Mean radius, r.m.s. radius of nucleus

[russdot]

Hello,
Given a particular charge distribution p(r) = p_0*exp(-r^{2}/a^{2}), I was wondering if the proper way to calculate the mean radius <r> would be \intp(r)*r*p(r) dV ?
Which would make <r^{2}>^{1/2} = (\intp(r)*r^{2}*p(r) dV)^{1/2}, correct?

 

[pam]

The mean radius is not generally used.
Your equation for the rms radius is correct.

 

[russdot]

Great, thanks!
I'm assuming if the rms equation is correct, then the mean value equation is also correct..

 

[malawi_glenn]

I have always used:

&lt;r^2&gt; = \int \rho (r)r^2 d\vec{r}

since the wave function(s): \psi (r)^* \cdot \psi (r) = \rho (r)

If the density is normalised to unity: \int \rho (r) d\vec{r} = 1

Otherwise:
&lt;r^2&gt; = \int \rho (r)r^2 d\vec{r} / \int \rho (r) d\vec{r}