# Does positronium have a stable crystalline phase?

This is a long shot, but while the 100YSS conference is going on at Houston, i haven't been able to get a grip on myself and think in other, more mundane and short-term rewards as normal people do. The main thing that has been taking up my mind is scalable ways to stabilize and store positronium in a way that the mass of storage device is negligible to the antimatter fuel

It is known that excited Ps atoms with high n (rydberg or rydberg-like) have estimated lifetimes of the order of years. Since positronium seems to be quite reactive (di and tri-positronium molecules have already been observed) I've been wondering if it could be possible to grow large crystals from positrons and electrons in a simple cubic lattice, where Na and Cl in the lattice being replaced by $e^{+}$ and $e^{-}$.

Question: is possible that positronium can have a crystalline bulk phase with enough ion distances to avoid annihilation?

The reason why i'm interested in positronium and not antihydrogen, which looks relatively easier to manipulate, is that proton-antiproton annihilation is extremely messy, with more than half of the mass-energy decaying into end products like neutrinos, which won't contribute anything to kinetic energy. In contrast, positronium decays in relatively soft gamma rays of 511 KeV (and 380 KeV for orthopositronium) that in theory we could reflect with extremely low grazing angles with efficiencies up to 90%

As an addendum to the larger question of positronium storage methods, i can't avoid mentioning that there have been other ways proposed over the years to keep the antimatter from touching the walls. If we want to store positron and electron separated, we have to deal with the Brillouin density limit that affects all existing and future Penning traps ($10^{12} e/cm^{3}$ for a field of 1 Tesla), so a simple calculation shows that a cylindrical container with weight ratio of 1 between container and antimatter masses, with 100 Tesla and 10 cm of thickness will have to have a radius of $10^{12}$ meters, roughly the radius of Neptune orbit! so in order to explore more viable alternatives, we are forced to consider only neutral antimatter (unless we find materials able to sustain over large regions magnetic fields 5-6 orders of magnitude higher than the current state of the art)

This report gives a nice overview of some of the alternatives that have been explored, the most interesting is paraelectricity (which is an effect where induced electric fields create virtual mirror charges on the wall that repels charges and possibly dipoles). Quantum reflection between antimatter BEC and wall is also mentioned, but i have reservations toward this one, since even if positronium BEC will form theoretically at higher temperatures (roughly 1-10 Kelvin), it is still complex to keep a large mass of BEC isolated enough from the environment (think of accelerations on a hypothetical ship) to make this a viable alternative. Basically if you sneeze, you and your ship will become a mininova.

There is one patent online proposing using photonic bandgap crystals to disallow the decay band of rydberg positronium, but it seems to me that requires cavities that are of the order of one wavelength of the decay radiation, which put us again in a scenario with low ratios of container-fuel masses

PS: Glad i've finally written this down, hopefully i'll be able to take my mind off a bit from this subject

• Just an off-the-wall thought after reading this, but if positronium by itself doesn't have a stable crystalline phase, perhaps positrons, electrons and neutrons might be able to form some kind of stable configuration. Or perhaps there could be some molecules of normal matter that could stably (and neutrally) trap positrons somehow, which might allow a reasonable storage density. – Nathaniel Sep 16 '12 at 17:29
• @Nathaniel, in that case, antihydrogen would do the job very well. Unless the ratio of hadron doping to lepton is below $10^3$ (the ratio between electron and neutron/proton mass) most of the fuel will still be hadronic, so you get the associated inefficiencies (but, who knows, maybe they are not as bad as i think they are) – lurscher Sep 16 '12 at 17:36
• Ah ok, I see. But then, maybe the question shouldn't be (just) "how can we store positrons without hadrons?" but "how can we store positrons among hadrons in such a way that they can be easily separated?" – Nathaniel Sep 16 '12 at 17:45
• @Nathaniel that is a fair, more general question, but i am choosing to focus on pure positronium as a first approximation to the problem. – lurscher Sep 16 '12 at 17:47
• My basic question has to do with the lifetime of the positronium in any level. The longest in the wiki article is microseconds. How could a useful energy device work with such small lifetimes? – anna v Sep 17 '12 at 15:19