Densely packed positronium atoms interact chemically

Nature’s simplest atom does not appear in the periodic table. Positronium (Ps), the short-lived bound system of an electron and its antiparticle, the positron, was independently predicted by Arthur Ruark and John Wheeler after the positron was discovered in 1932. Four years before positronium itself was discovered in 1951, Egil Hylleraas and Aadne Ore had performed a variational calculation ¹ and concluded that Ps atoms could combine to form the diatomic molecule Ps₂. Two Ps atoms can also interact by swapping the spins of their two electrons or positrons.

Interactions of Ps atoms with each other are much more difficult to observe than to envision. To create Ps, researchers shoot positrons at a suitable target. If the Ps atoms are to be close enough to react, a large number of positrons must be accumulated and then quickly dumped onto a small-diameter spot. That’s a challenge, because the positrons are available only at low currents; to be accumulated, they must be drastically cooled and also must be isolated from ordinary matter to prevent their rapid annihilation with electrons. In addition, the Ps formed in the target quickly decays into annihilation photons, so experimenters need nimble detectors to discern any reactions. In late 2005 David Cassidy, working with Allen Mills and colleagues at the University of California, Riverside, successfully overcame those hurdles. ²

After collecting positrons in a trap whose basic design was developed by Clifford Surko and colleagues at the University of California, San Diego, Mills’s group shot positron pulses into a porous silica film, a material in which a dense gas of Ps atoms could form. They then tracked the photons produced by the annihilation of Ps atoms over a period of 300 ns. By compressing the positron beam—that is, by decreasing its cross section—they could increase the density of the Ps trapped in the silica. Differences in the photon profiles resulting from the compressed and uncompressed positron beams provided the evidence that densely packed Ps atoms reacted in the porous film.

The Mills group’s exploration of Ps reactions is part of a broader research program of which one goal is to study dense, many-Ps systems. Because the positron has the same light mass as the electron, the Ps atom cannot be envisioned as an electron cloud about an essentially stationary nucleus. The egalitarian relation between positive and negative entities may lead to unpredictable surprises.

One novel feature of the many-Ps system is a predictable consequence of the low Ps mass. When crowded together, Ps atoms have much greater wavefunction overlap than do conventional, heavier atoms. As a result, Ps should be able to form a Bose—Einstein condensate at significantly higher temperatures than do the atoms of the periodic table. Mills and company are working to increase the Ps density so as to form such a BEC. They estimate that if they can achieve a thousandfold increase—a challenge they believe they can meet—then a BEC will form at about 15 K. Ultimately, a BEC of Ps atoms may be a key component of a gamma-ray laser that emits photons with an energy of half an MeV.

A shot in the light

Figure 1 shows the setup of the Riverside group’s recent Ps experiment. To the left is the Surko-type trap, which collects positrons generated by sodium-22 decay. By applying an effectively rotating electric field ³ as the positron plasma is accumulated in the trap, the experimenters can exert a torque that compresses the plasma in the plane perpendicular to the trap axis. If the rotating field is turned off, the plasma relaxes to an expanded state.

The trap collects some 15 million positrons before a rapidly applied dumping voltage expels the positrons and narrows them along the trap axis; once released from the trap, the positron pulse has a length of about 20 ns. After the positrons leave the accumulator, they are focused onto a thin, porous silica film where they combine with electrons to form Ps.

To observe the photons resulting from the annihilation decay of the Ps, Mills and company invented a new technique: single-shot positron annihilation lifetime spectroscopy. The photons created in the silica film enter a scintillating crystal, which in turn generates a photomultiplier signal. A fast oscilloscope, triggered by the release of positrons from the trap, records that signal in real time. The single-shot technique’s temporal resolution is limited by the positron pulse width and the response time of the photon detector (about 15 ns).

Single-shot spectra for compressed and expanded initial positron pulses appear together in figure 2. After 40 ns or so, the spectrum derived from the compressed beam dips below its counterpart derived from the expanded beam. The late-time depletion in the compressed spectrum’s signal is the sign that earlier reactions have removed densely packed Ps atoms from the silica film.

The key to interpreting the figure in greater detail is understanding how Ps decay depends on the atom’s spin state and environment. In vacuum the lifetime of Ps states with total spin ħ (ortho-Ps) is 142 ns, whereas spin-zero, para-Ps decays with a lifetime of 0.125 ns. In a material like porous silica, Ps can interact with its host, and the new reaction channel decreases the Ps lifetime. Specifics depend on the details of the pore structure; typical lifetimes for ortho-Ps range from 2 to 40 ns. The presence of a magnetic field can also affect the lifetime of Ps. In particular, for the 1-tesla field present in the Mills experiment, the lifetime of the m = 0, antiparallel spin state of either ortho- or para-Ps is much shorter than the lifetime of the m = ±1 ortho-Ps states in which the electron and positron spins are aligned. Indeed, any decays of m = 0 states are hidden below the broad initial peak in figure 2.

Once the compressed and expanded spectra defined in the figure have diverged, the expanded spectrum is consistent with a single lifetime of 36 ns; it tracks m = ±1 ortho-Ps reacting with the silica film. Beyond about 100 ns, the compressed and expanded spectra are parallel. Evidently, after several lifetimes the compressed-beam Ps has been thinned enough that its only reaction is with the film. But the lower position of the compressed spectrum at late times (and the inability to fit earlier times with a single interaction lifetime) indicate that other reactions remove m = ±1 ortho-Ps from the system. The two most plausible possibilities are formation of the diatomic Ps₂ molecule and spin-exchange formation of m = 0 Ps. In both cases, the decay of the product would be hidden under the prompt peak that dominates the first 40 ns of the spectrum, and so the experiment cannot directly distinguish between Ps₂ formation and spin exchange. The Riverside researchers are working to increase the resolution of their single-shot technique so that they can peek under the peak and tease out the reaction channels hidden there.

Indirect evidence suggests that Ps₂formation could be significant: The total cross section that Mills and colleagues deduce for Ps depletion in the silica film is some four times the theoretical cross section for spin exchange. That factor of four does not seal the argument for Ps₂ formation because the film’s pore structure could shepherd Ps atoms into regions of unexpectedly high density. In that case, the Mills estimate of the total cross section would be too high, and the actual value of the total cross section could be compatible with pure spin exchange being the only mechanism for Ps depletion.

One loose end must be tied up to clinch the interpretation of the data in terms of Ps interactions. When a high-energy positron passes through a silica film, it strips electrons from the film. Those electrons and the positive ions they leave behind are, in principle, available to participate in spin-exchange reactions with Ps atoms created in the silica. In other words, the depletion of Ps formed via the compressed positron beam might not have been caused by interactions of Ps with Ps, but rather by interactions of Ps with surface radicals. Exactly how to calculate the effect of those radicals is not clear, but Mills and the University of Tokyo’s Toshido Hyodo have made independent estimates and both conclude that the radicals do not have a significant impact. Neither researcher, however, regards the case as closed.

Antihydrogen coda

The many-Ps systems being studied by Mills and company may, in time, be useful to antihydrogen researchers. Within the past few years, two independent groups located at CERN—the ATHENA and ATRAP collaborations—have succeeded in producing and characterizing slowly moving antihydrogen atoms (see Physics Today, November 2002, page 17 , and January 2003, page 14 ). Rolf Landua, a member of the ATHENA group, notes that colliding a dense gas of Ps with cold antiprotons could be an efficient way to produce cold antihydrogen. And with that antihydrogen, the CERN groups might ultimately test the equivalence principle of general relativity and the CPT theorem, which asserts physics is invariant under the combined operations of charge conjugation C, spatial inversion P, and time reversal T. Ironically, in addition to being an aid to antihydrogen researchers working to test the equivalence principle, Ps is also a competitor: The neutral electron—positron system might itself serve to test equivalence.