Phase Shifts for Elastic P-³H Scattering

Abstract

The elastic scattering data of protons on tritons which had been obtained between 4 and 12 MeV ¹⁾ using the Erlangen polarized proton beam²⁾ has been extensively phase shift analysed. An inspection of the contour plot of the analyzing power A(θ,E) (fig.1), which also includes other data³’⁴⁾ and ranges up to 20 MeV exhibits a structureless dependence of the analyzing power with respect to θ and E. Therefore, a smooth energy behaviour of the phases should be expected. During the phase shift analysis, which included S,P and partially D-waves, two sets of phases (set I and II) have been found which describe the experimental data equally well (fig.2). The phases of set I are identical to the preliminary ones⁵⁾. At higher energies (E_p>8MeV) both set of phases are identical with the p two sets found by Hardekopf et al.³⁾. And indeed the phases of set II of the present analysis were found by starting the search with one of these phase sets. In the present analysis it was also tried to get an estimate of the sensitivity of the fit with respect to the determination of the various phases. For this purpose χ²-contour plots were calculated for each (δη)- combination separately. (An element of the S-matrix is related to δ and ηby S=ηexp (2iδ)). The dashed areas in fig.2 correspond to a 10% change of χ² with respect to its minimum value. Generally, the absorption parameters are less accurately determined by the analysis than the real phases. For the different partial waves the fit is less sensitive to the determination of the S-waves compared with the determination of the P-waves. The D-waves are rather small and not displayed in fig.2. Additionally fig.2 displays a comparison with theoretical phases⁶⁾ (solid lines) which were obtained by a resonating group calculation. They exhibit an overall good agreement with the experimental ones. Within these calculations the coupling of the dd-channel to the p³H-channel has been neglected. The experimental results seem to justify this approximation. But there is a problem concerning the absolute value of the P-phases. The theoretical calculations⁶⁾ predict no crossing of the δ ₁₁ ⁰ -phase through 90^°. Therefore, one gets a level sequence 2⁻,0⁻,1⁻, because δ ₁₁ ² >δ ₁₁ ⁰ >δ ₁₁ ¹ .