Positronium ortho

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]. 

Importantly, both for liquid CgFg and CS2, there is a relatively high yield of ortho-positronium (o-Ps) observed in e irradiation of these fluids [34]. The o-Ps is formed in the e e" recombinations that occur in the end-of-track spurs. The higher the negative charge mobility, the higher the probability that these e e" recombinations occur before the e ... 

Positron annihilation lifetime spectroscopy (PALS) provides a method for studying changes in free volume and defect concentration in polymers and other materials [1,2]. A positron can either annihilate as a free positron with an electron in the material or capture an electron from the material and form a bound state, called a positronium atom. Pnra-positroniums (p-Ps), in which the spins of the positron and the electron are anti-parallel, have a mean lifetime of 0.125 ns. Ortho-positroniums (o-Ps), in which the spins of the two particles are parallel, have a mean lifteime of 142 ns in vacuum. In polymers find other condensed matter, the lifetime of o-Ps is shortened to 1-5 ns because of pick-off of the positron by electrons of antiparallel spin in the surrounding medium. 

Positronium can exist in the two spin states, S = 0, 1. The singlet state (5 = 0), in which the electron and positron spins are antiparallel, is termed para-positronium (para-Ps), whereas the triplet state (5 = 1) is termed ortho-positronium (ortho-Ps). The spin state has a significant influence on the energy level structure of the positronium, and also on its lifetime against self-annihilation. 

Experiments on these two gases, reported by Griffith and Heyland (1978), showed that a fast component, with a density-dependent decay rate, was present in the lifetime spectra, and this was tentatively linked to the dearth of long-lived ortho-positronium. Furthermore, it was found for mixtures of krypton with helium that the maximum value of F, which was observed at a concentration of around 0.01% of krypton, was in excess of the sum of the individual F-values for the two gases when pure. 

Fig. 6.5. Examples of positron lifetime spectra for (a) argon and (b) xenon gases. The argon data are for a density of 6.3 amagat at 297 K. The channel width is 1.92 ns. In (a), (i) shows the raw data, (ii) shows the signal with background removed, (iii) shows the free-positron component and (iv) shows the fitted ortho-positronium component. In (b), the spectrum for xenon is for room temperature and 9.64 amagat and has a channel width of 0.109 ns. The inset shows the fast components as extracted and discussed by Wright et al. (1985).

Once the background is subtracted, the component of the spectrum due to the annihilation of ortho-positronium is usually visible (see Figure 6.5(a), curve (ii) and the fitted line (iv)). The analysis of the spectrum can now proceed, and a number of different methods have been applied to derive annihilation rates and the amplitudes of the various components. One method, introduced by Orth, Falk and Jones (1968), applies a maximum-likelihood technique to fit a double exponential function to the free-positron and ortho-positronium components (where applicable). Alternatively, the fits to the components can be made individually, if their decay rates are sufficiently well separated, by fitting to the longest component (usually ortho-positronium) first and then subtracting this from the... 

Note that, as can be seen from the discussion in subsection 1.2.1, the contributions from the higher order annihilation modes are negligible at the present levels of precision. Thus, the rate for the annihilation of ortho-positronium into five gamma-rays is only 10-6 of that for three gamma-rays, with a similar value for the ratio of the rates for para-positronium annihilation into four and two gamma-rays. 

Fig. 7.1. Schematic illustration of the positronium formation chamber and detector arrangement used by Westbrook et al. (1987, 1989). Reprinted from Physical Review A40, Westbrook et al., Precision measurement of the ortho-positronium vacuum decay rate using the gas technique, 5489-5499, copyright 1989 by the American Physical Society.

Fig. 7.2. The left-hand boxes show the fitted ortho-positronium decay rate at two values of isobutane pressure, for various start times of the fit to the component. The right-hand plot shows the observed decay rates, and their extrapolation to zero density, of Westbrook et al. (1989). The error bars on the individual points are approximately equal to the thickness of the line.

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... 

Fig. 7.4. Extrapolations of the measured ortho-positronium decay rates in A /V and S/V (see text). Reprinted from Physical Review Letters 65, Nico el at, Precision measurement of the ortho-positronium decay rate using the vacuum technique, 1344-1347, copyright 1990 by the American Physical Society.

The experiments were performed at two values of the magnetic field, 0.375 T and 0.425 T, and at various densities of N2 gas with small admixtures of isobutane to quench the free-positron component (see subsection 6.3.2). Al-Ramadhan and Gidley (1994) derived a quantity A(p) from their measured values of A Ps and Ao-ps, for the mixed and unmixed ortho-positronium states respectively, at a gas density p given by... 

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