The calculation of annihilation rates

A given system in a given state has only one annihilation rate. The terms two-photon annihilation rate, three-photon annihilation rate , and spin-averaged annihilation rate, sometimes seen in the literature, have no operational meaning and are not measurable [5]. 

Despite this, the spin-averaged annihilation rate is a useful concept. If a positron is immersed in an electron-rich medium in which all electron 

While this exact value is not the annihilation rate for any real system, it is remarkable how many diverse closed-shell systems have annihilation rates close to it. Presumably, this is because the buildup of electron density at an embedded positron quickly saturates due to moderating Coulomb repulsion and exclusion effects except in media of extreme electron densities. One estimation of the effective number of electrons gathered around the positron in closed-shell systems is its annihilation rate divided by the rate on the right side above. 

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

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. 

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