Positronium vs Hydrogen atom

  • #1
I have a question about the stability of positronium.

Positronium consists of an electron and a positron whereas hydrogen consists of an electron and a proton. The energy levels of positronium, ignoring fine structure, are -6.8eV/n2 whereas those for hydrogen are -13.6eV/n2.

My question is, why is positronium unstable resulting in the annihilation of the positron-electron pair while hydrogen is stable? Why does positronium not simply remain in its lowest energy level -6.8eV?
 

Answers and Replies

  • #2
SpectraCat
Science Advisor
1,399
2
I have a question about the stability of positronium.

Positronium consists of an electron and a positron whereas hydrogen consists of an electron and a proton. The energy levels of positronium, ignoring fine structure, are -6.8eV/n2 whereas those for hydrogen are -13.6eV/n2.

My question is, why is positronium unstable resulting in the annihilation of the positron-electron pair while hydrogen is stable? Why does positronium not simply remain in its lowest energy level -6.8eV?

Because the ground state wavefunction has non-zero probability density at the nucleus. So there is always a finite change that the electron and positron will come close enough together to annihilate.

EDIT: Of course which particle you consider the "nucleus" is arbitrary in positronium, since both have identical masses. However their respective wavefunctions still overlap, which provides non-zero probability of annihilation.
 
Last edited:
  • #3
mathman
Science Advisor
7,955
498
There is one interesting factor prolonging the life of positronium. If the spins are in the same direction, they can't end up as 2 photons, since the spins of the positron and electron add up to 1, while 2 photons must have an even number for total spin.
 

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