# Orbital quantum number in the shell model

#### burgjeff

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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#### dauto

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.

#### Bill_K

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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