Perturbation of hydrogen energy due to nucleus

[JamesJames]

Consider the ground state of the hydrogen atom. Estimate the correction \frac{\Delta E}{E_1s} caused by the finite size of the nucleus. Assume that it is a unifromly charged shell with radius b and the potential inside is given by \frac{-e^2}{4\pi \epsilon b}

Calculate the first order energy eorrection to the ground state and expand in \frac{b}{a_0}. Keep the leading term and observe \frac{\Delta E}{E_1s} for b = 10^-15m.

Ok, I need help in constructing the interaction W (or H'). Once I get that, I would then calculate the expectation value of it by sandwiching it between \psi_1s. Is this correct and how would I construct the interaction?

Here is what I have so far

H0 = (p^2)/2m - e^2/r and H = H0 for r > r0

H = (p^2)/2m -e^2/(4pi epsilon b) = H0 + H' for r < r0

Then I would solve for H' and use the perturbation equation. Is this correct ?

James

 

[JamesJames]

Ok, i tried it and it is not making any sense. H' somehow does not depend on r. What am I doing wrong?

James

 

[JamesJames]

Anything guys...whatever you can suggest would be great.

James

 

[dextercioby]

The perturbation is a constant,indeed...The radius of the nucleus is a constant.And because the \psi_{1,0,0} (r,\theta,\phi) is normalized,the integration will be trivial.

Daniel.

 

[JamesJames]

Are the steps I used correct?

 

[JamesJames]

Ok, I think I made a mistake. H' does in fact depend on r.

H' = H0 + e^2/r - e^2/(4pi epsilon b)

So I am going to get a constant term plus a term that depends on r so there will be some dependence. Where am I slipping up?

James