Annihilation rate calculation

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

Electron-positron annihilation in Ps2 was investigated by Tisenko (1981), who, using the relatively simple wave function of Hylleraas and Ore (1947), obtained the annihilation rates into two and three gamma-rays as 16 ns-1 and 0.043 ns-1 respectively. No such calculations have been performed using the more elaborate wave function of Ho. 

We first review some elementary physics that establishes the kind of quantum mechanics that can be profitably applied to mixed electron-positron systems. Next we describe some methods of calculation that have proven to be useful recently. Finally, all the binding energies and annihilation rates that are known for atomic and molecular systems are listed in tables and discussed. 

The most interesting quantities of mixed systems that can be both calculated and measured today are binding energies, annihilation rates, and momentum distributions of the annihilation photons. A system has a binding energy in some state if it is chemically stable in that state, meaning that it stays in that state until it annihilates. More properly, we say that a system is chemically stable in some state if its annihilation rate is greater than the sum of the rates of all other processes that depopulate that state. 

When an accurate wave function is calculated by some effective method, we can calculate an accurate annihilation rate with the use of an effective annihilation operator [5] ... 

The SVM method gives the energy directly, and the wave function provided by SVM is well-suited to the calculation of annihilation rates. 

The QMC method is ideally suited for mixed systems because electron-positron correlation, which is difficult to treat with Cl methods, is automatically treated correctly. Systems of up to a bit more than ten leptons are routinely treated. Effective core potential methods can be used to extend the method to larger systems. Expectation values of local operators for the distribution k 2 are calculated by straightforward sampling procedures, but nonlocal operators, such as those for the annihilation rate, are problematic and are under active investigation [12],... 

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 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 positron lifetimes for different defects in MgO are calculated using the insulator model of Puska and co-workers. In this model, the annihilation rates are determined by the positron density overlapping with the enhanced electron density that is proportional to the atomic polarizability of MgO [8, 9]. Based on comparison between experimental and calculated values [5, 6], the positron lifetime of the embedded Au nanoparticle layer, 0.41 ns, suggests that positrons are predominantly trapped in clusters consisting of... 

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. 

The hadronic wavefunction in equation (13) is obtained numerically after performing a partial-wave decomposition, as is described in Ref. [5]. With the aid of (R) and P R) the direct leptonic annihilation rate can be calculated according to equation (19). 

For such low values of Q many important annihilation channels involving two heavy mesons (p, co, ri, rj, . ..) are simply closed. Other two-body channels such as np, Ttco are considerably suppressed due to the closeness to the threshold. As is well known, the two-pion final states contribute only about 0.4% of the annihilation cross section. Even in vacuum all above mentioned channels contribute to OA not more than 15% [53]. Therefore, we expect that only multi-pion final states contribute significantly to antiproton annihilation in the SBN. But these channels are strongly suppressed due to the reduction of the available phase space. Our calculations show that changing Q from 2 to 1 GeV results in suppression factors 5, 40 and 1000 for the annihilation channels with 3, 4 and 5 pions in the final state, respectively. Applying these suppression factors to the experimental branching ratios [54] we come to the conclusion that in the SBNs the annihilation rates can be... 

The lifetime distribution for PTMSP at ambient ten rature is shown in Figure 1. Using this distribution, the size distribution of FV was calculated by means of Equation 1. Naturally, the o-Ps size distribution consists of two peaks (Figure 2). The dashed line in Figure 2 shows the calculated dependence of the annihilation rate (Xi=l/Xi ns ) versus FV radius used in conq>uting the size distribution by means of Equation 1. 

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