  The electromagnetic scattering of a spin-0 charged particle off a fixed
center is calculated in first-order quantum perturbation theory.
  This implies evaluating the square of a `Dirac delta-function,' an operation
that is not defined in Schwartz distribution theory, and which in elementary
text-books is dealt with according to `Fermi's golden rule.'
  In this paper these conventional calculations are carefully reviewed, and
their crucial parts reformulated in a Colombeau algebra -- in which the product
of distributions is mathematically well defined.
  The conclusions are: (1) The Dirac delta-function insuring energy
conservation in first order perturbation theory belongs to a particular subset
of representatives of the Schwartz distribution defined by the Dirac measure.
These particular representatives have a well-defined square, and lead to a
physically meaningful result in agreement with the data. (2) A truly consistent
mathematical interpretation of these representatives is provided by their
redefinition as Colombeau generalized functions. This implies that their
square, and therefore the quantum mechanical rule leading from amplitudes to
probabilities, is rigorously defined.
