Unification of intermediate energy hadron spectra with small energy losses

Abstract

Proton beams near 1GeV may serve as prolific generators of secondary neutrons, with some neutron energies near the beam energy. These very energetic secondary neutrons in turn may generate further reactions in thick samples. Direct measurement of the cross sections for GeV-scale neutrons is difficult, leading to uncertainties in flux calculations for many proposed applications. The present work uses a simple kinematic reaction model to form a scaling response suited to compare (p,nx) spectra for a wide range of beam energies, angles and target nuclei, to enable comparisons, interpolations and perhaps extrapolations of these difficult data. If the approximations of the method below are valid, one could also relate (p,nx) and easier (p,px) measurements. The goal of this work is to compare a wide range of (p,px) and (p,nx) spectra with small energy losses for intermediate energy proton beams by way of scaling relations found to be success- ful for the simple (e,ex) reaction. This method must assume incoherent, quasifree factorization of the nuclear response and simple scattering of the proton from a single bound nucleon. Free (off-shell) singly differential cross sections are used for the reaction, and the response is taken to be proportional to the number of nucleons seen once and only once by the projectile, as calculated in the eikonal Glauber manner. This computation uses in-medium total cross sections for proton- nucleon scattering. For low energy losses, the most useful scaling is that due to Bjorken, with the kinematic variable xB = (q 2 − ω 2 )/2Mω, with q the lab frame 3-momentum transfer from the projectile, ω the lab frame energy loss of the projectile and M the free nucleon mass (1). Free proton-neutron charge exchange would occur at xB = 1, and the variable xB can be understood as the fraction of the total nuclear momentum found in that one single struck nucleon. Important corrections for charge and binding energy are used, as presented for the (p,px) spectra in (2). The Bjorken response is then FB = d 2 σ/dω dΩ