Attenuation

  A name given to phenomena of reduction of intensity according to the law

resulting in an exponential decay

In this equation t may be time (e.g. attenuation of a circulating beam) or length (e.g. attenuation of light in a light guide (fibre) or scintillator), or any corresponding continuous variable. The attenuation time or attenuation length is given by , the time (length) over which the intensity is reduced by a factor . Frequently I is a discrete variable (number of particles), and the factor is due to the exponential distribution of individual lifetimes. then is the expectation value of the distribution, i.e. the mean lifetime .

If the intensity at time zero is I₀ and is the lifetime or attenuation time, then the average intensity over a time is given by .