Annihilation event

The camera actually images the annihilation events, not the radioactive decay events directiy. Thus imaging of high energy positron emitters can have a limiting resolution owing to the range of the positron. 

MLCT) state occurs with an efficiency < es approaching 100%. Consequently, the overall, actinometrically determined ECL efficiency ( ci expressed in emitted photons produced per annihilation event) is close to the luminescence quantum... 

A positron in an electronic media can pick up an electron and form a neutral atom called Positronium (Ps) [9], The existence of Ps and its chemical reaction with molecules was detected from annihilation photons in 1951 [10], Ps is formed in most molecular systems. Due to the different combinations of positron and electron, there are two states of Ps the para-Ps (p-Ps) from the anti-parallel spin, and the ortho-Ps (o-Ps) from the parallel spin combination. The lifetime and the annihilation events for p-Ps and o-Ps are very different from each other, as given by electromagnetic theory. Figure 1.1 shows basic physical properties of Ps and compares them with the H atom, although it should not be considered an isotope of H (see problems 1.5 and 1.6 and answers at the end of this chapter). 

The Feynman diagram for the simplest annihilation event shows that annihilation is possible when the two particles are Ax h/mc 10 12 5 m apart, and that the duration of the event is At h/mc2 10-21 s. The distance is the geometric mean of nuclear and atomic dimensions, which is probably not significant. The distance is so much smaller than electronic wave functions that it may be assumed to be zero in computations of annihilation rates. The time is so short that, during it, a valence electron in a typical atom or molecule moves a distance of only ao/104, so that a spectator electron can be assumed to be stationary and the annihilating electron can be assumed to disappear in zero time. Thus the calculation of annihilation rates requires the evaluation of expectation values of the Dirac delta function, and the relaxation of the daughter system (post-annihilation remnant) can be understood with the aid of the sudden approximation [4], These are both relatively simple computations, providing an accurate wave function is available. 

The duration of the annihilation event should not be confused with the positron lifetime, which is the time required for the electron and positron... 

Since both 511 keV photons resulting from a 2y-annihilation event transmit equivalent information, one photon may be used to determine the age of the annihilating positron and the other for the correlated measurement of the momentum of the annihilating positron-electron pair by measurement of the... 

In Eq.lO the Boltzmann population is assumed. Although the model predictions and experimental data are consistent, it is very difficult to state firmly that the equilibrium population of the states has already been reached. The population depends exponentially on the energy, and this in turn depends on the square of the oid radius, thus it is extremely sensitive to the accepted radius value. The pore radii acting in annihilation processes need not be identical with. say. the hydraulic pore radius. Additional distortion of experimental s. R dependence can be due to the difference in the efficiency of registration of 2y and 3y annihilation events. However, the results presented abo e indicate that the model parameter AR = 0.19 nm allows us to accept the commonly used LN pore radius in annihilation experiments... 

From Eqs. (5.4) and (5.5) it follows that each appearance of is associated with the creation or annihilation of a photon. It is thus readily apparent that the first non-zero contribution from Eq. (5.7) is the fourth-order term, corresponding to four separate photon creation and annihilation events these comprise the two annihilations of real photons from the incident light, and the creation and annihilation of the virtual photon which couples the two molecules. 

In fact, the photon creation and annihilation events at each molecule appear simultaneous, as far as real experimental measurements with finite time resolution are concerned. However, the time-energy uncertainty relation does permit short-lived states that are not properly energy-conserving. This helps explain why it is necessary to include diagrams corresponding to time sequences in which a virtual photon is created before either real photon arrives. It nonetheless transpires that such apparently unphysical cases produce the smallest contributions to the matrix element. 

Figure 3.1. (a) True coincidence events (b) Random coincidence events detected by two detectors connected in coincidence along the dotted line. The two 511-keV photons originated from different positron annihilations, (c) Scattered coincidence events. Two scattered photons with little loss of energy originating from two annihilation events may fall within PHA window and also within coincidence time window to be detected as a coincidence event by two detectors. 

The last step in data acquisition is the storage of the data in the computer. Unlike conventional planar imaging where individual events are stored in an (X, Y) matrix, the coincidence events in PET systems are stored in the form of a sinogram. Consider an annihilation event occurring at the position in Fig. 3.3a. The coincidence event is detected along the LOR indicated by... 

A sinogram is a (a) hie containing individual annihilation events, (b) a matrix of parallel projection data, (c) a matrix of fan beam projection data, and (d) reconstructed image. 

Further analysis of Eq. (17) demonstrates, as noted for Eq. (15), that the intensities one observes for the probe-surface energy transfer through singlephonon creation and annihilation events are modified by a surface-temperature-dependent factor analogous to the Debye-Waller factor that appears in neutron and x-ray scattering [44]. In HAS file Debye-Waller exponent 2W is often approximated as [44], where kg is the Boltzmann con-... 

The annihilation constant A is given as the number of annihilation events per unit density and unit time. It is obtained from the life time of positronium, which for the singlet state (para-positronium) is T2y = 1.25 X 10 ° s [13], and for the triplet state (ort/io-positronium) is = 1.42 X 10 s [14]. The positronium decay rate is related to the decay constant via... 

In order to reduce errors resulting from the detection of Compton scattered photons (which can be as high as 35%[ 1), which lead to anomalous positioning of annihilation events, energy selection of the photons is... 

It is possible to subtract a contribution due to annihilation events in the source... 

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