Positronium annihilation measurements

Several versions of positronium annihilation measurements are sensitive to the differences between open and closed porosity. The detection geometry, the annihilation types and the lifetime change when closed pores with no... 

Roughly speaking, 3-to-2 photon annihilation ratio measurements can be considered as a BET technique, which is sensitive to both open and closed pores. Positronium can be considered as the smallest atom possible. No pore will be too small. Positrons are implanted rather than adsorbed and forms positronium. Positronium annihilates into 2 or 3 photons from within pores, or into 3 photons only after escape (desorption) out of the sample through open porosity. In addition, depth dependent information can be provided. 

Kilburn, D., Wawryszczuk, J., Dlubek, G., Pionteck, J., Hassler, R., and Alam, M. A., Temperature and pressure dependence of the free volume in poly isobutylene from positron lifetime and pressure-volume-temperarnreexperiments,Macromol. Chem. Phys., 207,721-734(2006b). Kim, S. H., Chung, J. W., Kang, T. J., Kwak, S.-Y, and Suzuki, T., Determination of the glass transition temperature of polymer/layered silicate nanocomposites from positronium annihilation lifetime measurements. Polymer, 48, 4271-4277 (2007). 

In the course of the positronium lifetime measurements, radioactive isotopes of positron decay serve as sources, e.g., sodium-22, copper-64. At the moment of the emission of the positron from this source a y-photon is also released. (In the case of, e.g., sodium-22 its energy is 1.28 MeV.) This y-photon serves as the start signal in the coincidence equipment used. The y-photon produced by the 2y-annihilation process to be studied (0.51 MeV) is the stop signal. The magnitude of the time measured between the start and stop signals (the positronium lifetime) is in the range 10 —10 s. To get a lifetime curve of adequate statistics, the apparatus repeats the time measurement about 10 — 10 times. For the details of the experimental technique see, e.g., refs. [De 53, Fe 56, Go 71a]. 

Free volume or hole volume is ostensibly measured experimentally by positronium-annihilation-lifetime spectroscopy (PALS). In organic glasses, including amorphous polymers, the ortho-positronium (o-Ps) bound state of a positron has a strong tendency to localize in heterogeneous regions of low electron density. In vacuo, an... 

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

PALS is based on the injection of positrons into investigated sample and measurement of their lifetimes before annihilation with the electrons in the sample. After entering the sample, positron thermalizes in very short time, approx. 10"12 s, and in process of diffusion it can either directly annihilate with an electron in the sample or form positronium (para-positronium, p-Ps or orto-positronium, o-Ps, with vacuum lifetimes of 125 ps and 142 ns, respectively) if available space permits. In the porous materials, such as zeolites or their gel precursors, ort/zo-positronium can be localized in the pore and have interactions with the electrons on the pore surface leading to annihilation in two gamma rays in pick-off process, with the lifetime which depends on the pore size. In the simple quantum mechanical model of spherical holes, developed by Tao and Eldrup [18,19], these pick-off lifetimes, up to approx. 10 ns, can be connected with the hole size by the relation ... 

In this chapter we consider the physics of the positronium atom and what is known, both theoretically and experimentally, of its interactions with other atomic and molecular species. The basic properties of positronium have been briefly mentioned in subsection 1.2.2 and will not be repeated here. Similarly, positronium production in the collisions of positrons with gases, and within and at the surface of solids, has been reviewed in section 1.5 and in Chapter 4. Some of the experimental methods, e.g. lifetime spectroscopy and angular correlation studies of the annihilation radiation, which are used to derive information on positronium interactions, have also been described previously. These will be of most relevance to the discussion in sections 7.3-7.5 on annihilation, slowing down and bound states. Techniques for the production of beams of positronium atoms were introduced in section 1.5. We describe here in more detail the method which has allowed measurements of positronium scattering cross sections to be made over a range of kinetic energies, typically from a few eV up to 100-200 eV, and the first such studies are summarized in section 7.6. 

Systematic effects arising from the disappearance of ortho-positronium through the cavity entrance aperture, and the rate of annihilation by collisions with the cavity walls, were taken into account by expressing the measured annihilation rate as... 

Abstract. The current experimental situation regarding tests of fundamental physics using positronium is reviewed. Five measurements are discussed and compared with theoretical predictions the singlet and triplet annihilation decay rates, the ground state and the n = 2 energy intervals, and the Doppler-free two-photon excitation of the IS to 2S transition. Previous results, recent progress (where appropriate), and the outlook for future improvements in these measurements are discussed. 

Positronium still presents rather formidable theoretical challenges [39], since it is a relativistic two-body system which cannot be approximated by the motion of a particle of reduced mass in a fixed Coulomb potential. In addition, QED calculations must include annihilation terms. First laser measurements of the 1S-2S two-photon transition frequency in positronium [40] give a result about five standard deviation lower than the theoretical predictions, after taking a recalibration of the tellurium reference line into account [41]. On the other hand, as yet uncalculated higher order terms could well account for this discrepancy. 

Positronium can pick-off an electron during a collision with a pore wall and annihilate into two photons. Between collisions, only three photon annihilations occur, just as in vacuum. Quantum mechanically, the overlap with the wall-electron wave functions decreases with the distance from the wall and pick-off (two photons) becomes less likely. With increasing pore size collisions become less frequent. The ratio of 3 photon annihilations to 2 photons probes the combination of pore size and total pore volume as well as their link to the sample surface, and can be measured by examining the energy distribution of annihilation photons. This 3-to-2 photon ratio can be calibrated to absolute fractions of positronium in the annihilation spectrum [16, 17]. 

The difference in the annihilation ratio for positronium at the surface and in the sample is used to measure the effective range of positronium. Implantation profiles for a range of incident energies (density 1 g/cm3) were calculated. In this simulation the fraction that stops within a diffusion length of the surface can reach it and annihilates into 3 photons the remainder annihilate 10% into three photons and 90% into two photons, as shown in Figure 7.4. The fractions are chosen as an example. A short effective range appears as a sharp transition from surface measurement to bulk measurement value. 

The contribution of positron diffusion length (L+ = 10 nm [22]) was removed from the escape depth values. The diffusion constant in a material is a function of diffusion length and annihilation rate D = L2X. Here, the rates for positrons and positronium are similar (X 2 ns 1). Thus the measured combined effective diffusion length of positrons L+ and positronium escape Lesc is l eff = L2+ + L2esc [30],... 

The 3-to-2 photon technique, simple counting setups and, possibly mean lifetime measurements could fulfill these criteria. A simple setup, shown schematically in Figure 7.28, is suitable for the first two applications. Positrons are implanted into the sample. Focusing into micron-sized areas is possible. Positronium forms, traps in pores and annihilates in closed pores or escapes through open porosity. Two detectors, one behind the sample and a second with an aperture on the side, observe all positronium (and positron) annihilations and only those from within the sample, respectively. The former detector is also set up to provide 3-to-2 photon ratios. 

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