Luminosity determination at HERA-B

A detailed description of an original method used to measure the luminosity accumulated by the HERA-B experiment for a data sample taken during the 2002-2003 HERA running period is reported. We show that, with this method, a total luminosity measurement can be achieved with a typical precision, including overall systematic uncertainties, at a level of 5% or better. We also report evidence for the detection of δ-rays generated in the target and comment on the possible use of such delta rays to measure luminosity.