Electromagnetic multipole moments and transitions

The magnetic transition operator is given by: $$ O(M\lambda)=\left[\mathbf{l}\frac{2g^{l }_{q}}{(\lambda +1)}+ \mathbf{s}g^{s}_{q}\right]\mathbf{\nabla}[r^{\lambda }Y^{\lambda }_{\mu }(\hat{r})]\mu _{N} $$ $$ = \sqrt{\lambda (2\lambda +1)}\left[[Y^{\lambda -1}(\hat{r})\otimes \mathbf{l}\,]^{\lambda }_{\mu }\frac{2g^{l}_{q}}{(\lambda +1)} + [Y^{\lambda -1}(\hat{r})\otimes \mathbf{s}\,]^{\lambda }_{\mu }g^{s}_{q}\right]r^{\lambda -1}\mu _{N}, $$ where \( \mu_{N} \) is the nuclear magneton, $$ \mu _{N}=\frac{e\hbar }{2m_{p}c} = 0.105 \; e {\rm fm}, $$ and where \( m_{p} \) is the mass of the proton.