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What is the minimum distance between an electron and a positron so that they do not annihilate?

I want to assume that the location of an electron can be determined with an accuracy of 0.004 Angstroms, as described here: https://books.google.de/books?id=U0UeBAAAQBAJ&pg=PA127&lpg=PA127&dq=ort+eines+teilchens+exakt+bestimmen&source=bl&ots=X9uDI8Yd2n&sig=ACfU3U1aplcTG4_yFhmoqApeQs9_a5Kz-A&hl=de&sa=X&ved=2ahUKEwjVtsDZ1NLgAhVMzaQKHXDtCFk4FBDoATAGegQIBRAB#v=onepage&q=ort%20eines%20teilchens%20exakt%20bestimmen&f=false p.127

Under this premise, is there an exclusion criterion for annihilation concerning their spatial distance?

sanftwasser
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  • There is no minimum distance, they can annihilate at any distance, the probability just gets smaller. BTW, if the uncertainty in an electron's position is 0.004 Angstroms, the uncertainty in its momentum is relativistic: the uncertainty in its velocity is over 0.43c. – PM 2Ring Feb 23 '19 at 23:28
  • Thank you. I'm trying to understand: Can this probability be understood as a function mainly of distance? If yes, is there a significant decrease in the annihilation rate above 0.212 nm (Positronium diameter)? What is the shape of the curve? – sanftwasser Feb 24 '19 at 20:02
  • It's a function of distance and energy-momentum; I don't know the details. You can edit your question to make it clear you want that info, or ask a fresh question, but in either case you need to explain how your question isn't a duplicate of existing questions. When an electron & positron get close enough to interact they temporarily form a bound state called positronium, which has a classical size double that of a hydrogen atom, as mentioned here. – PM 2Ring Feb 24 '19 at 21:12
  • Note that an electron & positron don't necessarily annihilate to 2 (or more) photons. They may simply scatter off each other, this is known as Bhabha scattering. And if they have enough energy the annihilation can create a muon + antimuon, or even a quark + antiquark. – PM 2Ring Feb 24 '19 at 21:33
  • Thank you for your explanations. I mean, that's the point, as you wrote: "get CLOSE ENOUGH to interact"... It seems tu me: They mutually feel their place. – sanftwasser Feb 25 '19 at 21:44

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