First, you can't really maximize this function, since it's complex and the complex numbers aren't ordered. I suspect you want to maximize its absolute value.
You can drop all the complicated factors that don't contain $r$, so the basic problem is to maximize $r^2\mathrm e^{-r/a}$. This you can do by setting the derivative zero:
$ \frac{\mathrm d}{\mathrm dr}\left(r^2\mathrm e^{-r/a}\right)=2r\mathrm e^{-r/a}-\frac1ar^2\mathrm e^{-r/a}=\left(2r-\frac{r^2}a\right)\mathrm e^{-r/a}=r\left(2-\frac{r}a\right)\mathrm e^{-r/a}\stackrel{!}{=}0\;. $
This is fulfilled when any of the factors is $0$. The maximum you want is at $2=r/a$, and thus $r=2a$.