The resonant scattering integral; application to the analysis of elastic proton scattering

Abstract

A relationship is presented which permits a determination of the quantity Γ2/Γ, where Γ and Γ are the particle (proton) and total widths, respectively, of an isolated resonance of which the total spin and channel spin mixing parameter are known. The analysis depends upon observation at a zero of the relevant Legendre polynomial, and hence only resonances for which ≠ can be analysed. Since the relationship is independent of instrumental resolution, it can be expected to yield better values of the parameters than the usual curve fitting procedure. The results are independent of target thickness, counter efficiency and solid angle, and current integrator precision. The formula given is valid if there is no appreciable l-mixing, no overlap of resonances, and if the “hard-sphere” correction to the Rutherford scattering is negligible. Tables are given showing where the latter approximation may be expected to break down. The restriction on l-mixing can be removed if the parity allowed l's are odd, since observation at 90° (C.M.) makes all interference terms vanish. If the allowed l's are even it is still possible to apply the formula given if an angle of observation can be found where the interference terms vanish. In both cases difficulty will be encountered in evaluating the results since the l-mixing parameter must be known. It is also shown that if the off-resonant scattering can be quantitatively compared to the Rutherford scattering, the range of application of the formula can be extended to cover all well-separated resonances. The extended formula depends, however, on the constancy (not the absolute value) of target thickness, counter efficiency and solid angle, and current integrator calibration. The analysis is applied to published data on the elastic scattering at a bombarding energy of 1.286 MeV in the 23Na (, ) reaction.