How do a proton and an electron interact?

1) There is mainly a long range Coulombic interaction and a non Coulombic interation at short distances.

Further information:
- "interaction of proton and electron in free space":
http://npc.getmyip.com/book/export/html/3


2) "The 1926 European papers by Schrödinger showed that for purely Coulombic electron-proton interactions the Schrödinger equation yielded stationary state energy levels for atomic hydrogen that were identical with the energy levels obtained with Bohr's "old" quantum theory, the energy levels of which agreed very well with spectroscopic measurements. It also was known, however, that Bohr's theory had utterly failed to yield the energy levels of atomic helium, or of any other polyelectron atoms. After Schrödinger's triumph with atomic hydrogen, therefore, the obvious immediate task for atomic theorists was to determine whether the Schrödinger equation could correctly predict the measured spectroscopic properties of polyelectron atoms, especially their spectral line frequencies, relative line intensities, and selection rules. But the Schrödinger equation cannot be solved analytically for any atomic system with more than one electron, even when all non-Coulombic (e.g., spin-orbit) interactions are neglected and the mass of the nucleus is set equal to infinity (so that the atomic center of mass always resides on the nucleus)."
Source and further information:
http://astrophysics.fic.uni.lodz.pl/100yrs/html/chap04_intro.htm

3) "The non-Coulombic proton-electron interaction has been detected by experiments made by Don Borghi, described in a paper published in 1993."
Source and further information:
"Quantum Ring Theory By Wladimir Guglinski"
http://books.google.com/books?id=g4NpaLA222gC&pg=PA42&lpg=PA42&dq="proton+electron+interaction"&source=bl&ots=oMOR_8u3my&sig=lbOV0ELzh4ju0sVmCxoBzyrGgI4&hl=en&ei=gkSpSv_eBYXMmgPoktiLBQ&sa=X&oi=book_result&ct=result&resnum=6#v=onepage&q=%22proton%20electron%20interaction%22&f=false


4) Collisions:
"If an electron with enough energy collides with a proton, then what happens?
They just form a hydrogen atom?
Or they form a neutron?
If both are possible, then which factor controls the process?
I am asking because I heard that a neutron can decay to a proton and an
electron and the reverse is possible."
Source and further information:
http://www.newton.dep.anl.gov/askasci/phy00/phy00843.htm

Further information:
http://www.physicsforums.com/showthread.php?t=42951
http://www.chemicalforums.com/index.php?topic=34416.0
http://www.cheniere.org/books/excalibur/all%20mass%20is%20charged.htm
http://www.mail-archive.com/vortex-l@eskimo.com/msg02373.html

electrons orbit around a group of protons. the protons attract the electrons so that these don't go off, while the orbiting nature of the electrons prevents the protons from attracting the electrons too much. thus a balance is created.