Unification of intermediate energy hadron spectra with small energy losses

Abstract

Abstract. Proton beams near 1 GeV 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 successful 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 protonnucleon scattering.For low energy losses, the most useful scaling is that due to Bjorken, with the kinematic variable x B = (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 x B = 1, and the variable x B 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 thenusing measured doubly-differential cross sections. All published (p,nx) spectra to be found, from 345 to 1600 MeV, have been transformed in this fashion into responses F B . If these are the same for combinations of beam energy, scattering angle and nuclear target, several forms of scaling will have been identified. Once shown to be valid, one can use these relations to interpolate, extrapolate or evaluate the cases of interest. Since the determination of the cross sections for high energy neutrons is most difficult, these are the cases presented here, at large values of x B . Production of such high energy neutrons can lead to secondary or cascade reactions in thick samples, making these scaling relations an important tool for many applications of accelerator-produced neutrons.