Nuclear and Atomic energy levels

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SUMMARY

The discussion centers on the differences between nuclear and atomic energy levels, specifically highlighting the order of energy levels in the Shell Model of the nucleus (1s, 1p3/2, 1p1/2) compared to atomic energy levels (1S, 2S, 2P). Both systems accommodate the same number of particles per level, attributed to quantum numbers and the Pauli exclusion principle. The complexity of nuclear energy levels arises from the non-1/r² potential and the influence of the spin-orbit term, which contributes to the "magic numbers" of nuclei, a concept recognized by Nobel laureates Jensen and Goeppert-Mayer.

PREREQUISITES
  • Understanding of quantum mechanics and quantum numbers
  • Familiarity with the Shell Model of the nucleus
  • Knowledge of the Pauli exclusion principle
  • Basic concepts of nuclear potential and energy levels
NEXT STEPS
  • Research the Shell Model of the nucleus and its implications for energy levels
  • Study the concept of spin-orbit coupling in nuclear physics
  • Explore the significance of "magic numbers" in nuclear stability
  • Investigate the differences between atomic and nuclear potentials
USEFUL FOR

Students and professionals in nuclear physics, quantum mechanics enthusiasts, and researchers focusing on the structure of atomic nuclei and energy level theories.

QuarkDecay
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I've noticed that in the Shell Model of the nucleus, the order of the energy levels is 1s, 1p3/2, 1p1/2, etc. While in the atomic energy levels it goes 1S 2S 2P, ... But they still take the same amount of particles for each level in both the atomic and nucleus.

Am I missing something here? Or why does this happen? I mean, their order being different, but all of the rest is the same just changing electrons with nucleons
 
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The nuclear potential is not an 1/r2 potential and it is created by the nucleons occupying it. That makes the energy levels more complicated. The number of particles that can occupy a given energy level depends on the quantum numbers only, if you compare matching quantum numbers you get the same number of particles that fit in.
 
The important point is the spin-orbit term, giving the "magic numbers" of nuclei. For that Jensen and Goeppert-Mayer earnt their Nobel.
 
They take the same amount of particles for each level because they are fermions and must obey the Pauli exclusion principle.
 

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