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Jun1-09, 04:58 AM
P: 986
First of all I must correct myself - the field for pp is not three but six orders of magnitude greater than the field for ee. And the field needed for ee pairs is on the order of 10^18 V/m. Below that, pair production is exponentially suppressed by a factor [tex](E_{crit}/E)^2 exp(-E_{crit}/E)[/tex]. You still see pairs, but, the lower the field, the less likely it is to create particle pairs. Already at the field 1% of critical the rate is so low that you're exceedingly unlikely to detect any pairs created during your lifetime.

The field needed can be estimated by a simple semiclassical argument. In the vacuum, virtual particle pairs appear and disappear all the time. A typical separation between two particles in such a pair is on the order of their Compton wavelength. You will see significant pair production if the field is so strong that the difference of potentials over the Compton wavelength is comparable to the rest energy of the pair.

If the field is strong enough, you will see ee pairs, pp pairs, all sorts of other pairs, muons, pions, etc. etc. The ratio of pp/ee in a strong enough field would probably be on the order of 1 - but protons and antiprotons are not elementary particles and the dynamic of their creation would be much more complicated.

Also, there's a big assumption we're making, namely that it's even possible to sustain a field of that magnitude. A system with field strength above ee creation threshold would be constantly losing energy to pair creation.