Indirect method to measure differential cross-sections for nuclear reaction analysis

Accurate knowledge of differential cross-sections is essential for studying concentrations of light elements in heavy substrates by nuclear reaction analysis (NRA). In this paper we present an indirect method of determining excitation functions of NRA taking the nuclear reaction ¹⁹F(p,α₀)¹⁶O as an example. The methodology is demonstrated in detail for a backscattering angle of 150° using a bulk CaF₂ sample and proton beam energies of 1335, 1535, 1735 and 1935 keV. The differential cross section is directly extracted from the yield of backscattered reaction particles for an energy range of 800–1900 keV. To validate the procedure, a further fluorine-containing sample (NaF) was measured for comparison. The method was additionally applied to backscattering angles of 90° and 170°. The results obtained were compared with known data found in literature and a good agreement is observed. The approach presented here offers the possibility for measuring the excitation functions in a simple manner for individual measurement configurations. The method can be applied if the detected reaction particles have larger energies than particles that are elastically backscattered from the heavy matrix and if the cross section does not exhibit a fine structure with a width of the resonances which is below the energy uncertainty caused by detector resolution and energy straggling