Nuclei as generators of quasireal photons: Testing an equivalent-photon method for calculating invariant-mass spectra

It is shown that the equivalent-photon method (Williams-Weizsäcker method) can be used to predict, with a good approximation, the invariant-mass spectra produced in various processes of inelastic scattering of high-energy nonhadronic particles (photons, charged leptons, neutrinos) in the electromagnetic field of nuclear targets. The test cases here considered are $\gamma +\mathfrak{N}\to \mu +\overline{\mu }+{\mathfrak{N}}^{\prime }$, $\mu +\mathfrak{N}\to \mu +\gamma +{\mathfrak{N}}^{\prime }$, $\mu +\mathfrak{N}\to \mu +{\gamma }^{*}+{\mathfrak{N}}^{\prime }\to +\mu +\mu +\overline{\mu }+{\mathfrak{N}}^{\prime }$, and $\nu +\mathfrak{N}\to \mu +W+{\mathfrak{N}}^{\prime }$. The nuclear targets involved in this study are ${}_1{}^{}{}_{}{}^{}\mathrm{H}_{}^1{}_{}{}^{}$ and ${}_{92}{}^{}{}_{}{}^{}\mathrm{U}_{}^{235}{}_{}{}^{}$. On the target side, both coherent scattering (in the case of uranium) and elastic plus inelastic scattering of individual nucleons are included in the calculations. For all four processes, both target nuclei and all partial contributions considered (as well as for the sum of these contributions), we compare the exact and the approximate values obtained for $\frac{d\sigma }{\mathrm{dW}}$, where $W$ is the invariant mass of the system produced at the incident-particle vertex. A factorization formula, based on a helicity treatment, is used in the exact calculation; the equivalent-photon spectrum introduced is also derived from that formula.