Fermi-Dirac statistics

Fermi-Dirac statistics concerns the way in which to calculate the properties of fermions. Physicists might also refer to them as “particles of spin 1/2.” The idea of spin arose in early models of the atom, which envisioned

This seemingly simple idea explains much of how the physical world works. For example, it explains why lithium is very active chemically, while helium is a very inert, noble gas, despite the fact that they differ (chemically) only in one extra electron.

electrons orbiting around a nucleus and spinning like a top at the same time. Things being restricted to only certain values in quantum mechanics, the spin of these particles could only be 1/2, 3/2, 5/2, etc. The restrictions were first noted by the Wolfgang Pauli. According to Pauli’s “exclusion principle,” no two fermions can have the same quantum numbers; in a sense, they cannot be in the same place at the same time in the same spinning state.

Fermi statistics explains ever so much more: how metals and semiconductors conduct electricity, why some substances are hard, even the workings of neutron stars and other astronomical entities.

The School of Physics in Rome

Though at the end of 1920s Fermi’s personal success was already guaranteed by his accomplishments to that date, he wanted something more than this: he wanted to build a school of physics, to have Italy assume its rightful place among the nations. That meant strengthening the research capabilities of the Institute of Physics.

The first step made by Fermi was to send his associates abroad to learn from more advanced laboratories.

“The speed at which it was possible to form a young physicist at that school was incredible. Naturally, a good deal of success was due to the immense enthusiasm aroused in the young people, never by exhortations or sermons, but by the eloquence of Fermi’s personal example.”

Rasetti went to the Caltech in Pasadena to work with Robert Millikan and, then, to Berlin to learn the techniques for studying radioactivity with the physicist Lise Meitner. Segrè and Amaldi were similarly dispatched to European laboratories where they extended their knowledge of advanced techniques in studying light and X rays.

Fermi himself spent the summer of 1930 lecturing at the University of Michigan in Ann Arbor, his first visit to America. His lectures on quantum electrodynamics became legendary among physicists, including future Nobel laureates. The process worked. The reputation of Rome and the Romans grew as did their international network of friends. And, starting in the 1930s, theoretical physicists of the first rank found it useful to visit with Fermi. Among these, we count H. Bethe, G. Placzeck, F. Bloch, R. Peierls, L. Nordheim, F. London, E. Feenberg, etc. In October 1931, Fermi and Corbino also organized a memorable Conference on Nuclear Physics which gathered the most authoritative scientists from any part of the world.

Nuclear Physics in RomeAround 1931, Fermi and his group had realized that the main interest of atomic physicists shifted to the study of the inner part of the atom, the nucleus, which is the densest part and is a hundred thousand times smaller in diameter. Then, they started to familiarize with current problems (the structure of the nucleus, its disintegrations, etc.).

Many properties of the nucleus were already known. It was clear that most nuclei in nature are stable, but others are radioactive; that is, they spontaneously turn into atoms of different elements, usually changing the value of their electric charge. The radioactive-process takes place by the expulsion of an alpha particle, i.e. a helium nucleus, or an

discovery of the neutron and Joliot-Curies’s discovery of the production of artificial radioactivity by alpha-particle bombardment, he took up neutron research both as an experimenter and as a theoretician.

electron, i.e. the beta particle. Both phenomena are often accompanied by the emission of electromagnetic radiation in the form of gamma rays.In 1933 Fermi’s activity entered a new stage, when after Chadwick’s

Fermi and his group thought neutrons would be much more efficient than alpha-particles (because their lack of an electric charge). They created and measured forty new radioactive elements. But they soon observed the unexpected effects of certain substances like water and paraffin; their simple presence around or near the bombarded element intensified its radioactivity.

In less than a day, Fermi found the explanation for this phenomenon. Neutrons slow down when they collide with the nuclei of hydrogen contained in those substances, thus increasing the probability of an effective reaction. Slow neutrons are a fundamental key for access to nuclear energy.

In the Fall of 1933, Fermi also solved a very serious problem regarding the process of beta decay: how can a nucleus emit electrons if it does not contain them? Fermi elaborated a complete theory, which immediately gave precise explanations of the experimental facts, by assuming that electrons are created in the same moment that they were emitted, together with another light, neutrally charged particle that Fermi later called neutrino: n → p + e + νOnly a few theories of modern physics have been so pregnant with results. It covers not onlythe usual processes of beta decay, but also various other transformations observed among unstable particles.

The Manhattan Project In 1938 many people feared that Hitler would build an atomic bomb after word spread

that German scientist had split the uranium atom (fission). However, one of Hitlers mistakes was his persecution of Jewish scientists. This persecution resulted in numerous scientists seeking asylum in the United States. One such scientist was Albert Einstein. Einstein, abandoning his belief in pacifism, urged then president Franklin Roosevelt to develop an atomic bomb before Hitler did. Eventually Roosevelt agreed and the United States attempt at building the atomic bomb was codenamed The Manhattan Project.

American military leaders decided they needed to build a laboratory to create a nuclear weapon. They searched for a location at least 200 miles from a coastline or international border. The site needed to be sparsely populated because an accident might cause horrendous damage. They settled on a secluded school for boys in the desert land of Los Alamos, New Mexico. Robert Oppenheimer led a group of almost 6000 scientists in what became known as the top secret Manhattan Project.

The scientists recruited to work on the Manhattan Project, and their families, had to work in complete secrecy. Their drivers’ licenses listed only numbers, not names. Even relatives could not know where the scientists were working. All of their mail was screened to ensure they said nothing to give away their location. Photographs could not include anything that might identify the landscape of New Mexico. The American government had to ensure that the Axis Powers had no idea what was happening at the isolated site in New Mexico.

Many of the scientists working at Los Alamos were Jewish refugees from Germany. Edward Teller left Germany for America in 1933. Otto Frisch and Felix Bloch were also German Jews who were instrumental in creating the bomb. Enrico Fermi was married to a Jewish woman. He left Italy at about the same time to escape anti-Semitism. Ant-Semitism is the hatred or persecution of Jews. If Jewish scientists had been allowed to stay in Germany, Hitler might have gotten the bomb before America

The Atomic Pile At Columbia, Fermi and his team continued investigations into the feasibility of controlled chain

reactions from nuclear fission. Experimentation led them to build an "atomic pile," beginning as a stack of pure graphite brick surrounding a neutron source. This first step enabled the examination of graphite's effect on neutron activity: absorption and re-emission, quantities, fissions. Step two was the addition of uranium to the experiment. The original stack was rebuilt with some of the graphite bricks being seeded with pieces of uranium. Observations on the effect of graphite resumed. Results showed Fermi that a stack larger than the current "pilot" version was needed to produce a measurable nuclear chain reaction, and a search for larger facilities began.

The expansion at Columbia was slowed by the U.S. government's decision to accelerate and centralize atomic research. Fermi's work eventually relocated to the University of Chicago in 1942. Secrecy covered all endeavors at this location, divertingly labeled the Metallurgical Laboratory. The physicists who gathered at the new facility concentrated on fundamental atomic research as an arm of the newly-named Manhattan Project, the first instance of "big science" with the research, materials production, and support personnel consolidated and directed to a single goal. Now Fermi had the space needed for his enlarged atomic pile. That space—about 200 sq. ft. in area and more than 26 ft. high in the unused squash court under the West Stands of Stagg Field Stadium in the middle of a city of over 3 million people was destined for lasting fame .

As everything went according to plan, Fermi, a creature of habit, declared a break for lunch. Work resumed after lunch and at 3:20 in the afternoon the last control rod had been carefully withdrawn in one-foot increments when Fermi gave the final instruction to remove it completely. All monitoring instruments showed rising radioactivity—the controlled nuclear fission chain reaction had been achieved!The message reporting success sent by the director, Arthur Compton, to the Office of Scientific research and Development said, "The Italian Navigator has reached the New World." A toast of Chianti was raised in celebration.Meanwhile the crash program to develop weapons incorporating this achievement had been proceeding. An atomic bomb, with an uncontrolled nuclear explosion, was envisioned.

The Fermi group in Chicago built and examined small piles, becoming confident that all parameters to create a pile of the critical size and composition for sustained chain reaction were known. In a period of just six weeks the final pile, standing less 26 feet high and completely encased in an enormous square balloon of rubberized cloth, was built. On December 2, 1942, Fermi managed the historic operation, directing the gradual removal of the control rods and monitoring the consequent increases in radioactivity.