How Does the Finite Size of the Nucleus Affect Hydrogen's Ground State Energy?

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SUMMARY

The discussion focuses on calculating the correction to the ground state energy of the hydrogen atom due to the finite size of the nucleus, modeled as a thin shell of radius r0. Participants emphasize treating the nuclear size as a perturbation, which leads to a shift in potential energy caused by the difference between the point charge model and the shell charge distribution. The conversation highlights the need for a clear mathematical expression to quantify this energy correction.

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  • Quantum Mechanics principles, specifically perturbation theory
  • Understanding of atomic structure and the hydrogen atom model
  • Familiarity with potential energy concepts in electrostatics
  • Basic knowledge of shell models in nuclear physics
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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
 
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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:

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

And another:

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.
 

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