Deep-inelastic structure functions for bound states in the ladder approximation

A simple relativistic expression for the structure function of a two-body $S$-wave bound state in $\lambda {\phi }^3$ theory is obtained at all values of the scaling variable in terms of the Deser-Gilbert-Sudarshan-Ida spectral function of the Bethe-Salpeter wave function in the ladder approximation. A similar result is given for a fermionantifermion bound state with approximate wave function derived from conformal invariance. At small $x$ the structure function has the expected peak broadened by the binding effect and for a fermion-antifermion $S$-wave bound state it behaves like ${\mathrm{}(1-x)\mathrm{}}^2$ as $x\to 1$.