Positronium annihilates

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. 

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. 

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.

The reason for this divergence can be understood as follows. The integral (124) represents the cumulative intra-positronium annihilation as positro-nium leaves away from the proton until the channel wavefunction decays as exp( KimR)/R. The extremely slow decay of this wavefunction near e = 0, together with the nearly constant F(e) as e ->-0, causes the S-wave divergence. 

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]-... 

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. 

Data were accumulated for a set of samples made of MSSQ with porogen loads from 0 to 90% (Figure 7.6). The samples have different thickness (350 to 780 nm) and the density drops as the porogen load increases. At the silicon interface the density changes and positronium annihilates fast into two photons, causing the near vertical drop in the ratio to the equivalent of no 3-photon events. 

The 2 dominant components are due to the annihilation of positrons in the sample MSSQ material independent of pores ( 0.5 ns) para-positronium (-0.1 ns). Ortho-positronium annihilations in the MSSQ cage structure occur with a -4 ns lifetime. Lifetimes of 10 ns and greater are due to positronium in pores and tend to increase with increasing porogen load. Open porosity is associated with a lifetime of -100 ns (80% case, dashed line). 

Figure 7.20 Lifetime results versus porogen load shown on three separate time scales. The shortest lifetimes on the bottom frame are due to annihilations of positrons and positronium in the MSSQ material. The middle frame shows the positronium annihilations from closed pores and from open pores in the top frame. Statistical errors are shown or smaller than the symbols. See text.

Figure 7.21 Intensities corresponding to the lifetimes shown in figure 7.20. The intensities associated with positrons and positronium annihilation in the MSSQ matrix are shown in the bottom panel and the positronium annihilations (ortho positronium) from pores and open porosity in the top panel. The line-and-star in the bottom panel indicates 1/3 of the sum of all ortho positronium annihilations. Statistical errors are shown or smaller than the symbols. See text.

With position sensitive detectors the deviations from antiparallel emission of two annihilation photons can be observed. The small angles on the order of millirad are translated into two dimensional electron (or positronium) momentum distributions. The resolution is sufficient to distinguish positron from para-positronium annihilations and to determine the velocity distribution of positronium. 

The data and methods discussed in the previous sections show the power of positron and positronium annihilation methods for the characterization of porous materials and low-k dielectrics in particular. The obvious question is, whether this power can be harnessed for an online diagnostic tool in a semiconductor production line. Such a tool should be reliable, compatible with existing processes, rapid, and not more complex than any other system. 

Since positron annihilation spectroscopy is highly sensitive to atomic defects in solid materials, positron annihilation experiments have been carried out extensively on silicon (Si) and silicon dioxide (Si02), both of which are extremely important for the microelectronic device industry. While several reviews are available [1], those reviews are mainly focused on positron (not positronium) annihilation behavior because positronium (Ps) formation dose not occur in bulk crystalline Si. Recent positron annihilation experimental studies revealed that Ps formation occurs in some Si-based thin films, such as porous Si and hydrogenated amorphous Si furthermore, Ps formation is dominant in high-purity amorphous Si02 thin films. In this chapter, Ps annihilation characteristics in Si and Si02 thin films will be discussed from the experimental point of view. 

Positronium formation and annihilation behavior in Si and Si02 thin films are reviewed. Positronium is highly sensitive to pore (or void) sizes, surface properties of pores, defects near pore surfaces, etc., in various Si and Si02 samples. Therefore, not only positron annihilation spectroscopy but also positronium annihilation spectroscopy is useful for characterization of Si and Si02 materials. 

Sausa, O., Zrubcova, J., Band, P., Kristiak, J., Bartos, J. (2000) A study of time dependence of ortho-positronium annihilation in a poly(butadiene) at... 

Muramatsu, H., Matsumoto, K., Minekawa, S., Yagi, Y., Sasai, S. ortho-Positronium annihilation parameters in polyvinyl alcohol with various degree of polymerization, saponification and crystallinity . Radiochim acta, 89,119. 

The progress in the determination of porosity of various types of materials has arisen over the past ten years from advances in application of new spectroscopy techniques. In the present paper the application of small angle X-ray scattering (SAXS), positronium annihilation lifetime spectroscopy (PALS) and low temperature nitrogen adsorption methods to the characterization of mesoporosity is reviewed using different types of silica gels with chemically modified surface. The results from the three methods are compared and discussed. 

Figure 7.12 Jens Zom sculpture depicting positronium annihilation. Outside University of Michigan Physics Building. (Courtesy of Professor Jens Zorn.)...

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