Definition of Energy Spectra

A particle energy spectrum is a function giving the distribution of particles in terms of their energy. There are two kinds of energy spectra, differential and integral. 

The differential energy spectrum, the most commonly studied distribution, is also known as an energy spectrum. It is a function n(E) with the following 

TTie integral energy spectrum is a function N E where N E) is the number of particles with energy greater than or equal to E. The quantity NiE) is represented by the hatched area of Fig. 9.1. The integral energy spectrum N(E) and the differential energy spectrum n(E) are related by 

The two examples that follow illustrate the relationship between a differential spectrum and an integral spectrum. 

Example 9.1 Consider a monoenergetic source emitting particles with energy Eq. The differential energy spectrum n(E) is shown in Fig. 9.2. Since there are no particles with energy different from Eq, the value of n(E) is equal to zero for any energy other than E = Eq. 

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