C. Transition Rules

C. Transition Rules¶

The following transition rules (also known as selection rules) must be satisfied for an electron to transition between two atomic states:

General rules for all atoms:

• $\varDelta L = \pm 1$: The electronic orbital angular momentum quantum number must change by 1.

• $\varDelta S = 0$: The spin quantum number must remain unchanged.

• $\varDelta J = -1,~0,~+1; \quad J=0 \not \rightarrow J=0$: The total electronic angular momentum quantum number must change by 1, 0, or -1. However, transitions between $J = 0 \rightarrow J = 0$ are forbidden.

• Parity must change: A transition must occur between states of opposite parity. Parity is indicated by a circle in the term symbol. For example, a state with odd parity has a small circle, like ${ }^{1}\text{P}^{\circ }_{1}$. A state with even parity does not have a circle, like ${ }^{1}\text{S}_{0}$.

For atoms with no nuclear spin:

• $\varDelta m_J = -1, 0, +1$: The z-component (projection) of the total electronic angular momentum ($m_J$) can change by 1, 0, or -1. However, if $\varDelta J = 0$, the transition between $m_J = 0 \rightarrow m_J = 0$ is forbidden.

For atoms with nuclear spin:

• $\varDelta F = -1,~0,~+1; \quad F=0 \not \rightarrow F=0$: The total atomic angular momentum quantum number including nuclear spin (F) must change by 1, 0, or -1. However, transitions between $F = 0 \rightarrow F = 0$ are forbidden.

• $\varDelta m_F = -1,~0,~+1$: The z-component (projection) of the total atomic angular momentum including nuclear spin ($m_F$) can change by 1, 0, or -1. However, if $\varDelta F = 0$, the transition between $m_F = 0 \rightarrow m_F = 0$ is forbidden.