Electron Proton Scattering vs Tunneling

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When a beam of electrons (near relativistic or non-rel.) intersects with a beam of protons or a "fixed" proton target, what percentage of the electrons tunnel through the proton(s) or is there an absence of electrons on the exact opposite side (the backside) of the proton?

This question is a rate of scatter vs rate of tunneling question?
 
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Electrons incident on fixed protons : this seems similar to Rutherford's (?) experiment with a gold film (electrons on Au nuclei). I may not be answering your specific question (never did proton beams), but I can say that the considerable fraction of e- that reflected of thin gold films led to the discovery of atomic nuclei (early late 1800's or early 1900's). A very common experiment in school. The fraction reflecting must be around 1% to 10% if I remember correctly. The fraction tunneling is not measurable in this classic experiment, but must be unbelievably small in reality.
 
Thanks for the feedback.

I checked McDaniel's book on Atomic Collisions, but did not find electron scattering from protons. This question is aimed at resolving whether or not electrons can or can not tunnel through the nucleus of an atom. Admittedly an electron in an orbit may be different in structure and energy than a free electron, but I really do hope to get some help with this question.
 
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