The positronium radius isn't equal to the Bohr radius-it's closer to two times the Bohr radius, since the reduced mass of positronium is close to half the reduced mass of the hydrogen atom.

The fact that positronium is unstable doesn't have anything to do with quantization of space, but is due to to the fact that there do exist states, namely composed of photons (two or three, depending on the value of the angular momentum-that *is* quantized), to which positronium can transform. That's all.

I don't find any source for your premise - can you provide a reference?  See http://en.wikipedia.org/wiki/Positronium and https://sites.google.com/site/positronlaboratoryofcomovepas/positron-electron_annihilation.mp4?attredirects=0.

Hello,

I will find more better source than this, I have read this long time back.

http://physics.stackexchange.com/questions/38460/is-the-minimum-radius-of-a-positronium-system-of-the-order-of-compton-wavelength

Regards,

Bhushan Poojary

I have seen Above two expert researchers links. I think these are sufficient for solving your problem. Thanks.

Hi Haradhan Kumar Mohajan,

I would like to get that sufficient details Sir.

Can you please elaborate on answer I was expecting.

Regards,

Bhushan  Poojary

Hello James,

If you refer this article https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Positronium.html

You will find as per spin of of both electron and positron ground state of postronium varies.

"The ground state of positronium, like that of hydrogen, has two possible configurations depending on the relative orientations of the spins of the electron and the positron."

I hope this article will help you understand my question, thank you for taking time for this.

Regards,

Bhushan Poojary

Hi Bhushan,

The princton.edu link is actually extracted from the Wikipedia entry above. The Wikipedia entry references 15 documents, including http://arxiv.org/abs/hep-ex/0609059 and https://www.researchgate.net/publication/235498266_Branching-ratio_measurements_of_multiphoton_decays_of_positronium.

However, I’m specifically wondering how it is determined that “Positronium annihilates even before the [e]lectron and positron meet”. While there are at least 2 decay paths for positronium, what determines how long it takes for the two particles to collide? Perhaps it’s explained in one of the two references above, but I’m unable to determine.  Perhaps I'm missing the obvious?

Thanks,

Jim

Article Branching-ratio measurements of multiphoton decays of positronium

Thanks James,

I will go through these links and get back to you.

Regards,

Bhushan Poojary

The positronium radius isn't equal to the Bohr radius-it's closer to two times the Bohr radius, since the reduced mass of positronium is close to half the reduced mass of the hydrogen atom.

The fact that positronium is unstable doesn't have anything to do with quantization of space, but is due to to the fact that there do exist states, namely composed of photons (two or three, depending on the value of the angular momentum-that *is* quantized), to which positronium can transform. That's all.

Stam - excellent point, in that the lower collective mass is, I guess, critical to that instability when compared to hydrogen.  However, I take the question to revolve around the the annihilation time compared to the orbital decay time...

No, the lower reduced mass doesn't have anything to do with it. Hydrogen is stable because the (e,p) system can't decay to photons due to baryon and lepton number conservation, whereas positronium has total lepton and baryon number zero and can decay to photons.

Stam - fine, but as I understand the question is not whether or why positroniium is unsable - it's how electron/positron annihilation time relates to orbital decay time.  How does your point relate to the assertion that "`Positronium annihilates even before the [e]lectron and positron meet"?

I don't know what the statement ``before electron and positron meet'' can possibly mean. It's possible to compute the decay rate of positronium to photons and to find a finite answer, which means that the lifetime is non-zero. On the other hand it's possible to compute the spectrum of positronium, too.  The energy values have a real and imaginary part, the latter indicative of the instability. I'm not sure that the statement that positronium annihilates in a time shorter than the ``orbital period'' is true, however, since  it is, precisely, possible to measure the energy levels of positronium.  

In short I wanted to ask if positron and electron go below ground state or not. If yes then my question is invalid.

The electron and positron can form a bound state. However this bound state has a finite lifetime. The electron and positron don't go ``below'' the ground state of positornium-the bound state decays into photons. That's all. If you start, in the infinite past with the bound state, in the infinite future you will end up with photons only. And the bound state is *defined* through an analytic continuation, since it's unstable.   

Hello Stam,

Thanks for reply, as you said it doesn't go below the bound state that means they do not touch right, my question was when they dont have contact how come then annihilate each other.  

Regards,

Bhushan .

Particle-antiparticle annihilation doesn't come about through ``contact''. It comes about as an allowed  transition of the physical system from the state (particle, antiparticle) to the state composed of the appropriate number of photons.