Orbital quantum number in the shell model

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The orbital angular momentum quantum number in the nuclear shell model is not restricted by the principal quantum number as it is in the atomic shell model because the nuclear potential differs from the Coulomb potential. In the atomic model, energy levels correspond to the principal quantum number, following the relationship E ~ 1/n². However, in the nuclear shell model, the levels are defined in a central potential that does not adhere to this relationship. The numbers used in spectroscopic notation, like 1d or 2p, serve as serial identifiers rather than principal quantum numbers. Consequently, the principal quantum number does not correspond to energy in either the nuclear or atomic shell models.
burgjeff
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Why isn't the Orbital angular momentum quantum number in the nuclear shell model restricted by the principal quantum number like it is in the atomic shell model? Also, does the principal quantum number even correspond to energy in the shell model?
 
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burgjeff said:
Why isn't the Orbital angular momentum quantum number in the nuclear shell model restricted by the principal quantum number like it is in the atomic shell model?
Who says it isn't?
Also, does the principal quantum number even correspond to energy in the shell model?
No it doesn't. Neither does it correspond to energy in the atomic shell model.
 
burgjeff said:
Why isn't the Orbital angular momentum quantum number in the nuclear shell model restricted by the principal quantum number like it is in the atomic shell model? Also, does the principal quantum number even correspond to energy in the shell model?
burgjeff, Atomic states correspond to energy levels in a Coulomb potential, the energy E ~ 1/n2, where n is the principal quantum number.

In the nuclear single particle shell model, the states are levels in a central potential which is not Coulomb. Although a similar spectroscopic notation is used to denote these levels, such as 2p or 1d, the first number is not a principal quantum number, it's just a serial number. That is, 1d simply denotes the lowest level with ℓ = 2.
 

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