Neutron scattering studies of the even-A tin isotopes

The tin isotopes 116118120122124Sn make a uniquely interesting set for neutron scattering studies. Because they are proton magic, these isotopes are very similar. Important differences between them are correlated with the neutron excess, (N - Z/A). Differential neutron scattering cross sections at bombarding energies of 1.00, 1.63 and 4.02 MeV, and neutron total cross sections from 0.3 to 5.0 MeV have been measured for >90% enriched samples of these isotopes using the time-of-flight technique. At 1.00 MeV the scattering is all elastic. At 1.63 MeV one inelastic scattering state was excited and detected. At 4.02 MeV, many inelastic scattering channels are open and inelastic scattering was measured up to an excitation energy of about 2.7 MeV. Some of the measurements have been fitted with a spherical optical model plus statistical model. The effect of different parameters in the equation for nuclear radius is explored. The need for channel coupling among the ground state and the 2- and 3- vibrational states is evident from the 4.0-MeV inelastic scattering from these states. The four data sets were separately analyzed with a model including vibrational coupling. A single coupled channels potential has been derived that fits all the measured cross sections within 2 or 3 standard deviations. In all the analyses, the well depths are dependent on energy and neutron excess. The imaginary well depth neutron excess dependence in all analyses is 3 to 5 times the global value of 12 MeV