Velocity Dispersion and the Steepest Slope Theorem for Beam-foil Spectroscopy

An integral equation is derived which relates the decay curve measured by the method of beam-foil spectroscopy to the true time-dependence of the excitation. Approximate solutions are given for a model in which the distributions in angle, speed and excitation are independent and the angle and speed distributions are of Gaussian form; also for this case it is shown that an upper limit to the mean life may be obtained directly and unambiguously from the measured decay curve. The applicability of the model to beam-foil experiments is discussed and an expression obtained for an upper limit to the mean life which should apply in practice to many beam-foil experiments.