What is Fermi: Definition and 383 Discussions

Enrico Fermi (Italian: [enˈriːko ˈfermi]; 29 September 1901 - 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and the "architect of the atomic bomb". He was one of very few physicists to excel in both theoretical physics and experimental physics. Fermi was awarded the 1938 Nobel Prize in Physics for his work on induced radioactivity by neutron bombardment and for the discovery of transuranium elements. With his colleagues, Fermi filed several patents related to the use of nuclear power, all of which were taken over by the US government. He made significant contributions to the development of statistical mechanics, quantum theory, and nuclear and particle physics.
Fermi's first major contribution involved the field of statistical mechanics. After Wolfgang Pauli formulated his exclusion principle in 1925, Fermi followed with a paper in which he applied the principle to an ideal gas, employing a statistical formulation now known as Fermi–Dirac statistics. Today, particles that obey the exclusion principle are called "fermions". Pauli later postulated the existence of an uncharged invisible particle emitted along with an electron during beta decay, to satisfy the law of conservation of energy. Fermi took up this idea, developing a model that incorporated the postulated particle, which he named the "neutrino". His theory, later referred to as Fermi's interaction and now called weak interaction, described one of the four fundamental interactions in nature. Through experiments inducing radioactivity with the recently discovered neutron, Fermi discovered that slow neutrons were more easily captured by atomic nuclei than fast ones, and he developed the Fermi age equation to describe this. After bombarding thorium and uranium with slow neutrons, he concluded that he had created new elements. Although he was awarded the Nobel Prize for this discovery, the new elements were later revealed to be nuclear fission products.
Fermi left Italy in 1938 to escape new Italian racial laws that affected his Jewish wife, Laura Capon. He emigrated to the United States, where he worked on the Manhattan Project during World War II. Fermi led the team that designed and built Chicago Pile-1, which went critical on 2 December 1942, demonstrating the first human-created, self-sustaining nuclear chain reaction. He was on hand when the X-10 Graphite Reactor at Oak Ridge, Tennessee, went critical in 1943, and when the B Reactor at the Hanford Site did so the next year. At Los Alamos, he headed F Division, part of which worked on Edward Teller's thermonuclear "Super" bomb. He was present at the Trinity test on 16 July 1945, where he used his Fermi method to estimate the bomb's yield.
After the war, Fermi served under J. Robert Oppenheimer on the General Advisory Committee, which advised the Atomic Energy Commission on nuclear matters. After the detonation of the first Soviet fission bomb in August 1949, he strongly opposed the development of a hydrogen bomb on both moral and technical grounds. He was among the scientists who testified on Oppenheimer's behalf at the 1954 hearing that resulted in the denial of Oppenheimer's security clearance. Fermi did important work in particle physics, especially related to pions and muons, and he speculated that cosmic rays arose when material was accelerated by magnetic fields in interstellar space. Many awards, concepts, and institutions are named after Fermi, including the Enrico Fermi Award, the Enrico Fermi Institute, the Fermi National Accelerator Laboratory (Fermilab), the Fermi Gamma-ray Space Telescope, and the synthetic element fermium, making him one of 16 scientists who have elements named after them. Fermi tutored or directly influenced no fewer than 8 young researchers who went on to win Nobel Prizes.

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  1. phos19

    I Fermi energy for a Fermion gas with a multiplicity function ##g_n##

    I ran across the following problem : Statement: Consider a gas of ## N ## fermions and suppose that each energy level ## \varepsilon_n## has a multiplicity of ## g_n = (n+1)^2 ##. What is the Fermi energy and the average energy of this gas when ## N \rightarrow \infty## ? My attempt: The...
  2. J

    I What is the derivation of the Fermi golden rule?

    Dear Forum, I have a question about the derivation of the Fermi golden rule in Kenneth Krane's Introduction to Nuclear Physics. I understand everything up to equation 9.20. However, it is unclear how he goes directly to equation 9.21. Here is equation 9.20, ## d\lambda =...
  3. B

    Statistical physics, using the ideas of Fermi Energies, etc. for a star

    a) V=(4/3)pi(r^3) N=M/m_n (M=mass of neutron star, m_n=mass of neutron) Subbed into E_f = (hbar^2 / 2m) (3(pi^2)N / V)^(2/3). T_F = E_F / k_B b) dU = (dU/dS)_s dS + (dU/dV)_s dV p = -(dU/dV)_s dV V=(4/3)pi(r^3) -> r = cubedroot(3V/4pi) subbed into U_g = -(3/5)(G M^2 / r) take (dU/dV) plug into...
  4. L

    I Fermi Gas Model: Energetic Degeneration & the Pauli Exclusion Principle

    In the fermi gas model, there is assumption that there is a 3D potential well, but there is "energetic degeneration" for each three index "nx, ny, nz". Now the problem is with that image, if there is degeration, for some level En there may be 10 distinctive state with same energy, so there is 20...
  5. chikchok

    I Chemical potential and Fermi level

    Does fermi level (in metals) depend on the density of states? I am asking this because from fermi-dirac distribution it seems like that fermi level is non-dependent of DOS, but there is chemical potential in fermi-dirac distribution, which is said to be dependent of DOS.
  6. chikchok

    I Fermi energy definition and Fermi-Dirac distribution

    1)In my book , there is a definition of fermi energy as topmost filled level in the ground state of an N electron system. This definition holds only for absolute zero,right? If it is not absolute zero,fermi energy is the energy at which the probability of a state being occupied is 50 percent...
  7. chikchok

    I Is the Fermi-Dirac distribution equal to zero at the state of highest energy?

    I`m sorry if this seems too obvious, just trying to clarify something. When Fermi-Dirac distribution is equal to zero , can we assume it is the state of the highest energy? (Because the propability of occupation is zero)
  8. chikchok

    I The meaning of the Fermi energy

    The Fermi energy Ef is defined as the energy of the topmost filled level in the ground state of the N electron system. Ground state is n=1 level. And in the ground state there can be only one orbital right? One orbital can have only up to 2 electrons. Does this mean that fermy energy is the...
  9. J

    Crypto-cancer fade out end of civilization for Fermi paradox?

    Imagine civilization gets a positive feedback mechanism for wasting resources, like cryptocurrencies: “one gets $100 banknote if burning $99 worth resources”, leading to exponential growth of waste at individual gains. We can observe exponential growth of their energy consumption (below)...
  10. LuccaP4

    Solid-state Physics: Fermi surface and necks in an FCC structure

    Does anyone have some bibliography about necks in FCC structure Fermi surface? I have to solve this problem and I have no idea how to start. Thanks.
  11. J

    Doubt regarding functional derivative for the Thomas Fermi kinetic energy

    I have some doubts with respect on how the functional derivative for the kinetic energy in density functional theory is obtained. I have been looking at this article in wikipedia: https://en.wikipedia.org/wiki/Functional_derivative In particular, I'm interested in how to get the...
  12. B

    How to Estimate the Fermi Energy for Potassium Metal?

    I have completed part a, from which I got the expression: Cv = 3KTn/(T_f) For part b, the first term is the electron contribution and the second term is the phonon contribution. I'm stuck on how to estimate the fermi energy for the potassium metal. I'm thinking I only need to consider the...
  13. T

    Calculating Fermi Coupling Constant (muon)

    I am trying to determine the Fermi Coupling Constant which is measured to be ##1.1663787 *10^{-5}\text{Ge}V^{-2}##. The formula for Fermi is ##\frac{G_F}{(\hbar c)^3}=\sqrt{\frac{\hbar}{\tau_\mu}\cdot\frac{192\pi^3}{(m_\mu c^2)^5}},## where ##m_\mu## is the mass of a muon which is ##\approx...
  14. Helena Wells

    I Fermi level change in semiconductors

    Suppose we have a crystal lattice of doped Si with dopant Boron atoms. The energy level of the holes of the Boron atoms are just some eV above the valence band of Si. My question: If we replace all the Si atoms with Ge atoms will the acceptor level change or not? I don't think it will change...
  15. B

    I What is the Fermi wavelength of a graphene lattice in the tight binding model?

    I am trying to figure out what the Fermi wavelength of my system is. Specifically I am looking at simulation a graphene lattice in the tight binding model. For this, I know that the Fermi energy (undoped) of my system is 3t (for simplicity I set t = 1). But how do I figure out what the Fermi...
  16. M

    I Trying to get a physical understanding of a Fermi gas

    I would like to get a more physical interpretation of conduction electrons (fermi gas) in a metal. I imagine ionized valence electrons close to the ions, with the fermi level (highest energy electrons) of the gas participating in conduction. A point of confusion for me...the first ionization...
  17. BWV

    Can Coal Deposits Explain the Fermi Paradox?

    Reading McGhee's excellent book on the Carboniferous period and he explains in detail the unique circumstances behind the creation of 90% of the world's coal deposits - receding ocean in an ice age that created low lying swamps, high concentrations of oxygen in the atmosphere that would have...
  18. vintagelover007

    Fermi Motion of Nucleons due to a Beam of Neutrinos

    Stable nuclei have radii that are approximately given by the formula: R = r0_A^1/3 Where r0 = 1.25 × 10−15m and A is the atomic mass number. In many experiments of interest to modern particle physics, beams of neutrinos scatter from nucleons within the nucleus. Even though the nucleus is at...
  19. Mayan Fung

    I Fermi gas in relativistic limit

    In a statistical mechanics book, I learned about the degenerate pressure of a Fermi gas under the non-relativistic regime. By studying the low-temperature limit (T=0), we got degenerate pressure is ##\propto n^{5/3}## (n is the density). And then I was told that in astrophysical objects, the...
  20. B

    I Fermi level in a nonuniformly doped semiconductor

    Fermi level is known to be constant in a equilibrium state. It is also known to vary according to the number of donors/acceptors. In a nonuniformly doped semiconductor that has varying number of donors/acceptors at different position, how is the fermi level decided? Is it the average number of...
  21. Saptarshi Sarkar

    I Query regarding Fermi Gas model

    I was reading an introductory text on nuclear models and came across the Fermi Gas model. I understand that the depth of the potential well of the proton should be less than the depth of the potential well of the neutron due to the Coulombic repulsion between the protons. But I did not...
  22. dRic2

    I Spin density in an (ideal) Fermi gas

    Hi, some time ago our professor told us (en passant) to evaluate this quantity: $$<F|n_m( \mathbf x) n_{m'}(\mathbf x) |F> - <F|n_m( \mathbf x)|F><F|n_{m'}(\mathbf x) |F>$$ And then he said: "you'll find that this quantity may not be zero. In particular when the electron are correlated it will...
  23. Diracobama2181

    Heat Capacity of a Fermi Gas at Low Temperature

    I find that $$U=\int Z \epsilon D(\epsilon) e^{-\epsilon β}d\epsilon=\frac{gV}{(2\pi)^3}\int Z \frac{(\hbar)^2k^2}{2m}k^2 (4\pi)e^{-β\frac{(\hbar)^2k^2}{2m}}dk$$ where g=2s+1=2, $$Z=e^{βµ}$$ and $$D(\epsilon)=\frac{gV}{(2\pi)^3}k^2 4\pi$$ for the density of states From here, I can use $$c_v...
  24. K

    I Wiki definition of Fermi coordinates

    Is the wikipedia definition of Fermi coordinates accurate? https://en.wikipedia.org/wiki/Fermi_coordinates
  25. cynth

    A Fermi surface and electronic correlations

    why an increase of fermi pockets leads to a reduction of electronic correlations
  26. F

    I Solving the Quantum Mechanics of a Hydrogen Atom

    Hello, I have a little problem understanding the quantum mechanics of a hydrogen atom. Im troubled with the following question: before i measure the state of a (simplified: without fine-, hyperfinestructure) hydrogen atom, which is the right probability density of finding the electron? is it...
  27. fluidistic

    A What can the Fermi surface tell us about a material's properties?

    I would like to know every bit of information one can retrieve by looking at the Fermi surface of a material. Here's what I think is correct thus far: 1) The fact that the material has a Fermi surface already tells us a lot. The material could be a metal or something that resembles a metal...
  28. fluidistic

    A Fermi liquid theory vs Hohenberg-Kohn theorems + Kohn-Sham equations

    Are the Hohenberg-Kohn theorems insanely more powerful than the Fermi liquid theory? At first glance it looks like I'm comparing apples to oranges. But here is my reasoning. The Fermi liquid theory describes well the normal state (i.e. non superconductive and other exotic behaviors) of metals...
  29. M

    Fermi energy in a quantum well

    Problem Statement: See below Relevant Equations: 2D density of states ##g\left(E \right)=\frac{m^{*}}{\pi\hbar^2}## Fermi energy in a quantum cascade laser ##E_{F}=E_{i}+k_{B}Tln\left[exp\left(\frac{\pi\hbar^2n^{2D}}{k_{B}Tm^{*}} \right)-1\right]## I've been stuck on this problem for a few...
  30. S

    Average speed of molecules in a Fermi gas

    My first most obvious attempt was to use the relation ##<\epsilon> = \frac{3}{5}\epsilon_F## and the formula for kinetic energy, but this doesn't give the right answer and I'm frankly not sure why that's the case. My other idea was to use the Fermi statistic ##f(\epsilon)## which in this case...
  31. W

    Thermal Physics: Fermi Gas and chemical potential

    Hi all, I have an issue trying to understand the following paragraph from Blundell's book. How, exactly, does the definition of ##\mu_0 = E_F## "make sense"? In the sentence after 30.21, it seems to say that the mean energy for a system with ##N## particles differs from that of a system with...
  32. ChinoSupay

    A Magnetic response of a degenerate Fermi gas

    I know that in a Fermi gas, the two common responses to a lo field are Pauli par. and Landau dia. and the last becomes the H-VA effect My question is, it is the same treatment in degenerated Fermi Gas?
  33. ChinoSupay

    A Fermi gas in a magnetic Field?

    I am currently working in astromagnetism. My question is, somebody knows if a fermi gas (degenerate electrons) can increase or decrease de total magnetic field due to an influence of an external magnetic field and if somebody have information about that. I know that an external magnetic field...
  34. confusedius

    Solid State Physics: Draw the Dispersion Relation from the Fermi Surface

    Homework Statement ln the figure below you (b, which is taken from Jenö Sólyom Fundamentals of the physics of solids. Volume 2 chapter 19) see the Fermi sphere of radius k_F inside one section in two dimensions of the Brillouin zone of Na. Draw the dispersion relation E(k) from the I point in...
  35. J

    I Some questions about electrons and the Fermi energy

    Hello ,evreyone.I have two questions about fermi energy. 1,Can I claim that 'fermi energy ' play the role of chemical potential? 2,I have learned from thermal physics that only electrons near fermi level can conduct in metals.How can electrons behave like this? I can't figure out why only...
  36. M

    I Fermi Energy Calculations About Non Parabolic Dispersions

    Greetings! It is easy to understand that for a free electron, we can easily define the energy state density, and by doing the integration of the State density* Fermi-Dirac distribution we will be able to figure out the chemical potential at zero kelvin, which is the Fermi-Energy. Hence, we can...
  37. B

    I How did Fermi calculate the strength of first nuclear explosion?

    Hi There is a story that Enrico Fermi calculated the intensity of the first nuclear test at Los Alamos from the distance moved by scraps of paper. Are there documented details of the calculation in any paper / book ? TIA
  38. QuarkDecay

    When is the Boltzmann equation applicable in a Fermi plasma?

    When do we use the Boltzmann equation for density in a Fermi plasma? n in [cm-3] and when do we use the ρ=m/V, ρ in [Kg/m3 ] (this is not an example, I just added the equations to make my question more understandable) Is the ideal gas only when we have electron and ions? Is the Boltzmann...
  39. binbagsss

    Tensor Covariant Derivative Expressions Algebra (Fermi- Walk

    Homework Statement Hi I am looking at part a). Homework Equations below The Attempt at a Solution I can follow the solution once I agree that ## A^u U_u =0 ##. However I don't understand this. So in terms of the notation ( ) brackets denote the symmetrized summation and the [ ] the...
  40. N

    I Valence band and Fermi level difference?

    I was wondering what the difference was between the valence band and fermi level? How do we distinguish between the two? Thanks in advance.
  41. DrClaude

    Fermi temperature of a 1D electron gas

    Homework Statement Consider a one-dimensional metal wire with one free electron per atom and an atomic spacing of ##d##. Calculate the Fermi temperature. Homework Equations Energy of a particle in a box of length ##L##: ##E_n = \frac{\pi^2 \hbar^2}{2 m L^2} n^2## 1D density of states...
  42. R

    Derivation of the Eqation of Motion from Fermi Lagrangian density

    Homework Statement Hello, I am trying to find the equations of motion that come from the fermi lagrangian density of the covariant formalism of Electeomagnetism.Homework Equations The form of the L. density is: $$L=-\frac{1}{2} (\partial_n A_m)(\partial^n A^m) - \frac{1}{c} J_m A^m$$ where J...
  43. Pushoam

    Conduction band, valence band and Fermi energy

    Homework Statement Homework EquationsThe Attempt at a Solution The probability of getting a state with energy ## E_v## is ## \frac { N_v } { N_v +N_c } = \frac1{ e^{-(E_v – E_f)/k_BT} +1} ## ………….(1) Since, ## E_v < E_f, e^{-(E_v – E_f)/k_BT}>>1 ## as ## E_f – E_v>> k_BT ##……….(2) So...
  44. S

    A Fermi and Bose gas in statistical mechanics

    In statistical mehcanics(pathria, 3rd edition), I have some questions for ideal fermi and bose gases. The textbook handles the approximation for z(=e^βµ) and nλ^3 (n=N/V, λ : thermal de Broglie wavelength). It considers the cases that z<<1, z~1, nλ^3~1,<<1,→0 and so on. In here, I am confused...
  45. J

    I Fermi gas at the absolute zero T

    I'm currently studying Thermodynamic properties of a Fermi gas at the absolute zero temperature. I get how the internal energy, pressure... etc of the gas are derived. For example, in computing the internal energy, one sums up all the energy of states weighted by its average occupation...
  46. S

    I Exploring Fermi Pressure in Relativistic Conditions

    Hello! I am reading a derivation for Fermi pressure and the author assumes that the electrons in a box are cooled so much that they occupy all the states in the momentum space from p=0 up to a maximum value of p. Then after he obtains a formula for the pressure, he simplifies the formula...
  47. davidge

    I Parallel transport vs Fermi Transport

    Since for a general contravariant vector, ##\nabla_{\nu}V^{\mu}## will not in general be zero, is it correct to say that all of them are transported by Fermi Transport? (With the only vector being parallel transported being the four velocity vector?)