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Nuclear Spin

Atomic nuclei possess intrinsic angular momentum, known as nuclear spin, which is a fundamental property influencing their behavior in magnetic fields.

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The statement of the theorem

Let

\mathbf{I}

be the nuclear spin angular momentum operator, defined in the context of quantum mechanics. The magnitude of the spin is quantized by the spin quantum number

I

, such that the allowed eigenvalues of the squared spin operator

\mathbf{I}^2

are

I(I+1)\hbar^2

. The projection of the spin onto an external magnetic field

B_0

is quantized by the magnetic quantum number

m_I

, yielding the eigenvalues

m_I\hbar

, where

m_I \in \{-I, -I+1, \dots, I\}