Does the mass difference between p+ and e+ explain differences wrt e- ?

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SUMMARY

The discussion centers on the differences in behavior between electrons and positrons, particularly in the context of a hydrogen atom where a positron replaces the proton. The annihilation of the electron and positron does not occur due to their classification as particles rather than antiparticles, despite the presence of Coulomb forces. The longevity of positronium, a bound state of an electron and a positron, is highlighted, with lifetimes reaching up to 100 ns when spins are aligned, significantly longer than some neutral mesons that decay via the weak force.

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  • Research the properties and behavior of positronium in quantum mechanics
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nomadreid
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My question is best explained by a Gedankenexperiment. First we have a hydrogen atom, with the electron not collapsing into the nucleus for the well-known reason of its minimum energy being above that needed to overcome the Coulomb force. Fine. Now replace the proton in the nucleus with a positron. Blip! the electron and positron annihilate. But the Coulomb forces are the same, the electron's energy is still quantised, so why doesn't the same mechanism work?
 
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The electron wave function does not vanish at the origin so the electron does have a finite probability of being at the location of the proton. They do not annihilate because they are not antiparticles.
 
Thank you, Meir Achuz. I had not considered this aspect. That puts a new light on the problem.
 
The effect you're talking about does contribute in positronium: in some sense it helps explain why positronium should live so long (0.1 ns). This is enormous in the sense that it is larger than the lifetime of some neutral mesons which can only decay through the weak force. (I'm thinking of the K short here).

If the electron and positron are spin aligned, you actually can have it live even longer: on the order of 100 ns
 
BHamilton: thank you for that information; it is very interesting and enlightening.
 

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