Finite nuclear size correction to hydrogen ground state energy

[andyfreesty1e]

Homework Statement

Find an expression for the correction to the energy of the ground state of the hydrogen atom due to the finite size of the nucleus. Treat the nuclear charge as a thin shell of radius r0.

what i have been thinking is that you the size of the nucleus as a perturbation, but i don't know where to go from here.

Just really looking for a step in the right direction
Thanks

 

[aubergine]

There will be a shift in the potential energy resulting from the difference between the point charge (presumably this is what your model previously assumed) and the shell charge distribution.

Another hint:

Spoiler

The energy shift will be <psi*(r)|delta V |psi(r)>

And another:

Spoiler

The difference in potential is only really significant over a range of r much less than the Bohr radius, so the wavefunctions are essentially constant and can be taken outside the integral. Don't forget the 4pi r^2 in the integral over space.