Electric Quadrupole Moment of the Deuteron. 1/4 factor

Sometimes in books I use to see this expression
$$widehat{Q}_{0}=left(3 z^{2}-r^{2}right)=sqrt{frac{16 pi}{5}} r^{2} Y_{20}(theta, phi)$$
for quadrupole electric moment of the deuteron but sometimes i can see
$$widehat{Q}_{d}=frac{1}{4} widehat{Q}_{0}$$
I know that $1/4$ factor it could be related with the center of mass reference frame but I don’t understand how to get it. The thing is that in some books explain it from
$$r_{d}=frac{1}{4} int_{0}^{infty}left[u^{2}(r)+v^{2}(r)right] r^{2} d r$$
the rms of the deuteron, but I’m in the same place, i don’t understand where it comes from the 1/4 factor and how to use it in the $widehat{Q}_{0}$ to obtain $widehat{Q}_{d}$.