True and accidental coincidences

This time difference, called the correlation time, is stored in a histogramming memory, and after the necessary processing time (dead time the TDC is reset and waits for the next START signal. The histogramming memory collects all individual coincidences by sorting them according to their correlation times. In this way, a time spectrum is obtained which can be transferred to a computer. 

Even if each electron pair were emitted at exactly the same moment, the associated START-STOP time difference would vary from pair to pair. This is because of the different travelling times of the coincident electrons from their places of origin to the electron detector as well as the different processing times of the electron detector, including the construction of the electronic pulse. Hence, the coincident electrons will lead to a certain time spectrum as shown in the section of the spectrum in Fig. 4.48 which is labelled true coincidences. The name true coincidences implies that these are the coincidences in which one is interested. 

Obviously, the coincidence resolving time At, shown in Fig. 4.48, has to be large enough to accept all these true coincidences. However, this finite value of At then leads to the recording of not only the desired true coincidences, but also of accidental coincidences (also called random or false coincidences). As indicated by the name, these accidental coincidences accidentally follow one another within the time At. Hence, they are due to any two electrons which match the conditions set by the experimenter for the selected double ionization process they might originate from two different double-ionization processes, two single-ionization processes, or 

In the calculation for the probability of START signals accepted by the coincidence 

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After this detailed treatment of true and accidental coincidences, all the statements derived so far for a good performance for coincidence experiments can be summarized ... 

Figure 5.31 Time correlation spectrum between 4d5/2 photoelectrons and N5-O2 3O2 3 S0 Auger electrons in xenon, recorded with a time-to-digital converter. Note the repetition rate, 208 ns, of the circulating electron bunches in the storage ring. The large second peak contains true and accidental coincidences, and the periodic structure is due to accidental coincidences only. From [KSc93].

Following the general discussion in Section 4.6.2, the rates of true and accidental coincidences can be estimated. This possibility is of special interest because it allows better control of the experiment, and it can open ways to improve the experimental conditions further. Using subscript 1 for photoelectrons and subscript 2 for Auger electrons, in the present case the following parameters for such an estimation of coincidences are needed ... 

If n is the target gas density and / the incident current, the number of true and accidental coincidences in time T can be written respectively as... 

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