Rutherford's Gold Foil Scattering Experiment

Rutherford

Rutherford (1900) measured the rate of decay by the level of ionization the radiation would produce in air as a function of time, and he noted the following when he measured the half-life of a radionuclide sample to be 60s [writer's comments are in brackets]:

From: Radioactivity (Second Edition) , 2016

Hall of Fame

Michael F. L'Annunziata , in Radioactivity (Second Edition), 2016

Ernest Rutherford (1871–1937)

Earnest Rutherford was born on August 10, 1871 in Nelson, New Zealand. He was awarded the Nobel Prize in Chemistry in 1908 "for his investigations into the disintegration of the elements, and the chemistry of radioactive substances." He was still a young man of 37  years at the time of this award, and most of his major achievements and contributions to the science of radioactivity and the field of nuclear physics were made by Rutherford after receiving the Nobel Prize.

Rutherford grew up as a farm boy in New Zealand, raised by parents who had emigrated from Britain with modest means but who had instilled in their children the power of knowledge and the importance of completing all their schoolwork to the best of their abilities. Ernest excelled in science and mathematics, and could only achieve a higher education through financial aid with scholarships. He won a scholarship to Nelson College, where he learned elementary science and mathematics and excelled to win another scholarship to continue his education at Canterbury College, which is now the University of Canterbury in New Zealand. Although Rutherford worked hard and had an inquisitive mind, he credited his teacher, Prof. Alexander Bickerton at Canterbury, who displayed such an enthusiasm for science, it gave him the stimulus to pursue scientific research on his own. At Canterbury Rutherford won another scholarship as a research student at the Cavendish Laboratory, University of Cambridge under J.J. Thomson, who would later in life also win the Nobel Prize in Physics. At Cambridge, Rutherford stood out as a great experimenter and thinker, who could make major discoveries concerning radioactivity and atomic structure without expensive equipment and only limited resources.

Rutherford was captivated with the recent discoveries of X-rays by Röntgen and the subsequent discovery by Becquerel of the mysterious natural radiations from uranium. Because Becquerel showed that the radiations from uranium could, as well as X-rays, discharge an electrified body (ie, cause ionization), he decided to examine the effect of placing successive layers of aluminum foil over uranium oxide on the efficiency of the emanations to cause the electrical discharge. From this experiment he made his first discovery concerning radioactivity, stating at his Nobel address:

"…[I] was led to the conclusion that two types of radiation of very different penetrating power were present – one that is very readily absorbed, which will be termed for convenience the α-radiation, and the other of a more penetrative character, which will be termed the β-radiation, … and when a still more penetrating type of radiation from radium was discovered by Villard, the term γ-rays was applied to them.

These terms devised by Rutherford soon took acceptance and came into common use by the scientific community as the convenient nomenclature, which remains today, for identifying these three types of radiation.

In addition to the different penetrating powers of α-, β-, and γ-radiation, other properties were used to identify these mysterious radiations, such as the differing deflections that the three radiations undergo in electric or magnetic fields. Alpha radiation was known to possess a positive charge, because it would be deflected toward the negative electrode in an electric field potential, while beta particles were known to be negatively charged due to their deflection in the opposite direction toward the anode or positive electrode. Gamma radiation would not undergo any deflection whatsoever, as illustrated in Fig. I.7. Likewise, the alpha and beta radiations, when traveling in a path perpendicular to the lines of force of a magnetic field, will be deflected in opposite directions, which is a characteristic of charged particles. Radiation that carries no electric charge would continue along a straight undeviating path in either electric or magnetic fields.

Figure I.7. Paths of travel of collimated beams of alpha, beta, and gamma radiation in (A) electric and (B) magnetic fields. Beam collimation is provided by placing the radiation source in a hole drilled within shielded containers (eg, lead) of which cross-sections are illustrated. The electric field in (A) is illustrated by positive and negatively charged electrodes separated by a space through which the radiations pass; and the magnetic field in (B) is illustrated by the circle to depict the pole of a magnet through which the lines of force of magnetic flux (marked by the symbol x) are directed into the plane of the page (z-axis) perpendicular to the radiation paths in the xy-axis.

After 3   years at the Cavendish laboratory, Rutherford moved in 1898 to McGill University in Montreal at the age of 27 to take on the position of professor of physics. It is at McGill University where he began to make his major discoveries in the field of nuclear physics. The first of these was the discovery that radioactive atoms that emit α-particles or β-particles disintegrate into atoms of lighter weight, in other words, atoms of an element such as radium that emit α-particles undergo transformations to atoms of a lighter and consequently different element. Rutherford and coworkers were able to demonstrate that the alpha particle was an atom of helium (later to be determined to be a nucleus of helium), and that helium gas would accumulate or be entrapped in minerals that contained radium. Furthermore, he demonstrated that the lighter atom produced as a product of the decay of radium would likewise be radioactive, and in turn, decay to another even lighter atom, and so on until the final product atom was stable. It was for this work that Rutherford received the Nobel Prize in Chemistry. Although a great honor for such a young scientist, it was ironic for Rutherford to go through life as a Nobel Laureate of Chemistry. He was a physicist and considered physics as the most important science of all. At the Nobel Prize presentation address on December 10, 1908, Prof. K.B. Hasselberg, President of the Royal Academy of Sciences, explained:

Though Rutherford's work has been carried out by a physicist and with the aid of physical methods, its importance for chemical investigation is so far-reaching and self-evident, that the Royal Academy of Sciences has not hesitated to award to its progenitor the Nobel Prize designed for original work in the domain of chemistry.

Rutherford's work in conjunction with numerous collaborators including Frederick Soddy, led to the conclusion that one chemical element can transform into other elements, which was previously only a centuries-old belief of alchemists, who tried to change lead into gold. Prof. Hasselberg in his speech of award presentation, had foresight when he added further:

[Rutherford's] disintegration theory [of atoms] and the experimental results upon which it is based, are synonymous with a new department of chemistry.

We can thus give credit to Rutherford for giving birth to the field of radiochemistry.

Rutherford's best work was yet to come after the Nobel Prize. In 1907 he moved to England to fill the position of professor of physics at Manchester University. It was at Manchester where Rutherford had a list of research topics to explore, and one of these was the deflection that alpha particles would undergo when passing through thin foils (approx. 5   ×   10⁻⁵  cm thick) of materials such as mica, aluminum, gold, etc. He knew that the alpha particles, as they travel at high speed, would traverse the foils as if the foil material was not even in the alpha-particle path, and that the flux of alpha-particle radiation would undergo only a very slight dispersion upon exiting the foils. This was understandable to him as strong electrical charges, expected to occur in atoms, could cause the slight deflection of the positively charged alpha particles.

The story goes that he was approached by his research assistant at Manchester, Dr. Wilhelm "Hans" Geiger (best known as the person who developed the Geiger counter, still used today for the monitoring of radioactivity). Geiger had asked Rutherford "What do you suggest we give the new student Ernest Marsden to do?" Rutherford proposed that they try to see if any alpha particles would bounce back, that is, not traverse the foil but be deflected by over 90   degrees back toward the direction from which the particle had originated. Rutherford did not expect to see any such deflection, but it had to be investigated. They could observe the alpha-particle path of travel and see and count the deflections by means of a zinc sulfide screen that would produce a microscopic fluorescence (flash of light scintillation) in the dark when each individual alpha particle hit the screen. They used radium as the source of the alpha-particle beam to bombard a thin foil of gold. Geiger later informed Rutherford that they could see the occasional deflection by greater than 90   degrees of one alpha particle for every 8000 particles traversing the gold foil. (See the following biographical sketch of Wilhelm "Hans" Geiger for a detailed description of this experiment.) The commemorative postage stamp above illustrates this phenomenon. The stamp illustrates a central nucleus surrounded by five electrons and the path (arrows) of three alpha particles. One of the alpha particles is illustrated hitting the nucleus of an atom of gold and bouncing back. In a presentation given by Rutherford years later, he described his reaction to this discovery by stating:

It was quite the most incredible event that ever happened to me in my life. It was as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.

Rutherford grasped this discovery to conclude that there had to be a massive core or nucleus in the atoms of materials that would cause colliding alpha particles to bounce back. By using high-energy (7.7-MeV) alpha particles, that would travel at highest speeds, Rutherford was able to calculate the distance of closest approach and consequently the radius of the atomic nucleus to be approx. 5   ×   10⁻¹⁵  m (see chapter: Alpha Radiation).

In addition to the alpha-particle scattering experiment described above, which was carried out with the assistance of Hans Geiger, Ernest Rutherford undertook numerous ground-breaking experiments with Geiger. Some of these are described in the following biographical sketch on Wilhelm "Hans" Geiger. One very important experiment, which he undertook with Geiger (Rutherford and Geiger, 1908a), confirmed the charge and nature of the alpha particle. Rutherford had determined in previous years that the alpha particle was positively charged (Rutherford 1905a,b); however, a few years later Rutherford and Geiger (1908a) described their detailed measurement of the double charge on the alpha particle and their determination that the alpha particle was equivalent to a nucleus of the helium atom.

Rutherford and Geiger's precise determination of the charge on the alpha particle made use of the apparatus illustrated in Fig. I.8. As described by Rutherford and Geiger (1908a), the apparatus consisted of a 4-cm diameter cylindrical glass tube HH closed at both ends with ground glass stoppers D and E. The radioactive source is located at R, which is attached to the lower stopper E. The radiation travels into the testing chamber, which is attached to the upper stopper D via an ebonite tube F. The testing chamber contains two parallel plates, A and B, situated approximately 2   mm apart. Plate B was made of brass with a circular opening, 1.92   cm in diameter, covered with a thin sheet of aluminum. Likewise, the upper chamber AC consists of a shallow brass plate with an opening of 2.5   cm, which is also covered with a thin sheet of aluminum foil. The aluminum foil exhibited only a minimal stopping power for alpha particles equivalent to ∼5   mm of air. Plate B was connected via a side glass tube to a battery, while the other pole was earthed. The chamber AC, insulated from plate B, was connected to an electrometer. The entire apparatus was situated between the poles NS of an electromagnet, which is illustrated with dashed lines in Fig. I.8. The magnetic field was required to deflect beta particles, that are emitted from the radioactive source, away from the detector plates AC and B.

Figure I.8. Apparatus used for the measurement of the charge on the alpha particle. The illustrated paths of deflections of alpha and beta particles was added by the author.

From Rutherford and Geiger (1908a).

A vacuum pump was attached to the arm at the left of the figure to remove air from the chamber, as best as possible, in order to minimize any ionization of air molecules by alpha particles. Ionization within the chamber could produce variation in the measurement of positive charge of the alpha particles by the upper collection plate. The source of radium used by Rutherford and Geiger, emits both alpha and beta particles. The magnetic field would deflect all beta particles away to one side of the glass tube, as illustrated in Fig. I.8, so that beta particles do not deposit any charge on the collecting plate AC and interfere with the charge collected from alpha particles.

With the apparatus under a strong magnetic field, the upper plate AC receives a positive charge. The positive charge received by the upper plate was measured under two conditions, namely with the lower plate B connected to a positive potential (+V) or negative potential (−V). Rutherford and Geiger (1908a) made calculations based on the basis of current collected i ₁, when plate B was connected to a positive potential, and i ₂, the current collected when plate B was connected to a negative potential. The magnitude of i ₂ was always smaller than i ₁; and their magnitudes depended on the level of vacuum inside the vessel. The chamber was not under a perfect vacuum; and Rutherford and Geiger (1908a) thus named the current collected when the alpha particle traveled through the gas of the chamber as i ₀. Thus, they defined the current observed when the voltages on plate B were positive as:

[I.1] $i_1=i_0+nE$

where n is the number of alpha particles passing into the upper plate AC per second and E is the charge on each alpha particle; and when the voltage on plate B is reversed, the ionization current caused by the alpha particles was reversed, although equal in magnitude, and:

[I.2] $i_2=nE-i_0$

Adding Eqs. [I.1] and [I.2] gives:

[I.3] $i_1+i_2=2nE$

or:

[I.4] $nE=1/2\left(i_1+i_2\right)$

The number n of α-particles reaching the upper collection plate AC of Fig. I.8 was defined as:

[I.5] $n=KQN$

where K is the fraction of the total number of α-particles emitted by the radioactive source reaching the upper collection plate AC, Q is the quantity of pure radium in grams, and N is the number of α-particles emitted per second per gram of pure radium. Thus, the number of α-particles emitted per second by the radioactive source in the apparatus is R  = QN. The values of K and Q are measured, and the value of N is determined from measurements of count rate. The value of K, that is the fraction of α-particles striking the upper plate AC, was calculated easily to be K  =   0.0172 on the basis of the geometry of the apparatus and under the assumption that all of the α-particles are emitted equally from the source in all directions. The value of N, ie, the number of α-particles emitted per second per gram of radium, was determined to be 3.4   ×   10¹⁰. (Rutherford's calculation of Q was amazingly close to the true value, which is known currently to be 3.65   ×   10¹⁰ α-particles per second per gram of radium.) Thus, Rutherford and Geiger (1908a) measured the charge on each α-particle with the apparatus illustrated in Fig. I.8 using the equation:

[I.6] $E=\left(i_1+i_2\right)/2KQN$

Following the collection of numerous values of i ₁ and i ₂, Rutherford and Geiger calculated a mean value of E for a single α-particle in electrostatic units (e.s.u.) to be E  =   9.4   ×   10⁻¹⁰  e.s.u., and from additional experiments not described here for brevity they obtained the value of E  =   9.1   ×   10⁻¹⁰  e.s.u. An average of the two values was taken as the charge on the α-particle, E _α, or:

[I.7] $E_{\text{α}}=9.3\times {10}^{-10}\text{e}\text{.s}\text{.u}\text{.}$

Rutherford and Geiger noted that the charge on the electron, E _e, from early work of Millikin and Begeman (1908), was:

[I.8] $E_{\text{e}}=4.1\times {10}^{-10}\text{e}\text{.s}\text{.u}\text{.}$

which is approximately one-half that of the α-particle. Thus, Rutherford and Geiger found the α-particle charge to be twice that of the electron but of opposite sign. On the basis of their calculation of the charge on the α-particle to be E  =   9.4   ×   10⁻¹⁰  e.s.u., Rutherford reported that the charge on the electron E _e should be one-half of their determined charge on the α-particle or E _e  =   4.65   ×   10⁻¹⁰  e.s.u., that is:

[I.9] $\frac{E_{\text{α}}}{E_{\text{e}}}=\frac{2e}{e}=\frac{9.3\times {10}^{-10}\text{e}\text{.s}\text{.u}\text{.}}{4.65\times {10}^{-10}\text{e}\text{.s}\text{.u}\text{.}}$

After determining the charge on the α-particle to be +2e, Rutherford and Geiger (1908a) went further to make measurements of the deflection of the α-particle relative to that of the proton in a magnetic field by measurements of the charge/mass or e/m ratio for each particle. They concluded that the α-particle had a mass that was four times that of the proton and equivalent to the mass of the helium nucleus. Also, it was concluded that the loss of an α-particle from an atom would create another different atom with the reduction in mass number of 4. They worded their finding as follows:

Taking into account probable experimental errors in the estimates of the e/m for the α-particle, we may conclude that an α-particle is a helium atom [i.e., helium nucleus], or, to be more precise, the α-particle, after it has lost its positive charge is a helium atom…There is direct evidence in the case of radium that each of the α-ray changes is accompanied by the expulsion of one α-particle from each atom. Consequently, since the atomic weight [i.e., mass number] of radium is 226, the atomic weight of the emanation is 222, and of radium A is 218.

What Rutherford and Geiger were reporting was eventually reconfirmed by others that radium-226 decays with the successive emission of an α-particle according to the following:

[I.10] ${}_{88}{}^{226}\text{R}\text{a}\stackrel{\text{α}}{\to }{}_{86}{}^{222}\text{R}\text{n}\stackrel{\text{α}}{\to }{}_{84}{}^{218}\text{P}\text{o}\dots$

From here on, Rutherford was able to begin to formulate the structure of atoms with a central massive nucleus, the structure that holds today. Rutherford's findings were the initial step that provided the foundation upon which other physicists, including Niels Bohr, Werner Heisenberg, and others, were able to elaborate the structure of the atom as we know it today.

In a letter to the editor of the journal Nature, concerning the structure of the atom, published on December 11, 1913, Rutherford postulated correctly the atomic nucleus as the origin of α- and β radiation. In his letter he stated the following:

There appears to me no doubt that the α-particle does arise from the nucleus, and I have thought for some time that the evidence points to the conclusion that the β particle has a similar origin. This point has been discussed in some detail in a recent paper by Bohr (Phil. Mag., September 1913). The strongest evidence in support of this view is, to my mind, (1) that the β ray, like the α ray transformations, are independent of physical and chemical conditions, and (2) that the energy emitted in the form of β and γ rays by the transformation of an atom of radium C is much greater than could be expected to be stored up in the external electronic system.

Rutherford's next great discovery came in 1919, when he reported the first evidence of a manmade nuclear reaction, that is, the splitting of the atom. This he was able to demonstrate when a high-speed alpha particle would strike the nucleus of an atom and rearrange it into two different atoms. Rutherford observed that when alpha particles would strike air, he could detect scintillation on a zinc sulfide screen produced at a distance well beyond the distance of alpha-particle range of travel corresponding to the range of travel of hydrogen atoms (protons). He demonstrated that the production of high-speed hydrogen atoms by collision of alpha particles with air arose from the collision of the alpha particles with nitrogen atoms only, because the effect would not occur with other constituents of air such as oxygen or carbon dioxide. Furthermore, when pure nitrogen was the target, the scintillations produced by the product hydrogen nuclei (protons) were greater then when air was bombarded with alpha particles (air contains only 79% nitrogen). Rutherford was also able to show that the number of swift atoms of oxygen produced by the alpha-particle collisions was about the same as the corresponding number of hydrogen nuclei (protons). This first manmade nuclear reaction is illustrated in the commemorative stamp from New Zealand shown here. The stamp illustrates the historic nuclear reaction where an atom of nitrogen-14, the most common isotope of nitrogen, denoted as ${}_7{}^{14}\text{N}$ , because its nucleus contains seven protons and seven neutrons, interacts with the colliding alpha particle or helium nucleus $\left({}_2{}^4\text{H}\text{e}\right)$ . In the collision, a proton $\left({}_1{}^1\text{H}\right)$ is ejected and two protons and two neutrons from the alpha particle can coalesce with the remaining nucleons of the original nitrogen to yield a nucleus having eight protons and nine neutrons, namely, the isotope oxygen-17 denoted above as ${}_8{}^{17}\text{O}$ . This was the very first artificial transformation of one element into another, which was the age-old dream of alchemists.

Nobel Laureate Cecil Powell (1903–69) in his autobiography published in 1987, related that he was only 19   years of age when he arrived at the Cavendish Laboratory as a research student to C.T.R. Wilson, and at this time he recalls Rutherford researching alpha-particle induced transmutations. Powell related his following recollections:

When I arrived in 1922, Rutherford had already, in 1919, demonstrated the artificial disintegration of the light elements by bombarding them with fast alpha-particles from radioactive sources. We used to see him disappearing from time to time into a partitioned corner in his laboratory, with his assistant [George] Crowe, to count the scintillations which recorded the ejected protons. This involved long periods of darkness viewing a zinc sulfide screen under a low-powered microscope, and they used to emerge after an hour or so, blinking in the sudden light, like miners coming out of the pit.

As a result of the above manmade nuclear reaction where protons were emitted as a product, Rutherford has been given the honor of discovering the third elementary particle in matter, the proton. To put this discovery in perspective, the first elementary particle to be discovered was the electron from the work of J.J. Thomson in 1897 (see biographical sketch further on in this chapter), and the second elementary particle to be discovered was the photon from the work of Albert Einstein in 1905 (see Radioactivity Hall of Fame, Part III).

Rutherford contributed much more to the study of radioactivity and nuclear physics, including the fact that all radioactive atoms have differing rates of decay, including the concepts of half-life and decay constant that are invariable properties of each radioactive nucleus or radionuclide of given atomic number (proton number) and mass number (number of protons   +   neutrons in the nucleus (see chapter: Radionuclide Decay, Radioactivity Units, and Radionuclide Mass)).

Another contribution among many others made by Rutherford deserves mention. This is the development, together with Hans Geiger, of the first electronic means of detecting and counting individual alpha-particle emissions from radioactive atoms. (See the next biographical sketch on Johannes "Hans" Geiger for a detailed description of this electronic counter of alpha particles.) The alpha-particle emissions were allowed to travel through a small opening or window into a vessel containing air or other gas exposed to an electric potential. The vessel is referred to today as an ionization chamber. Upon entering the vessel, the alpha particle, which carries a double positive charge, would cause ionization of the gas, and the ions produced by the alpha particle would accelerate toward electrodes of the chamber, thereby magnifying the ionization within the gas. The positive and negative ions produced by the alpha particle would be collected by their opposing electrodes and thereby produce a pulse that would cause a deflection of the electrometer needle. This instrument was the precursor of more modern Geiger counters, but it served its purpose, as Rutherford and Geiger were able to count each alpha-particle emission from a radium sample and calculate its specific activity. In the words of Rutherford in his Nobel lecture:

In this way it was shown that 3.4   ×   10¹⁰ alpha-particles are expelled per second from one gram of radium.

This was very close to the real value of 3.7   ×   10¹⁰, which is the unit used today to define the unit of radioactivity known as the Curie (Ci), where 1Ci   =   3.7   ×   10¹⁰ disintegrations per second (see chapter: Radionuclide Decay, Radioactivity Units, and Radionuclide Mass). For the entire text of Rutherford's Nobel lecture as well as those of other Nobel Laureates in chemistry and physics, the reader may consult the website of the Nobel Foundation (http://nobelprize.org) as well a book edited by Elsevier entitled Nobel Lectures, 1901–1970.

At Manchester, many famous nuclear physicists and future Nobel Laureates worked and collaborated with Rutherford including Frederick Soddy, Henry G.J. Moseley, George de Hevesy, and Niels Bohr. At Rutherford's laboratory in Montreal, Otto Hahn, who later discovered nuclear fission with the collaboration of Fritz Strassmann and Lise Meitner, also worked with Rutherford. At the Cavendish laboratory, other future Nobel Laureates of physics collaborated with Rutherford including James Chadwick, Patrick Blackett, John Cockroft, Ernest Walton, George P. Thomson, Edward V. Appleton, Cecil Powell, and Francis W. Aston, among others. The commemorative stamp from Canada illustrated above celebrated the centennial of Rutherford's birth. The stamp illustrates a reprint of Ray Webber's art work as described by the Canada Post Office as a burst of light symbolizing, "the great energy that the harnessing of the atom has given to us and which, unseen, affects so much of all our lives." It is said that Ernest Rutherford was the greatest experimental physicist of the 20th century, while Albert Einstein was the greatest theoretical physicist of the century.

For further reading on the life and accomplishments of Rutherford, the reader may peruse books by Boltz (1970), Heilbron (2003), and Pasachoff (2005).

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The Atomic Nucleus

Michael F. L'Annunziata , in Radioactivity (Second Edition), 2016

20.1 Introduction

Ernest Rutherford (1911, 1919, 1920a,b) Rutherford, 1911 Rutherford, 1919 Rutherford, 1920a Rutherford, 1920b was the first to discover the atomic nucleus and measure the size of the nucleus of an atom. A detailed account of this work is given in Hall of Fame, Part I of this book. In brief, Rutherford bombarded very thin gold foil (4   ×   10⁻⁵  cm thick) with alpha particles. Most of the alpha particles traversed the gold foil almost as if the foil was not in their path; however, one alpha particle for every 20,000 particles would bounce back from the foil by more than 90 degrees from the direction of travel. Rutherford concluded that within much empty space of the atom there exists a massive central nucleus capable of knocking back the alpha particle to the direction from which it came. Rutherford expressed his reaction to the observed alpha particle back-scattering with the following statement, related by Feather (1940) in a biographical essay a few years following Rutherford's death:

It was quite the most incredible event that ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized that the scattering backwards must be the result of a single collision, and when I made calculations I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus.

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Niels Bohr Models the Hydrogen Atom as a Quantized System with Compelling Exactness, but His Later Career Proves that Collaboration and Developing New Talent Can Become More Significant than the Groundbreaking Research of Any Individual

Gary G. Tibbetts , in How the Great Scientists Reasoned, 2013

When Rutherford saw the results, he enthused [2]

It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized that this scattering backward must be the result of a single collision, and when I made calculations I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus. It was then that I had the idea of an atom with a minute massive center, carrying a charge.

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Quantum Mechanics

Albert Thomas FromholdJr., in Encyclopedia of Physical Science and Technology (Third Edition), 2003

I.A Structure of the Atom

Ernest Rutherford's (1871–1937) interpretation of his extensive scattering experiments in 1911 gave overpowering evidence that atoms consist of a dense, positively charged nucleus surrounded by a cloud of electrons. The electron had been discovered a few years earlier in 1887 by Joseph John Thomson (1856–1940), who attributed a definite charge-to-mass ratio to the particle. Before the discovery of the wave-like properties of the electron in 1927 by George Paget Thomson (1892–1975), the son of J. J. Thomson, it was expected that the mechanical properties of atoms could readily be explained by applying classical mechanics in a straightforward way to this model. In fact, the successful model of planetary motion around the more massive sun, under the action of gravitational forces between the planets and the sun, and the perturbations to such motion due to the gravitational forces between planets, provide the closely related classical analog model for describing the motion of electrons about a single, massive nucleus: the electrical forces between charged particles replace the gravitational forces in the solar system.

The forces between electrons are repulsive instead of attractive, and these repulsive forces are of the same order of magnitude as the attractive forces between an electron and the nucleus. Therefore these forces between electrons are not merely perturbations, as is the case for the gravitational forces between planets orbiting the sun.

However, it was expected that the hydrogen atom, containing only a single electron and thus free of the repulsive Coulomb force between electrons in two-electron and many-electron atoms, should be easily amenable to treatment by classical mechanics. The model is a simple picture in which the single electron orbits the far more massive proton nucleus under the action of a centripetal force provided by the attractive electrical force between electron and nucleus.

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Complementarity Beyond Physics (1928–1962)

David Favrholdt , in Niels Bohr Collected Works, 1999

THE RUTHERFORD MEMORIAL LECTURE 1958: REMINISCENCES OF THE FOUNDER OF NUCLEAR SCIENCE AND OF SOME DEVELOPMENTS BASED ON HIS WORK (1958)

Versions published in English, Danish and German

English: The Rutherford Memorial Lecture 1958: Reminiscences of the Founder of Nuclear Science and of Some Developments Based on his Work

A

Proc. Phys. SOC. 78 (1961) 1083–1115

B

"Rutherford at Manchester" (ed. J.B. Birks), London 1962, pp. 114–167

C

"Essays 1958–1962 on Atomic Physics and Human Knowledge", Interscience Publishers, New York 1963, pp. 30–73 (reprinted in: "Essays 1958– 1962 on Atomic Physics and Human Knowledge, The Philosophical Writings of Niels Bohr, Vol. 111", Ox Bow Press, Woodbridge, Connecticut 1987, pp. 30–73)

Danish: Rutherford mindeforelæsning 1958. Erindringer om grundlæggeren af kernefisikken og om den uduikling, der bygger på hans uark

D

"Atomfysik og menneskelig erkendelse 11", J.H. Schultz Forlag, Copenhagen 1964, pp. 43–94

E

"Naturbeskrivelse og menneskelig erkendelse" (eds. J. Kalckar and E. Rüdinger), Rhodos, Copenhagen 1985, pp. 167–228

German: Rutherford-Gedenkvorlesung 1958: Erinnerungen an den Begründer der Kernphysik und an die uon seinem Werk ausgehende Entwicklung

F

"Atomphysik und menschliche Erkenntnis 11", Friedr. Vieweg & Sohn, Braunschweig 1966, pp. 30–74

All of these versions agree with each other, with the exception that the next to last paragraph is omitted in B.

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SURFACE AND INTERFACE ANALYSIS AND PROPERTIES

S. Speller , ... M. Schleberger , in Handbook of Surfaces and Interfaces of Materials, 2001

2.1 High Energy Ion Scattering

In the RBS regime the binary collision model is extended to take into account that those primary ions that penetrate to greater depth are backscattered from atoms inside the bulk of the solid [15, 16]. On the path to this target atom and back to the surface the primary ion loses energy due to excitations of electron gas and ionization by target atoms. These losses are called electronic or inelastic losses. The losses are widely known and can be found in many tables [17]. As a function of depth t and using the "kinematic factor" K = E ₁/E ₀ (Eq. (1)) the energy of the backscattered ion is

(14) $E_1(t)=K\{E_0-t{(dE/dx)}_{\text{in}}\}-t{(dE/dx)}_{\text{out}}/\left|\cos {\theta }_1\right|$

This expression can be simplified for thin layers or short path length assuming dE/dx = const. The depth resolution in the "surface approximation" is then:

(15) $\Delta t=\Delta E_1/\{K(dE/dx){|}_{E_0}+(dE/dx){|}_{E1}/|\cos {\theta }_1\}$

Computer programs are available for estimating RBS spectra and evaluating depth profiles [18]. A typical RBS spectrum is shown in Figure 3 using 1.9 MeV He⁺ [19]. It is a PtSi layer system on alumina, Al₂O₃, with a thin W layer deposited first, followed by a Pt layer, which is covered with Si. During annealing of the sample the Pt and Si react and form a silicide. The low energy part of the spectra is in the intensity steps and is due to the Al and the O at the Al₂O₃-W interface. The position of these steps agrees with binary collision Eq. (1) for Al and O shifted by the additional energy loss occurring when the He⁺ ions pass through the overlayers. The extended continuous spectrum towards lower energies is due to the backscattered particles. The shape of this part of the spectra would be the same for a pure alumina sample. After annealing the thin layers of W, Pt, Si, and PtSi give rise to narrow features in the spectra. The energetic position is given by Eq. (1), modified where applied, by the additional energy losses of overlayers. The width of the layer spectra is related to layer thickness and the inelastic loss as expressed in Eq. (16). Yields Y in the different parts of the spectra are estimated from the general formula applicable in scattering experiments from:

Fig. 3. The RBS spectrum of a Pt/Si layer system on a Al₂O₃ substrate. The dashed line is the spectra as deposited; the dotted line is after annealing and the formation of a PtSi compound. The W is used as a thin layer between the Al₂O₃ and the original Pt layer. The Al₂O₃ backing is seen as a step of Al (lower Z) and of O (lower Z). Note that the Si and Pt areas, that is, the number density of atoms/cm², is not changed in the annealing process [19].

Reprinted with permission from Z. L. Liau et al., J. Appl. Phys. 49, 5295 (1978), © 1978 the American Institute of Physics.) Copyright © 1978

where I ₀ is the primary beam intensity [number of ions], N is the number of target atoms [atoms/cm²], and ΔΩ is the solid angle of detection [sr]. The differential scattering cross section is given as [cm²/sr]. Furthermore, 100% particle detection efficiency is assumed. For layers of thickness Dt at depth t the yield will assume a Rutherford cross section and a scattering angle of 180°:

(17) $Y(t)=I_0{\{Z_1{Z}_2{e}^2/4E(t)\}}^{2}N\Delta t\Delta \Omega$

A spectrum E ₁(t) is experimentally measured (Fig. 3) so Eq. (18) has to be converted to a spectrum Y ₁(t)dE ₁. With the kinematic factor K and the notion that in the range of ion energies used the energy loss is slowly varying with energy, the ratio between the energy loss on the way in, ΔE _in, and on the way out, ΔE _out, will be approximately constant, that is,

(18) $\begin{array}{c}A=\Delta E_{\text{out}/}/\Delta E_{\text{in}}+K(E(t)-E_1)/(E_0-E(t))\\ \approx (dE/dx){|}_{\text{out}}(dE/dx){|}_{\text{in}}\end{array}$

By using the proper dE/dx values, A can be estimated explicitly. However, for light ions like He⁺ and medium to high Z ₂ targets K ≈ 1 and an energy loss ratio out/in of approximately 1, Eq. (19) can be approximated by

which is in good qualitative agreement with the shape of the experimental "bulk" spectra.

Peak heights H and peak width ΔE of the Si and Pt peak of the annealed PtSi layer can be used to estimate the approximate composition of the layer. The ratio of the number of target atoms N_a to N_b is proportional to the peak height ratio, the width, and the inverse ratio of the cross sections. The latter ratio reduces to the square of the ratio of the respective atomic numbers Z:

(20) $N_a/N_b=(H_a/H_b)(\Delta E_a/\Delta E_b){(Z_b/Z_a)}^2$

The peak area of the spectrum of a thin layer is naturally proportional to the number of target atoms. For structural analysis using RBS or MEIS the shadow cone and the related effect of channeling are the basic tools. When a parallel beam of ions is directed onto a single crystal surface aiming at low index crystal direction most ions will penetrate into the crystal channels. These spectra are called aligned and show the surface peak. The scheme of an MEIS experiment and experimental spectra are shown in Figure 4 [20]. It shows the backscattering of 100.5 keV protons from a Pb(110) surface as a function of surface temperature. It is clearly seen that the surface peak intensity increases with increasing temperature and also broadens. There is no intensity increase below the surface peak due to the aligned geometry. Only at the highest temperatures close to the melting point of Pb is the typical bulk-scattering observed. Equation (7) is where we start if we are to understand the development of a surface peak. If we take two atoms, the flux distribution at the second atom f(s ₂) is related to the flux distribution of the first atom f(s ₁) by:

Fig. 4. Energy spectra of backscattered protons of 100.5 keV from Pb(110) with increasing target temperature from room temperature to close to the bulk melting point of Pb (600.8 K). The inset shows the shadowing/blocking geometry of the experiment [20].

Reprinted with permission from J. F. van der Veen, B. Pluis, and W. van der Gon, © 1990, Plenum Press. Copyright © 1990

(21) $f(s_2)2\pi s_{2}d{s}_2=f(s_1)2\pi s_{1}d{s}_1$

where the s are respective impact parameters. If the flux distribution at the edge of the shadow cone is small compared to the thermal vibrational amplitude f(s ₂) it can be approximated to a delta (δ) function. Hence the flux at atom 2 in the region at the edge of the shadow cone and outside, that is, for s ₂ ≥ r_c , will be

(22) $f(s_2)=1+(r_c^2/2s^2)\delta (s_2-r_c)$

The index c indicates that here a Coulomb potential is considered for the scattering. This flux distribution is then to be folded with the Gaussian position distribution Δ(s ₂) to obtain the probability P ₂ of hitting the second atom with a small impact parameter and thereby contributing to the backscattering yield. As large angle backscattering is considered here, the impact parameters will be small compared to the thermal vibrational amplitudes. Within the Debye model of thermal vibrations with amplitude r the position distribution is

(23) $\Delta (s)=1/\pi {\rho }^2\exp (-r_c^2/{\rho }^2)$

The probality for a close impact collision P ₂ is then

(24) $P_2=(1+r_c^2/{\rho }^2)\exp (-r_c^2/{\rho }^2)$

The total intensity of the surface peak is the sum of the scattering from the first atom and the second atom. More detailed studies show that depending on the ratio r_c /r, more atoms than two may contribute to the surface peak [15, 16]. Considering now the change of the surface peak in Figure 4 as a function of temperature, the initial increase is due to the increase of the thermal vibrational amplitude. The evaluation in terms of the number of atoms contributing to the surface peak shows this effect quite clearly (Fig. 5) [21]. At approximately 580 K, that is, 20 K below the bulk melting point, surface melting is observed which leads to the enhanced increase and broadening of the surface peak.

Fig. 5. Calibrated surface-peak area (Nr. of visible atoms) and the number of molten layers as a function of the temperature. The vertical line indicates the bulk melting point T_M . The arrow indicates the surface melting point. The inset is an expanded view of the highest 10-K interval.

Reprinted with permission from J. W. M. Frenken and J. F. van der Veen, Phys. Rev. Lett. 54, 134 (1985), © 1985, The American Physical Society. Copyright © 1985

From the example given here, it is obvious how channeling can be used for structural analysis. It adds to the RBS thin-film analysis the capability to locate impurities or defects with respect to a host lattice. With a single crystal target using an aligned scattering geometry the variation of the scattering angle using a rotable energy spectrometer or solid state detector yields intensity distributions with pronounced minima for all major low index crystallographic orientations. Impurities in the host lattice will alter these minima. An interstitial in the middle of a channel causes a peak at the respective total energy loss and so mass, position, and depth can be measured. These channeling techniques can be combined with the detection of recoils (ERDA) which is one of the few techniques that affords quantitative analysis of light ion impurities in solids (H, D, etc.). Another line of analysis is opened when measuring the X-rays emitted due to the inner shell ionization by fast protons—proton induced X-ray emission (PIXE). Compared to electron-induced X-ray analysis, for example, with electron microprobes or SEM, the proton beams allow not only structural analysis using the channeling effect, but the remarkable feature is the possibility of bringing the protons through a proper thin window into air. Degradation of beam quality is negligible and the PIXE technique is therefore applicable to archeological problems, art works, sculptures, paintings, and prints—essentially without damage [22].

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Origins of Quantum Theory

J.E. House , in Fundamentals of Quantum Mechanics (Third Edition), 2018

1.3 Electrons and the Nucleus

In 1911, Rutherford performed one of the revealing experiments in atomic physics that is now known as the gold foil experiment. Some radioactive heavy elements emit alpha particles (helium nuclei), and a beam of these particles was directed at thin gold foil, as depicted in Fig. 1.4.

Fig. 1.4. A depiction of Rutherford's experiment.

Following Thompson's idea, it was believed at the time that atoms consisted of positive and negative charges that were distributed throughout the atom. Although most of the particles continued on their original paths, a small fraction of the particles were deflected through large angles or even reversed direction. However, when the results of the experiment were analyzed, it was concluded that some of the positive alpha particles must have encountered a region of the target atoms from which they were strongly repelled. That positive region occupied a small fraction of the volume of the atom, and it is now known that atomic nuclei have radii that are on the order of 10^{−   13}  cm. With radii of most atoms being in the range of 10^{−   8}  cm, it is seen that most of the volume of an atom is empty space, which explains why the majority of the alpha particles were unimpeded as they passed through the gold foil. The gold foil experiment provided our view of atomic structure and was a pivotal point in the development of our knowledge of atoms.

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NUCLEI AND NUCLEAR POWER

JERRY B. MARION , in Physics in the Modern World (Second Edition), 1981

Modern Alchemy

One of the most ancient dreams of Man has been to transform some cheap and plentiful material, such as lead, into gold. Alchemists devised many fantastic recipes for such processes and were able to extract a great deal of gold from their unwary sponsors, but they obtained none from lead. No chemical or ordinary physical process can change one element into another. Radioactive decay processes alter the nuclear charge and therefore do transform the atoms of one element into atoms of a different element. It is actually possible to produce gold in this way, but in order to do so it is first necessary to prepare a radioactive isotope of platinum—certainly not a practical way of achieving the alchemists' dream!

Ernest Rutherford's experience with radioactivity led him to wonder whether there might be ways, other than radioactive decay, to transmute one element into another. He reasoned that if a high-speed α particle could be fired at another nucleus, this might disrupt the target nucleus and form a nucleus of a different element. Rutherford chose for his projectiles the α particles emitted in radioactive α decay. When these particles were projected through nitrogen gas, he found that some of the α particles struck and reacted with nitrogen nuclei, thereby producing two different elements—oxygen and hydrogen. The nuclear reaction first observed by Rutherford was

$\underset{\text{nitrogen}}{{}^{14}\text{N}}+\underset{\text{helium}}{{}^4\text{He}}\to \underset{\text{Oxygen}}{{}^{17}\text{O}}+\underset{\text{hydrogen}}{{}^1\text{H}}$

Figure 20-9 shows that the net result of this reaction is to transfer two neutrons and one proton from the helium nucleus to the nitrogen nucleus, thereby forming ¹⁷O.

FIGURE 20-9. The net result of the reaction ¹⁴N + ⁴He? ¹⁷O + ¹H is the transfer of one proton and two neutrons from the helium nucleus to the nitrogen nucleus, thereby forming ¹⁷O and leaving a single proton (a hydrogen nucleus).

Since the time of Rutherford's first observation of a nuclear reaction, thousands of reactions have been studied in the laboratory. Some of these reactions involve the simple capture of an incident particle by a target nucleus and others involve complex disintegrations. The techniques of reaction investigations have been refined to the extent that nuclear transmutations are now a routine laboratory practice.

A cloud chamber is a device for rendering visible the paths of nuclear particles by the condensation of water droplets on the ions that the particles leave in their wakes as they pass through the gas in the chamber. This photograph shows the disintegration of a nitrogen nucleus by a fast a particle in a cloud chamber. This picture, taken by P. M. S. Blackett in 1925, is the first photograph of a nuclear reaction. Only one reaction event is seen amidst the tracks of many a particles that do not induce reactions.

P.M.S. Blackett

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QUANTUM PHYSICS, LASERS, AND SQUIDS

George B. Arfken , ... Joseph Priest , in University Physics, 1984

42.2 Rutherford and the Nuclear Atom

The researches of Planck and Einstein introduced quantization into physics. The next thread in the fabric of quantum physics was Rutherford's development of the nuclear atom, which led to Bohr's quantum theory of the atom.

In 1909, Ernest Rutherford (Figure 42.4) and his associates H. Geiger and E. Marsden began analyzing the deflection of α-particles passing through thin metal foils. The α-particles were emitted by radioactive substances and had kinetic energies of several MeV (1 MeV = 10⁶ eV). The α-particle was known to have a positive charge and a mass several thousand times that of the electron. ^* Geiger and Marsden directed a beam of α-particles at a thin gold foil. Gold was chosen as a target because it can be rolled into a very thin film, and this minimizes the number of multiple collisions between an α-particle and the gold atoms. Geiger and Marsden wanted to avoid multiple collisions because successive deflections tend to cancel, thereby obscuring the details of atomic structure. If an α-particle collides with just one gold atom, its deflection can be related precisely to the electric force it experiences. The electric force, in turn, depends on the distribution of the negatively charged electrons and the positive charge of the atom. The gold film used by Geiger and Mars den had a thickness of approximately 10^-6 m. If we view the gold atoms as being stacked in layers, the thickness of the film was about 2000 such layers.

Figure 42.4. Ernest Rutherford, originator of the nuclear atom.

Figure 42.5 indicates the experimental arrangement used by Geiger and Marsden. A movable eyepiece was focused on a small screen that gave off brief flashes of light when struck by an α-particle. Most α-particles suffered very small deflections. But surprisingly, a tiny fraction of the α-particles were scattered backward, through angles as great as 150° (the largest angle observable with their apparatus). Such large deflections were completely unexpected.

Figure 42.5. Top view of the α-scatter apparatus of Geiger and Marsden. The radioactive source (R) gives a collimated beam of α-particles. The microscope (M) is focused on the screen (S). The foil and source are fixed. The chamber and microscope can rotate about the foil.

In 1911, Rutherford described an atomic model that accounts quantitatively for the alpha scattering observations. Rutherford argued that the alpha could "bounce back" only if it struck an object more massive than itself (Section 9.4). This would be the case if the positive charge and most of the mass of the atom were concentrated in a small portion of the atom rather than spread diffusely throughout the atom. Rutherford called this concentrated region the nucleus. That backward scattering is rare suggested that the nucleus was a small target—much smaller than the 1-angstrom (Å) size that characterizes the distribution of atomic electrons (1 Å = 10^-10 m = 0.1 nm).

Rutherford analyzed the scattering of α-particles by a nucleus, assuming that the only force between the two was the Coulomb force of repulsion between their positive charges. The classic experiments of Geiger and Marsden verified the pattern of scattering predicted by Rutherford (Figure 42.6).

Figure 42.6. Rutherford's theory (solid line) predicted the relative number of alpha particles that will scatter into different ranges of angle. The measurements of Geiger and Marsden (suggested by open circles and solid circles, respectively) confirmed Rutherford's "nuclear atom."

Knowing that the force between a nucleus and an α-particle is electrical, Rutherford was able to estimate the size of the nucleus. His method makes use of energy conservation. Figures 42. 7a, b show a head-on collision between an α-particle and a gold nucleus. When the α-particle is outside the gold atom, the Coulomb force of the nucleus is shielded by the atomic electrons. For this configuration we take the electric potential energy of the system (α + nucleus) to be zero. The total energy of the system is K _α, the kinetic energy of the α-particle. As the α-particle approaches the nucleus, it experiences the repulsive Coulomb force and slows down. In a head-on collision the α-particle is brought to rest momentarily, then repelled backward (180° scatter). At the moment when the α-particle is at rest, the total energy of the system is stored as electric potential energy. ^* If R is the center-to-center distance between the α-particle (charge + 2e) and the gold nucleus (charge +79e), the potential energy is (see Section 8.2)

Figure 42.7. (a) An α-particle approaches an Au atom. (b) During the head-on collision the α-particle comes to rest momentarily.

(42.13) $U=\frac{1}{4\pi {\epsilon }_o}\left[\frac{\left(2e\right)\left(79e\right)}{R}\right]$

The conservation of energy lets us write

(42.14) $K_{\alpha }=U$

Solving for R gives

(42.15) $R=\frac{1}{4\text{π}{\epsilon }_o}\left(\frac{158e^2}{K_{\alpha }}\right)$

.The alphas used by Geiger and Marsden had kinetic energies of 7.7 MeV. The resulting value for R is 3.0 × 10^-14 m. As Figure 42.7b suggests, R is an upper limit for the sum of the radii of the α-particle and the gold nucleus. We have seen that the angstrom characterizes the size of the atom. The atomic electrons spread themselves out over a roughly spherical volume 1 Å (10^-10 m) in radius. Rutherford's figure of 3 × 10^-14 m for R shows that the positively charged nucleus is much smaller—about 10,000 times smaller. This concentration of mass and charge explains why large-angle deflections of α-particles are infrequent. As the beam of α-particles races through the gold foil, most will pass a gold nucleus at relatively large distances (≈ 10^-10 m) and experience only a small deflection, A tiny fraction will experience head-on or nearly head-on collisions and be deflected through large angles.

The experiments of Geiger and Marsden and Rutherford's analysis of the Coulomb scattering helped establish the model of the nuclear atom. The nucleus carries the full positive charge of the atom and most of the mass. The atom's electrons contribute an equal negative charge and an insignificant fraction of the atomic mass. But the positions of the atomic electrons were not revealed by the α-particle scattering. Because of their small mass, the electrons are unable to deflect the α-particles significantly. Thus, observation of the α-particle scattering could not reveal how the electrons are distributed. However, it was clear that the electrons were not distributed in a static configuration. The strong attractive force of the positively charged nucleus would lead to the collapse of any static configuration—the electrons would "fall" into the the nucleus. If, on the other hand, electrons moved about the nucleus in orbits, they could achieve a dynamic stability, just as the motion of the planets about the sun prevents the gravitational collapse of the solar system. And so the planetary model of the atom developed. In the next section we will see how Niels Bohr combined the nuclear atom with the photon concept and quantization to develop a successful model of the hydrogen atom.

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History of CERN

Klaus Winter , in History of CERN, 1996

10.4.3 Precision Experiments

Following the first demonstrations that the decay ${\text{K}}_{\text{L}}^0\to {\pi }^0{\pi }^0$ indeed occurs [136] new experimental efforts led to consistent and precise results.

A CERN-Orsay-Rutherford group detected all four photons from K _L → 2π⁰ → 4γ decay in thick plate sparkchambers (borrowed from the first CERN neutrino experiment) and determined their direction from the pairs produced and their energy by spark counting. They observed interference of ${\text{K}}_{\text{L}}^0$ and ${\text{K}}_{\text{S}}^0\to 2{\pi }^0$ amplitudes behind a regenerator [136] and determined the absolute value and the phase of η₀₀. The authors performed [137] a phenomenological analysis of their results and those obtained on η₊₋.

They decomposed the K⁰ → 2π amplitudes into a T violating and CPT conserving part and a CPT violating and T conserving part. The data clearly established T invariance violation at a 10σ level while no evidence for CPT violation was found. However, the important question: 'is η₀₀ different from η₊₋', remained without answer.

An Aachen-CERN-Torino group [138] designed a new detector guided by the idea of measuring accurately the energies of all four γ rays and the direction of at least two γ's of the four from ${\text{K}}_{\text{L}}^0\to {\pi }^0{\pi }^0\to 4\gamma$ decay. The upstream part of the detector was the direction-measuring region with their converter foils and sparkchambers while in the downstream part the remaining γ's are converted and their energies measured in total absorption leadglass counters (see Fig. 10.24). This approach gave results of higher precision.

Fig. 10.24. Apparatus of the Aachen-CERN-Torino group for the measurement of the ${\text{K}}_{\text{L}}^0\to 2{\pi }^0$ decay rate [138].

The use of the new technique of multi-wire proportional chambers invented by Charpak [139] improved the position resolution and made a revolutionary change in the data analysis (see also Gambaro, this volume). Track positions were recorded electronically at the time of the experiment, the time consuming measurements of spark positions from films, either manually or by flying spot techniques, became obsolete.

A CERN-Heidelberg group led by Jack Steinberger recognized the power of this new technique and built a new detector for K⁰ decays [140] using these multiwire proportional chambers (see Fig. 10.25). A vast increase of statistics resulted in a corresponding improvement in precision.

Fig. 10.25. New type of detector for K⁰ decays using multiwire proportional (Charpak) chambers built by a CERN-Heidelberg group [140], (a) side view, (b) top view.

In order to be free of the complications of regenerators and of the phase of regeneration Rubbia and Steinberger [141] proposed a new technique. In proton collisions with a nuclear target an excess of K⁰ mesons over ${\overline{\text{K}}}^0$ is produced.

A K⁰ state is a coherent superposition of ${\text{K}}_{\text{S}}^0$ and ${\text{K}}_{\text{L}}^0$ amplitudes. Because of their different lifetimes and 2π decay rates maximal interference occurs about 12–14 ${\text{K}}_{\text{S}}^0$ lifetimes away from the target. The phases of η₊₋ and η₀₀ and their absolute values can therefore be directly determined with high precision. An example of such a high precision measurement is shown in Fig. 10.26.

Fig. 10.26. Example of precise interference experiment using K⁰ states produced by proton-nucleus interaction [141].

At the time of the 16th International Conference on High Energy Physics, Carlo Rubbia [142] concluded that data on were now η₀₀ consistent and, when compared with those on η₊₋, they excluded a large number of theoretical models proposed to explain CP violation. Only two classes of models survived, the so-called superweak model, postulating a very weak CP violating interaction with ΔS = 2 [124] and milliweak models invoking a small part (10⁻³) of the normal ΔS = 1 weak interaction as the source of CP violation. No significant deviations from the prediction of the superweak CP violation theory

${\eta }_{+-}={\eta }_{00}=\in$

were observed and no theory of milliweak CP violation gave a reliable estimate of how much it would expect to differ with these predictions. It was therefore difficult to assess which precision was needed to confirm or reject either of the two possibilities.

In 1973 Kobayashi and Maskawa proposed a specific milliweak model within the Standard Model [143]. At the time of the discovery of CP violation, only 3 quarks were known, and there was no possibility of explaining CP violation as a genuine phenomenon of weak interactions. However, the picture changes if six quarks exist in nature. Then the quark mixing of Cabbibo can be extended to a 3 × 3 mixing matrix containing three mixing angles and a phase. CP violating weak amplitudes can be constructed invoking box diagrams with transitions between quark flavors and families. A necessary consequence of this model of CP violation is the non-equality of η₊₋ and η₀₀. This 'direct CP violation' is due to so-called Penguin diagrams for K⁰ → 2π decay with an amplitude ∈′. The two models of CP violation differ significantly with respect to the value of ∈′: the superweak model predicts ∈′ = 0, and therefore η₊₋ = η₀₀ = ∈, while in milliweak models one expects ∈′ ≠ 0.

In the Kobayashi-Maskawa model the value of ∈′ can be estimated by inferring the magnitude of the mixing angles from other experiments. Typical values for the measurable quantity are [144]

$\mathrm{Re}\left(\in \prime /\in \right)=\left(1-{\left|{\eta }_{00}\right|}^2/{\left|{\eta }_{+-}\right|}^2\right)/6\sim \left(1-2\right)·{10}^{-3}.$

A measurement of this quantity to this level of precision therefore becomes a challenge for our understanding of CP violation. A measurement of the double ratio

$\text{R}=\frac{{\left|{\eta }_{00}\right|}^2}{{\left|{\eta }_{+-}\right|}^2}=\frac{\text{Γ}\left({\text{K}}_{\text{L}}\to 2{\pi }^0\right)/\text{Γ}\left({\text{K}}_{\text{L}}\to {\pi }^{+}{\pi }^{-}\right)}{\text{Γ}\left({\text{K}}_{\text{S}}\to 2{\pi }^0\right)/\text{Γ}\left({\text{K}}_{\text{S}}\to {\pi }^{+}{\pi }^{-}\right)}$

to a precision of 0.5% or better is therefore required to distinguish the remaining two models of CP violation and to test the Standard Model prediction. At the time of writing this report, five precise experiments have reported results [145] with a mean value of

$\mathrm{Re}\left(\in \prime /\in \right)=\left(1.5\pm 0.5\right)·{10}^{-3}.$

This result is in good agreement with the range of presently available predictions within the Cabibbo-Kobayashi-Maskawa Standard Model. Further improvements on the experimental side are underway at CERN and Fermilab aiming at a precision of ±0.2 · 10⁻³ [146].

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Rutherford's Gold Foil Scattering Experiment

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