Annihilation is a process fairly unique to the positron. When a positron encounters an electron, either in free space or bound to an atom, it may annihilate with the electron forming detectable gamma rays. (Alternatively, it may form a bound state with a free or freed electron, called positronium. This process is described in "Cross Section Experiments"). The rate at which a positron annihilates on a molecule is usually normalized by the rate at which it would annihilate on an electron. This rate, called Z_eff, was originally meant to be compared with the number of electrons per molecule Z. In this sense, it described the "effective" number of interacting electrons. The relationship between annihilation cross section σ and Z_eff can be expressed in terms of the electron radius r₀ and incident velocity v:

This extensive research still left a number of unanswered questions. As can be seen in the figure above, Z_eff/Z scales differently depending upon the chemical makeup of the species being studied. For instance, annihilation rate in perfluorinated alkanes grows much more slowly with size than it does in ordinary alkanes. One mechanism that had been proposed to explain this effect is the existence of positron-molecule resonances which may provide a means of enhancement of the annihilation rate. Advances in our positron trapping technology have allowed us to test this hypothesis.

Our current experiments use a cold (~25 meV), monoenergetic positron beam pulses from our buffer-gas trap. This has allowed us to perform energy resolved scattering and annihilation experiments. A schematic of our present annihilation experiment is shown in the adjacent figure. Positrons pulses from the trap stream into the gas cell from the left. By biasing the gas cell electrode, we can control the kinetic energy of the positrons as they interact with our test gas molecules. To detect positron-electron annihilation events, a CsI crystal and photodiode is placed to one side of the cell. When gamma-rays (511 keV) from annihilation hit the crystal, the high-energy gamma-ray photon is converted into lower energy visible light, which is then detected by the photodiode. Thus, Zeff can be measured as a function of this incident energy, opening a new avenue for investigation of annihilation effects.

One of the first molecules we examined with this technique was butane (C₄H₁₀). As shown in the figure below, this molecule displays a number of interesting resonant features at positron energies between 0.05 and 0.5 eV. In particular, it has a large peak around 0.33 eV, which is slightly below the energy of the C-H stretch vibrational mode of butane (0.36 eV). This is an indication that vibrational excitation of the molecule is responsible for the unusual propensity of large molecules to annihilate positrons. In fact, most molecules we have tested have vibration-mediated peaks like this one. They can be easily described by a vibrational Feshbach resonance (VFR) mechanism:
(1) A positron approaches the molecule with the resonant energy (E = ΔE_VIB + ε_B)
(2) The positron transfers its energy into a molecular vibration of energy ΔE_VIB and drops into a bound state of depth ε_B
(3) In this state, the positron wavefunction strongly overlaps the electron wavefunction resulting in enhanced probability of annihilation.
In this interpretation, each Z_eff peak is shifted below a vibrational mode by the binding energy ε_B.

When we re-examined the alkane series with this energy-resolved experiment, we noticed a number of interesting trends. As the size of the molecule grows, the height of the C-H stretch peak grows exponentially, just like it does for thermal Z_eff. In addition, all the peaks shift linearly to the left, indicating deeper binding. This is shown in the figures below. The true mechanism behind these trends is still unclear. It is thought that the exponential increase in Z_eff may be explained by a "doorway state" model. In this scheme, the positron may only be captured by exciting a fundamental vibrational mode. However, after capture, the energy of that mode is rapidly redistributed into a vast reservoir of degenerate combination modes. It is the exponential growth of this reservoir with molecular size that leads to the exponential growth of Z_eff.

Recently, we observed evidence of a "positronically excited" bound state in dodecane and tetradecane. In this case, the positronic attraction is sufficiently strong that a second, weakly bound, state shifts below the continuum. This results in a second smaller Z_eff peak just below the C-H stretch mode energy. We plan to examine this effect further.

Another unusual effect we have observed is a strong structural and chemical dependence for overall peak height and binding. Certain changes, such as the substitution of a single fluorine for a hydrogen or the transformation from a linear molecule to a ring, can dramatically reduce peak strengths. Other adjustments may change the binding energy. These effects seem inconsistent with model in which each resonance depends solely on local mode strengths. Hence, we classify these as global effects. We hope that future experiments can clarify the origin of these phenomena.

One particularly fruitful avenue is the examination of small molecules. These molecules have fewer vibrational modes to distinguish and are easier to model. This is particularly important if we want to quantitatively understand our resonances. The Z_eff spectra for the halo-methanes are a good example. They exhibit marked increases in peak Z_eff and binding with halogen size and have well-separated modes. Furthermore, their spectra have now been fit using a single-parameter model of Gribakin and Lee.

Though we've greatly improved our understanding of resonant annihilation in molecules, there are many frontiers left to be explored. We still need definitive proof that "doorway states" and vibrational relaxation are responsible for the exponential growth in Z_eff. We also need a better understanding of binding energy and the positron wavefunction around the molecule. Furthermore, there is still the unsolved mystery of chemical and structural dependence. The ultimate goal is a fully quantitative model which predicts binding, local peak strengths in small molecules, and global enhancement or suppression of peaks in large molecules. To address this, plans are underway to increase the range of molecules studied to include both larger and smaller molecules and improve energy resolution.

For a more in depth overview of positron annihilation experiments in our lab, consider reading some of our annihilation papers. In particular, the following articles may be helpful:

		L. D. Barnes, J. A. Young and C. M. Surko Phys. Rev A 74 (2006), 012706
		L. D. Barnes, S. J. Gilbert and C. M. Surko Phys. Rev A 67 (2003),032706
		K. Iwata, G. F. Gribakin, R. G. Greaves, C. Kurz and C. M. Surko Phys. Rev. A, 61 (2000)

If you wish to learn more about positron trapping and manipulation techniques, try visiting our trapping web page. In addition, our papers page contains plenty of further reading material and includes an article about positron physics written for a more general audience.