Pion elastic and inelastic scattering from Mg24 and Mg26

Reported are measurements of angular distributions of resonance-energy positive and negative pions exciting approximately 40 states in Mg24 and Mg26. These include the (ground state, 0+), (1.36 MeV, 2+), (4.14, 2+), (5.93, 4+), (6.44, 0+), (7.34), (7.55, 3-), (8.33, 3-), (9.32, 4+), (9.97, 5-), (11.08, 3-), (12.06), (13.26), (13.96, 3-), (15.1, T=1, 6-), and (15.4) states in Mg24 and the (ground state, 0+), (1.81, 2+), (2.92, 2+), (3.59, 0+), (4.31, 2++4+), (4.90, 4+), (5.31, 2+), (5.44, 4+), (5.69, 4+), (6.86, 3-), (7.33, 3-), (7.79, 3-), (8.17, 3-), (9.2, possible 6-), (10.30, 4+), and (18.1, T=2, 6-) states in Mg26. The distorted-wave impulse approximation with a Kisslinger form for the optical potential using a -nucleon t matrix at a shifted energy of -25 MeV was found to explain the elastic scattering data from Mg24,26 in the energy range 116-292 MeV that is spanned by these data. Inelastic distorted-wave impulse approximation calculations employing collective-model deformation parameters were simultaneously fitted to the + and - data for each state. The deformation parameters and matrix elements in most cases compare favorably with results from other studies. Published s-d shell-model calculations using one value for the effective charges were found to reproduce the trend of both the strengths and ratios of neutron-to-proton matrix elements for the 2+ and 4+ states. The data at the first maximum in the inelastic angular distributions for Mg24 and that from other studies for C12, Si28, and Ca40 show that the cross section for + scattering is equal to that for - scattering, which forces the proton deformation parameters to be greater than the neutron deformation parameters and gives a ratio of neutron-to-proton elements to be less than unity. This difference from unity is interpreted as a measure of the failure of the model and a systematic error of 11% is assumed to dominate the errors in the results for Mg26. Coupled-channels calculations employing monopole form factors are compared to data for low-lying 0+ states in Mg24 and Mg26.