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Fermi Gas Model

Fermi Gas Model. Particle in dx will have a minimum uncertainty in p x of dp x. p x. dx. Heisenberg Uncertainty Principle. Next particle in dx will have a momentum p x. Particles with p x in dp x have minimum x-separation dx. Phase space volume. Spatial volume.

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Fermi Gas Model

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  1. Fermi Gas Model

  2. Particle in dx will have a minimum uncertainty in px of dpx px dx Heisenberg Uncertainty Principle Next particle in dx will have a momentum px Particles with px in dpx have minimum x-separation dx

  3. Phase space volume Spatial volume Momentum volume =  Heisenberg Uncertainty Principle Identical conditions apply for the y, py, and z, pz -- Therefore, in a fully degenerate system of fermions, (i.e., all fermions in their lowest energy state), we have 1 particle in each 6-dimensionl volume --

  4. pz p py px Number of states in a shell in p-spacebetween p and p + dp Only Heisenberg uncertainty principle; completely general Heisenberg Uncertainty Principle In some dVps the maximum number dN of unique quantum states (fermions) is

  5. FGM for the nucleus Treat protons & neutrons separately Consider a simple model for nucleus--

  6. FGM for the nucleus Total energy eigenvalue degenerate eigenvalues unique states

  7. pz p py unique states px from Heisenberg uncertainty relation FGM for the nucleus quantized momentum states

  8. pz p py px FGM for the nucleus Assumeextreme degeneracy all low levels filled up to a maximum -- called the Fermi level(EF) All momentum states up to pF are filled (occupied) We want to estimate EF and pF for nuclei -- The number N of momentum states within the momentum-sphere up to pF is -- one p-state per dp3 1/8 of sphere because nx, ny, nz > 0

  9. 2 spin states Fermi energy(most energetic nucleon(s) protons N = Z neutrons N = (A-Z) Fermi momentum(most energetic nucleon(s) FGM for the nucleus

  10. FGM for the nucleus Protons Neutrons Assume Z = N

  11. FGM for the nucleus Protons Neutrons Assume Z = N

  12. FGM potential

  13. Test of FGM not FGM

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