Positronium thermal

Westbrook et al. (1989) considered a number of possible systematic effects which may have affected their data and caused the extrapolated value of oAo-ps to be higher than the theoretical prediction. The two most difficult possibilities to account for were those related to the production of excited state positronium, Ps, in the gas (see section 4.5 for a discussion of investigations of this phenomenon by Laricchia et al., 1985) and those related to positronium thermalization (see section 7.4). At the time both were ruled out, but subsequent work on the latter effect (Skalsey et al., 1998) has shown that the positronium was not completely thermalized, so that the energy dependence, or equivalently the temperature dependence,... 

Fig. 7.20. Fits performed by Skalsey et al. (1998) to Sauder s positronium thermalization model using their TRDBS data. The slopes yield the positronium thermalization rate, whilst the intercepts give the average initial energy. (For clarity only the fitted lines are shown for He, Ne and iso-C io-) Reprinted from Physical Review Letters 80, Skalsey et al., Thermalization of positronium in gases, 3727-3730, copyright 1998 by the American Physical Society.

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

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 ... 

Positron annihilation spectroscopy (PAS) was first applied to investigate [Fe(phen)2(NCS)2] [77]. The most important chemical information provided by the technique relates to the ortho-positronium lifetime as determined by the electron density in the medium. It has been demonstrated that PAS can be used to detect changes in electron density accompanying ST or a thermally induced lattice deformation, which could actually trigger a ST [78]. 

The formation potential is usually negative for nPs = 1, and therefore positronium emission is allowed. However, with the possible exception of a diamond surface (Brandes, Mills and Zuckerman, 1992), it is positive for nPs > 2, which therefore precludes the emission of excited state positronium following positron thermalization in the material. 

Mills and Pfeiffer, 1979 Lynn, 1979 Poulsen et al, 1991 see also the discussion in subsection 1.5.3 below) that heating the metal surface can thermally activate positronium formation, the activation energy Ea being given by... 

Perhaps of more general applicability for the study of the properties of positronium is its production by the desorption of surface-trapped positrons and by the interaction of positrons with powder samples. According to equation (1.15) it is energetically feasible for positrons which have diffused to, and become trapped at, the surface of a metal to be thermally desorbed as positronium. The probability that this will occur can be deduced (Lynn, 1980 Mills, 1979) from an Arrhenius plot of the positronium fraction versus the sample temperature, which can approach unity at sufficiently high temperatures. The fraction of thermally desorbed positronium has been found to vary as... 

Another model of positronium formation, the so-called spur model, was originally developed by Mogensen (1974) to describe positronium formation in liquids, but it has found some applications to dense gases. The basic premise of this model is that when the positron loses its last few hundred eV of kinetic energy, it creates a track, or so-called spur, in which it resides along with atoms and molecules (excited or otherwise), ions and electrons. The size of the spur is governed by the density and nature of the medium since these, loosely speaking, control the thermalization distances of the positron and the secondary electrons. It is clear that electrostatic attraction between the positron and electron(s) in the spur can result in positronium formation, which will be in competition with other processes such as ion-electron recombination, diffusion out of the spur and annihilation. 

Jacobsen (1984) gave a full discussion of the effect of thermalization and concluded that positronium formation by the spur mechanism is unlikely in atomic gases, since R > rc irrespective of density. This is not the case for molecular gases, where R can be of a similar order of magnitude to rc at high densities. Thus, the positronium formation fraction in molecular... 

In this section we review the results from positron annihilation experiments, predominantly those performed using the lifetime and positron trap techniques described in section 6.2. Comparisons are made with theory where possible. The discussion includes positron thermalization phenomena and equilibrium annihilation rates, and the associated values of (Zeff), over a wide range of gas densities and temperatures. Some studies of positron behaviour in gases under the influence of applied electric fields are also summarized, though the extraction of drift parameters (e.g. mobilities) is treated separately in section 6.4. Positronium formation fractions in dense media were described in section 4.8. 

The positron-trap technique has been used by Surko and coworkers to measure the Doppler broadening of the 511 keV line for positrons in helium gas. This method does not have the drawback of the experiment described above, in which both positronium and free-positron events overlap on the angular distribution curves here the positrons are thermalized prior to the introduction of the gas and therefore cannot form positronium. A comparison of the theoretically predicted and experimentally measured Doppler spectra (Van Reeth et al., 1996) is shown in Figure 6.16. The theoretical results were obtained from the variational wave functions for low energy positron-helium scattering calculated by Van Reeth and Humberston (1995b) see equations (3.75) and (3.77). 

The first discussion of the thermalization of positronium appears to have been that of Sauder (1968), who derived a general (classical) expression for moderation by elastic collisions of a particle in a medium, allowing for the thermal motion of the atoms or molecules of the medium. By assuming that the momentum transfer cross section, om, is a constant he found that the time dependence of the mean positronium kinetic energy,... 

Fig. 7.18. Derived momentum distributions for the perturbed m = 0 state of ortho-positronium, for various gases (Nagashima et al., 1995) in an applied static magnetic field of 0.29 T. Reprinted from Physical Review A52, Nagashima et al., Thermalization of free positronium atoms by collisions with silica-powder grains, aerogel grains and gas molecules, 258-265, copyright 1995 by the American Physical Society.

Fig. 7.21. Angular correlation curves for mixtures of O2 and CI2 gases with an overall pressure of 120 atmospheres, (a) Pure O2, (b) O2 with 0.02 atmospheres of Cl2, (c) O2 with 0.05 atmospheres of CI2, (d) 02 with 0.2 atmospheres of CI2 and (e) O2 with 1 atmosphere of CI2. Goldanskii and Mokrushin (1968) attributed the components labelled Wi, W2 and W3 to the annihilation of thermalized para-positronium atoms (Wi, the narrow component), the annihilation of free positrons in O2 (W2) and the annihilation of positrons in the PsCl compound (W3). The intensity of the last, i.e. W3, grows progressively with the addition of CI2 to the O2 buffer.

Mills Jr., A.P. and Pfeiffer, L. (1979). Desorption of surface positrons a source of free positronium at thermal velocities. Phys. Rev. Lett. 43 1961-1964. 

Poulsen, M.R., Charlton, M., Chevallier, J., Deutch, B.I., Jprgensen, L.V. and Laricchia, G. (1991). Thermal activation of positronium from thin Ag(100) films in backscattering and transmission geometries. J. Phys. Condens. Matter 3 2849-2858. 

Fast positrons are created by bremsstrahlung pair-production in an electron microtron accelerator. These are moderated and bunched into 25 ns packets at 30 Hz, each comprised of 2 x 104 slow positrons. The positrons are guided by a 150-G magnetic field and implanted at 1-2 keV kinetic energy onto an Al(lll) crystal heated to 576 5 K as shown in Figure 7a. About 30% of the incident positrons come off the surface as thermal positronium with a velocity distribution that is a beam Maxwellian. 

This article will outline the experimental techniques we have used in the laser spectroscopy of these atoms and briefly indicate current plans for the refinement of these measurements. As Fig. 1 shows, the laser spectroscopy of positronium and muonium is not competitive with comparable measurements in hydrogen, largely due to the low density sources of these atoms. In the case of positronium, the first measurements were done at peak densities of a few atoms/cm3 during a laser pulse. The muonium work was limited by atom densities 10 2 atom/cm3 per laser pulse. As feeble as these sources might seem to spectroscopisis of less exotic atoms, one must remember that these instantaneous densities represent many orders of magnitude improvement of above pre-existing sources of thermal positronium and muonium. Clearly, improved sources will lead to more precise measurements. 

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