The neutron magnetic form factor G_M^n(Q^2) from Quasi-Elastic inclusive scattering data on D and 4He

Abstract

We analyze cross sections for Quasi-Elastic inclusive scattering of electrons on nuclei and show that the observed isolated peaks for relatively low $Q^2$ are unique for the lightest targets. Focusing in particular on D and $^4$He, we investigate in two ways to what measure the above peaks can be allocated to nucleon-elastic processes. We first compute approximate upper limits for the nucleon-inelastic background in the Quasi-Elastic region due to inclusive $Δ$ excitation, and find those to be small. Far more precise is a semi-phenomenological approach, where the dominance of nucleon-elastic processes is translated into a set of stringent requirements. We show that those are very well fulfilled for recent D data, and to a somewhat lesser extent for older D and $^4$He data. With knowledge of $G_{E,M}^p$ and information on $G_E^n$, we then extract $G_M^n$ and find agreement with values obtained by alternative methods. We discuss the sensitivity of the extraction method and mention future applications.