proceeds as follows:
21H + 31H = 42He + 10n + 17.59 MeV.
nuclear fusion
Figure 1. The D-T nuclear fusion process.
An equally probable reaction can also occur between two Deuterium nuclei in one of two ways:
21H +21H = 32H + 10n + 3.27 MeV
or alternatively,
21H +21H = 31H + 4.03 MeV

Conditions for Break-Even

The heating of the plasma requires an enormous amount of energy and for the plasma to be self-sustaining it must produce at least the same amount of energy that it uses. There are three parameters that must be considered to 'break-even'.
  • The plasma temperature - the temperature for fusion to occur depends on the kinetic energy required by the nuclei to overcome the repulsive Coulomb barrier at a distance of 10-15 m.
  • The plasma density - once the temperature is high enough to initiate fusion, the ion density must be high enough to ensure that the collisions release more energy than they need to start.
  • The confinement time - the confinement time is defined as the time the plasma spends above the critical ignition temperature
Each of these factors is bundled into a performance figure known as the Lawson criteria. Its sets the lower bound on break-even. That is to say, if your plasma has a lower figure than the Lawson criteria you are using more energy than you are producing. Current fusion reactors use up more energy than they put in.
  • D-T fusion n τ ≥ 1014 cm-3 s-1
  • D-D fusion n τ ≥ 1016 cm-3 s-1


Cold Fusion

laser confinement
In 1989, an experiment performed at the University of Utah by Pons and Fleischmann's which claimed to have demonstrated fusion. The experiment was essentially an electrolysis cell, consisting of Platinum and Palladium electrodes placed in heavy-water (D2O). When the experiment was performed, it was found that the more heat was produced than can could be accounted for by chemical processes alone. Pons and Fleischmann concluded that the excess heating must be nuclear in origin.
The experiment hinges on the accuracy of the calorimetry used to determine the heating. More accurate calorimeters were tried and the heating effect was found to be significant. Other researchers found it difficult to reproduce the results so, after an initial media frenzy, the claims were widely dismissed.
Despite the general lack of acceptance by the mainstream scientific community, research continues by a few. In 2004, the Department of Energy peer reviewed the experimental evidence for cold fusion. It concluded that:
The experimental data shows evidence of: the existence of a physical effect that produces heat in metal deuterides.
The production of 42He in amounts commensurate with a 21H + 21H -> 42He reaction mechanism, a physical effect that results in the emission of energetic particles
The underlying process that produce these results are not manifestly evident from experiment. The scientific questions posed by these experiments are both worthy and capable of resolution by a dedicated program of scientific research.

Bubble Fusion

Sonoluminesence is the production of light from sound. It was first obversed in 1934, yet comparatively little is known about the process. Ultrasound in water can lead to the expansion and contraction of small bubbles dissolved in the water. In the reifaction, the bubble expands while during the compression, the bubbles collapse rapidly (1.4 km s-1 at the point of light emission) leading to a compression of the gas inside. The compression halts when the van der Vaals forces between molecules will not allow them to get any closer. The mechanism for the light emission is proposed by the shock-wave model.
The shock-wave model of sonoluminescence has the collapsing bubble generate an imploding shock-wave which focuses at a point. As the shock-wave propagates, it heats and intensifies the gas it passes through. At the focus, the shock-wave bounces back and makes the gas even hotter. Light is emitted because the shock-wave heats the gas enough to become ionised. The electrons emit light when they collide with the ions which results in the observed continuous emission spectra.
Experiments measuring the emission wavelength, show it to correspond to an energy of around 6 eV, which in turn, corresponds to a temperature inside a collapsing bubble of 70,000 K. There may be photons of even higher energy which would mean higher temperatures, but these wavelengths are absorbed by the water so it is not known what the maximum temperature inside the collapsing bubble is. It is at this point we turn our attention to fusion.
While 70,000 K is far below the 100 million K required for fusion, the temperature of the gas in the centre depends on the minimum size of the of the collapsing bubble. This is another unknown. The so-called shock radius, the radius of the bubble at the point of sonoluminescence, is around 0.1 μm but its minimum size could be smaller for an emission energy of 6 eV. If the radius of the bubble reaches 10 nm (just 10 times smaller) and the gas inside where deuterium, fusion could be ignited. Experiments producing sonoluminescence in deuterated acetone have claimed to produce nuclear fusion with the tell-tale emission of neutrons. Once again, the reproducibility of these results is at issue since it is very difficult to tell whether the neutrons were produced by nuclear processes or part of the background neutron count.
Binding Energy Curve


The mass of a nucleus is less than the sum of it constituent protons and neutrons. If we took the same number of protons and neutrons as in the nucleus we were trying to recreate, we would find the total mass of the individual protons and neutrons is greater than when they are arranged as a nucleus. The difference in mass between the products and sum of the individual nucleons is known as the mass defect. The binding energy is the amount of energy required to break the nucleus into protons and neutrons again; the larger the binding energy, the more difficult that would be. Figure. 1. Shows the binding energy for each element, against their atomic number.


binding energy curve
Figure 1. Binding energy of the elements.


Starting from Hydrogen, as we increase the atomic number, the binding energy increases. So Helium has a greater binding energy per nucleon than Hydrogen while Lithium has a greater binding energy than Helium, and Berilium has a greater binding energy than Lithium, and so on. This trend continues, until we reach iron. It begins to decrease slowly.
The binding energy curve is obtained by dividing the total nuclear binding energy by the number of nucleons. The fact that there is a peak in the binding energy curve in the region of stability near iron means that either the breakup of heavier nuclei (fission) or the combining of lighter nuclei (fusion) will yield nuclei which are more tightly bound (less mass per nucleon).
The binding energy is intimately linked with fusion and fission. The lighter elements up to Fe are available will release energy via the fusion process, while in the opposite direction the heaviest elements down Fe are more susceptable to liberate energy via fission.



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