Conclusions

We have made predictions of the observables of the elastic scattering of 200 MeV protons from the even-even isotopes of Sn from ¹⁰⁰Sn to ¹⁷⁶Sn. The model we have used for the structure of the isotopes is a Hartree-Fock-Bogoliubov model using the Skyrme interaction for which two parameterizations have been used. The matter densities obtained from those models show consistent trends: as mass increases from A = 100 to 176 the neutron central density increases and a neutron skin emerges. Also, as proton number is fixed, the addition of neutrons not only increases the volume but also engenders a dilution of the proton distribution.

The changes in the neutron density are reflected in the predictions made for the differential cross sections of 200 MeV proton elastic scattering. As neutron number increases, the first three minima tend to lower momentum transfers and the intervening first maximum becomes more pronounced. Such is the effect of the neutron skin as it becomes manifest. There is also some variation in the spin rotation, Q, as mass increases, although those variations are less striking. In the case of ¹¹⁸Sn and ¹²⁰Sn, comparison with available proton elastic scattering data shows some distinct features: there is very little difference between the densities obtained from the two HFB models considered. While those models do better in the specification of the density of ¹¹⁸Sn in comparison to a naive oscillator model, the predictions for the scattering from ¹²⁰Sn do not fare as well. This demonstrates the value of comparison to proton elastic scattering data in testing model specifications of the ground states of nuclei.

It is hoped that with the proposed new generation of radioactive beam facilities that data for the elastic scattering of heavy neutron-rich nuclei from hydrogen are obtained. The model we have used in obtaining our predictions is sensitive to the details in the neutron density and serves as an important testing ground for the models being developed to describe such nuclei.

This work was supported by a grant from the Australian Research Council, by DOE Contract no. W-7405-ENG-36, and by the Polish Committee for Scientific Research (KBN) under Contract No. 5 P03B 014 21. We also gratefully acknowledge the assistance of Mr. Dirk van der Knijff of the Advanced Research Computing group, Information Division, University of Melbourne not only for use of the high performance computers of that group to find all of the results displayed but also for the technological help to process that data to form the graphs themselves.