Time Dependence of Photon Emission

Since the photons are emitted as a result of decays of excited states, the time of their emission depends on the decay constants of the different states involved. Experiments show that the emission of light follows an exponential decay law of the form 

Most of the excited states in a scintillator have essentially the same lifetime 

In a counting system using a scintillator, the light produced by the crystal is amplified by a photomultiplier tube and is transformed into an electric current having the exponential behavior given by Eq. 6.1. This current is fed into an RC circuit as shown in Fig. 6.5, and a voltage pulse is produced of the form 

In practice, the value of RC is selected to be of the order of a few hundreds of microseconds. Thus, for short times—i.e., t RC, which is the time span of interest—Eq. 6.2 takes the form 

Notice that the rate at which the pulse rises (risetime) is determined by the decay time T. In certain measurements, e.g., coincidence-anticoincidence measurements (Chap. 10), the timing characteristics of the pulse are extremely important. 

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