Simplified formulas for equivalent-photon spectra of nuclear targets

On the basis of our former work showing that the equivalent-photon method can be used to predict with fairly good accuracy the invariant-mass spectra appearing in various processes of particle production by high-energy nonhadronic particles in the electromagnetic field of nuclear targets, we here propose and check simplified formulas for the equivalent-photon spectra of both a hydrogen target and a heavy nucleus (typically, uranium). In particular, we show that, by using a pointlike unexcitable Dirac proton and making an upper cutoff on the four-momentum transfer variable, one is able to predict reasonably well the total equivalent-photon spectrum (including the contribution of target-excitation effects) of a hydrogen target. Agreement with an exact calculation within ± 10% is achieved for both nuclei H and U by applying our formulas to the process $\gamma +\mathfrak{N}\to \mu +\overline{\mu }+{\mathfrak{N}}^{\prime }$ in an incident-energy range extending from 20 to 400 GeV, and for a wide range of values of the $\mu \overline{\mu }$ invariant mass produced.