  Given a rational elliptic surface X over an algebraically closed field, we
investigate whether a given natural number k can be the intersection number of
two sections of X. If not, we say that k a gap number. We try to answer when
gap numbers exist, how they are distributed and how to identify them. We use
Mordell-Weil lattices as our main tool, which connects the investigation to the
classical problem of representing integers by positive-definite quadratic
forms.
