Stability of Binary System with Anti-Particle Circulation in Quantum Physics

[Will_C]

Hi,
I have a question about anti-particle.
In the modern physics, we "know" (I don't think we really know it) the reason, why the shell electron did not collapse into its ion core, because of quantum theory.
But is it possible a electron "circulate" a positron without annihilation. Is there any possibility for such particle being stable?
Thx.
Will.

 

[James Jackson]

Yes, but it's short lived. It's called positronium: http://scienceworld.wolfram.com/physics/Positronium.html

 

[Will_C]

Thx James,
Thank you for your suggestion and guiding. According to the website: "quantum field interactions between the positron and electron cause positronium to be unstable."
How does it work? Is there any simple concept to explaine this (I have not get start on QEM yet)?

Will.

 

[Meir Achuz]

A small part of the wave functions of the electron and positron overlap.
This leads to eventual annihilation of the pair, producing two, and more rarely three, photons.

 

[Will_C]

Thx Meir!
When I pick up a textbook (modern physics), and look for the Schrödinger’s equation for Hydrogen atom. The equation of that is regardless anything about hydrogen (such as mass of hydrogen) except the charge. Thus, what I want is to replace the hydrogen with a positron and the Schrödinger’s equation doesn't any changes.
SO, is it too simple to counter with atom by QM?

Will.

 

[Meir Achuz]

You can use simple QM to get the WF, but you have to take into account the reduced mass of the particles. Just put in m/2.
Calculation of the annihilation rate needs QFT to convert the e-positron pair into photons.