Positronium annihilation rate

Fig. 7.17. Ortho-positronium annihilation rates at various values of ethane gas density D, at a temperature of 305.45 K. The solid line is a weighted average of the annihilation rates between 120 and 180 amagat. The broken line is the prediction for free ortho-positronium. The data are due to Sharma, Kafle and Hart (1984). Reprinted from Physical Review Letters 52, Sharma, Kafle and Hart, New features in the behaviour of ortho-positronium annihilation rates near the vapour-liquid critical point of ethane, 2233-2236, copyright 1984 by the American Physical Society.

Abstract. Free-volume structure in the lanthanum salt of laurinic acid in crystalline and liquid-crystalline states and an effect of dissolved Cgo molecules on the mean nanovoid radius and concentration were studied by means of the positron annihilation technique. La(Ci2H25COO)3 clathrate compound with dissolved C6o molecules was obtained, which is thermodynamically more stable than a simple mixture of components. Increased mean nanovoid radius (from 0.28 to 0.39 nm) after the inclusion of C6o molecules and concomitant decrease of the positronium annihilation rate by a factor of 2.7 indicate the decrease of the smallest nanovoid concentration. 

Increased mean nanovoid radius (from 0.28 to 0.39 nm) after the inclusion of C6o molecules and concomitant decrease of the positronium annihilation rate by a factor of 2.7 indicate the decrease of the smallest nanovoid concentration [2]-... 

The lowest order contributions to the annihilation rates for the nPs1So and nPS3Si states of positronium were first calculated by Pirenne (1946)... 

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... 

The analyses described above can be applied directly to the equilibrium region of a lifetime spectrum. However, in atomic gases, where slowing down below the positronium formation threshold is by elastic collisions only, the positron speed distribution y(v, t) varies relatively slowly with time. Consequently the annihilation rate also varies slowly with time. From Figures 6.5(a) and (b) the existence of a non-exponential, or so-called shoulder, region close to t = 0 is evident, and the analysis of this region must be treated separately, as outlined below. Further details of the shape and length of the shoulder can be found in subsection 6.3.1 below. 

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. 

In Chapter 1, the first order contributions to the annihilation rates from the dominant modes of decay of the S-states of both ortho- and para-positronium (for arbitrary principal quantum number nPs) were given as equations (1.5) and (1.6). These contributions are included in the following equations for the rates for the two ground states, which also contain terms of higher order in the fine structure constant, a ... 

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. 

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... 

A follow-up study at O2 pressures below 0.05 atmospheres (Kakimoto, Hyodo and Chang, 1990), where the para-positronium to ortho-positronium conversion is suppressed because it occurs at a rate lower than that for para-positronium annihilation, yielded cross sections in good accord with the estimates given above. 

It is now considered that this type of behaviour is caused by the selftrapping of ortho-positronium in bubbles in the low temperature gas. The bubbles are thought to form because the ortho-positronium-atom interaction at low energies is dominated by repulsive exchange forces, and this effect results in a lowering of the annihilation rate the bubble is so rarified in some cases that (q)p approaches zero. 

Fig. 7.16. The pick-off annihilation rate (q)p, see equation (7.11), for ortho-positronium in 4 He gas at various temperatures, observed by Hautojarvi and Rytsola (1979). At the lowest temperature (q)p is almost independent of density, indicating stable bubble formation. The behaviour gradually changes to that of free ortho-positronium, indicated by the straight line whose slope corresponds to (iZeff) = 0.125 (see table 7.2). The data at 77 K are due to Fox et al. (1977).

Binding energies and annihilation rates for polyleptons are given in Table 2.2. The current values for positronium are listed for completeness. Since Wheeler s seminal 1946 paper, the 3- and 4-particle polyleptons have been the subject of many studies, and their properties are well understood today. The annihilation rate of diatomic positronium, Ps2, is about twice the spin-averaged rate in Eq. (2.4) because there are two positrons and each of them sees spin-paired electrons. Recently a calculation of the 5-particle... 

The calculated annihilation rate of Ps2Li+ is close to twice the spin-averaged rate, suggesting a structure in which a relatively well-defined diatomic positronium molecule is bound to the Li+ core. 

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],... 

It should be noted that in a magnetic field the m=0 spin triplet component and the spin singlet component of positronium mix. The annihilation rate of the triplet increases with increasing field. In the present apparatus with a magnetic field of about 0.02 Tesla this lowers the vacuum lifetime of the triplet state from 142 ns to 140.8 ns. This is well within experimental uncertainties and will be ignored [2,17],... 

Abstract. We have collected all known theoretical contributions to the energy levels of positronium and present a complete listing for the states ra = 1, 2 and 3. We give the explicit dependence of the energy levels on the quantum numbers n, L, S and J up to the order Rood In the next higher order RccOi only the contributions to S- and P-states are completely known. The annihilation rates of para- and ortho-positronium are completely listed up to the orders Poo a and PooCt , respectively. We compare calculated values of energy levels and annihilation rates with experimentally observed quantities. 

Positroniums (Ps) have two spin states ortho (o-Ps) (triplet) and para (p-Ps) (singlet). In condensed matter 75% of the Ps formed will be o-Ps and 25% p-Ps and their existence will depend on the existence of regions with low electron density [4]. The lifetime of positrons depends on the overlap integral of the wave functions of the positron and local electrons and, thus, it is related with the electronic structure of the material [5]. Since the positrons thermalize after a few ps, and the subsequent lifetime is roughly two orders of magnitude higher than the thermalization time, the lifetime of positrons within the matter will effectively depend upon the local electron density [5]. Thus, PALS implies the measurement of the lifetime, t, which is the inverse of the annihilation rate, X, defined by [ 1 ] C p r)p r)dr (1)... 

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