Table 1.

Vector multipolar functions: Polarization character and eigenvalues of J ², J _z and parity Π.

	J 2	J z	Π	Polarization
${\mathbf{X}}_{jm}(\stackrel{\mathbf{ˆ}}{\mathbf{p}})$	j(j + 1)	m	(−1)j+1	⊥
${\mathbf{Z}}_{jm}(\stackrel{\mathbf{ˆ}}{\mathbf{p}})$	j(j + 1)	m	(−1)j	⊥
${\mathbf{W}}_{jm}(\stackrel{\mathbf{ˆ}}{\mathbf{p}})$	j(j + 1)	m	(−1)j	$\parallel$

The symbol ⊥ means transverse polarization. The symbol $\parallel$ means longitudinal polarization. Both j and m are integers, and $m=-j\dots j$. For ${\mathbf{X}}_{jm}(\stackrel{\mathbf{ˆ}}{\mathbf{p}})$ and ${\mathbf{Z}}_{jm}(\stackrel{\mathbf{ˆ}}{\mathbf{p}})$, j > 0. For ${\mathbf{W}}_{jm}(\stackrel{\mathbf{ˆ}}{\mathbf{p}})$, j ≥ 0.