Is positronium really an orbiting pair of electron/positron ?by xortdsc Tags: electron or positron, orbiting, pair, positronium 

#1
Jan3014, 05:19 AM

P: 55

Hi,
I'm a little confused about positronium. Accouring to this article http://www.answers.com/topic/positronium it states on the one hand that it is just an electron and a positron orbiting around their common center, held together by electromagnetic forces due to their charge. On the other hand it states it behaves very similar to a hydrogen atom just that the proton is replaced by the positron and due to its much lower mass the positron's movement will not be negligible (as it is for the proton). But still the energy of the system seems to be quantized (so the spinning particles are not continuously spiraling into each other until annihilation) and the electron/positron seems to move in orbitals just as electrons in a hydrogenatom (s/porbitals and so on) which would be somewhat in conflict of stating that the electron is actually orbiting the nucleus/positron because in hydrogen the electron would not orbit the nucleus but instead being "spread out" into an orbital cloud and not being in a single spot at any time. So now what is the valid picture here ? The spread out electroncloud orbital thing or actually (point) particles orbiting each other ? 



#2
Jan3014, 05:34 AM

P: 2,471

Its a positron orbiting an electron or viceversa.
http://en.wikipedia.org/wiki/Positronium Since its a QM system, it follows the electroncloud orbital thing but its an unstable configuration as they will quickly annihilate each other and go out in a blinding flash of light as an even number of gamma ray photons. 



#3
Jan3014, 06:02 PM

P: 364

Well, something orbiting the other doesn't really make sense in the Quantum Mechanic picture. What happens is that it's a bound state (unstable), in the same way the electron is a bound state to the hydrogen atom. If I would be asked how could that happen in the case of QM (forgetting the relativistic quantum mechanics allowing annihilation) it would mean that the potential could have a local minimum. Of course things are a bit different, because in the case of H you had the induced mass equal to the electron mass (because you assumed the mass of the proton>>> the mass of electron). In the positronium case the induced mass is not such...
In classical mechanics view, that would mean that both particles would rotate around a point that's not identified as one of the particles (in Hydrogen atom you had the electron rotating around a point that coincided with where the proton was). 



#4
Jan3114, 04:22 PM

P: 55

Is positronium really an orbiting pair of electron/positron ?
Thanks for the reply.
So it should be possible to calculate the electron density distribution for the 1s orbital relative to the systems common center of mass, right ? Since it should be radially symmetric it should only be a function of r (where r=0 is the common center of mass of both particles). The positron will always need to be at the opposite side for any hypothetical electronposition chosen from the distribution. If this is possible can someone give me the corresponding function ? 



#5
Jan3114, 04:39 PM

Sci Advisor
PF Gold
P: 1,111

Since the interparticle vector ##\mathbf{r}## is colinear with the position vector of the electron ##\mathbf{r}_\mathrm{e}## when the center of mass is taken as the origin, the angular distribution of the electron follows the angular distribution of ##\mathbf{r}##, so the electron is in a spherically symmetric orbital centered on the position of the centerofmass, as you expected. 



#6
Jan3114, 04:53 PM

P: 55

Okay, so it means that the probability of both particles at the common center of mass (r=0) is >0 which corresponds to the probability of annihilation of the entire structure ?




#7
Jan3114, 06:26 PM

P: 364

For the probability of that to happen you have to calculate the cross section of the interaction [itex] e^{+}e^{} \rightarrow γ γ [/itex] In the view of QM, you would have to calculate the probability for your particles to leave that "local minimum" of the potential as I said, which corresponds to their bound state.... 



#8
Feb114, 10:11 AM

P: 55

okay, thank you very much :)




#9
Feb114, 01:07 PM

Sci Advisor
PF Gold
P: 1,111

A nice source of information on positronium is S Berko and H N Pendleton, Ann. Rev. Nuc. Part. Sci. 30, 543 (1980). Unfortunately, it's behind a paywall, so you have to have an institutional access. 



#10
Feb114, 02:46 PM

P: 353

Is the probability of annihilation, for all s states of positronium, strictly proportional to the probability of electron and positron occurring at the same spot?
(That probability is zero for all states of positron orbiting electron, but all those states can emit photons to decrease their angular momentum by 1) Also, is the ratio between the annihilation probability of para and ortho positronium the same for all s states? All s states 3s or above can decay to any lower lying p state, as well as annihilate, but 2s obviously cannot. Thus the stablest positronium ought to be 2s ortho positronium. 



#11
Feb114, 03:18 PM

Sci Advisor
PF Gold
P: 1,111





#12
Feb114, 04:00 PM

P: 353

It is only the s states, that oscillate through the nucleus rather than orbit around it, which have a nonzero probability of interacting with the nucleus by annihilation or electron capture. So: For p, d etc. states of positronium, annihilation is impossible, but radiation to a lower angular momentum state is always possible For 1s state, radiation is impossible (it is the ground state) but annihilation is possible and fastest of all s states For 2s state, radiation is forbidden (like for all hydrogen like atoms), annihilation is possible but 8 times slower than for 1s state For 3s and all higher s states, radiation to all lower p states up to 2p is possible, but so is annihilation direct from the high s state... so these should be competing processes of comparable speed. 



#13
Feb114, 04:15 PM

Sci Advisor
PF Gold
P: 1,111





#14
Feb114, 04:39 PM

Sci Advisor
Thanks
P: 3,846





#15
Feb114, 05:45 PM

P: 364





#16
Feb114, 06:04 PM

Sci Advisor
Thanks
P: 3,846

Serious efforts are underway to create positronium hydride, dipositronium molecules, and even positronium BE condensates. 


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