Consider an atom with a single electron outside closed shells. Take the \(z\) component of a magnetic dipole transition with matrix element

\[\left\langle\ell^{\prime}, m^{\prime}, m_{s}^{\prime}\left|L_{z}+2 S_{z}ight| \ell, m, m_{s}ightangle .\]

Let

\[\ell=1 \quad m=0 \quad m_{s}=+\frac{1}{2}\]

For what values of \(\ell^{\prime}, m^{\prime}, m_{s}^{\prime}\) will this be an allowed transition?