Test of the DWBA in (3He, α) reactions leading to configuration and analogue states

The DWBA methods are re-examined to analyse the reactions 50, 52, 54Cr(3He, α) at EHe = 18 MeV. The use of the (3He, α) reaction as a spectroscopic tool is limited by the angular momentum mismatch which causes the nuclear interior to contribute significantly to the reaction. As a consequence, some of the usual approximations become critical. The “measured” elastic scattering parameters do not sufficiently determine the cross sections. In addition, the degenerate sets of parameters for composite particle scattering in both channels cannot be combined arbitrarily. However, the exact matrix element of the distorted wave theory indicates that the α potential should be roughly equal to the sum of the 3He and neutron potentials. This prescription was found to be valid by calculations of mismatch transitions using all the possible combinations of measured parameters in both channels. The effects of nonlocality and finite range are discussed. It is shown that a sharp radial cutoff is not permissible. The effects of spin-orbit coupling on the angular distributions and absolute cross sections are investigated; the J-effects of the data are partially overestimated by the calculations. The absolute normalization factor of the DWBA cross section, derived from the present analysis, agrees with theoretical predictions. The accuracy of the extracted spectroscopic factors is discussed. The bound state wave functions for the analogue state transitions are obtained by solving the coupled Lane equations. This leads to agreement of the derived spectroscopic factors with the sum rule predictions.