Can an orbital have both electrons and positrons?

[TheCanadian]

Can there be a stable nucleus where one has both electrons and antielectrons (either paired or unpaired) in the atomic orbitals? For example, in a $\beta ^+$ decay, could the antielectron released by captured by the atom and remain in orbit as an electron may?

 

[BvU]

Think ! For an orbit the least you need is an attractive potential !

 

[TheCanadian]

Think ! For an orbit the least you need is an attractive potential !

Yes, could not the anti electron occupy an outer shell (which is unoccupied), and thus depending on the number of protons in the nuclei versus closer electrons in the orbitals (which is attractive), these could be competing forces. I am wondering if such a scenario has been observed or if other plausible scenarios exist.

 

[BvU]

Ah, I get the idea. The remains after a $\beta^+$ is negative and that would provide an attractive potential ?
However, as a rule, the remains eject an electron to return to neutral.

In $\beta^+$ decay the kinetic energy of the e⁺ is a lot higher than the binding energy from a diffuse and unstable cloud with net charge 1e^-

 

[Khashishi]

But if a negative ion and a positron came together, I guess it should be possible for them to form a bond, at least temporarily.

 

[BvU]

No. They annihilate. See first sheet here

 

[Khashishi]

They only have some probability of annihilating. If you can have things like positronium or even crazier things like di-positronium, I see no reason why you couldn't have this, albeit for a short time.

 

[BvU]

I'm no QED expert but I suppose you can calculate probabilities. But annihilation should score 'rather' high...
@vela @Orodruin : Was my first answer overhasty ?

 

[Vanadium 50]

This hinges on the definition of "stable". I would say that this exotic atom is stable if a) it is neutral, and b) its lifetime in its ground state is long - say one second. Using that definition, the answer is "no".

The simplest system that satisfies a) is a positron orbiting an H- ion. An H- ion has a radius almost the same size (just a tiny bit larger than) as an H atom, and the radius of an atom formed by a positron orbiting a -1 charge object is the same as an H atom. So essentially the two electrons and the positrons will be in the same orbitals, and will therefore have substantial wavefunction overlap. That means they will annihilate quickly - on positronium-like time scales: nanoseconds.

This argument extends to Z+1 electrons and one positron orbiting a nucleus of charge Z: if you're in the ground state, the positron's S-wave wavefunction overlaps substantially with all the electrons in an S-wave.