Effects of Excited Levels on Coulomb Scattering

Abstract

It may be expected that, when excited levels of colliding nuclei are taken into considera­ tion, some corrections to the differential cross section of the Rutherford scattering are needed. When the projectile is heavy, it is also necessary to carry out a higher order approximation for the differential cross section of the Coulomb excitation. We have examined these effects of excited levels by using a perturbation expansion in quantum mechanics. For practical calculations, 62Sm 152 is used as a target nucleus, and a spinless proton (6.05 MeV) and an oxygen ion (50 MeV) are used as projectiles. In the case of head-on collision of the spinless proton, the differential cross section for elastic scattering is decreased by about one percent in comparison with that of the Rutherford scattering. In the case of 80 16 , the deviation from the Rutherford scattering is expected to amount to 10 percents. It is shown that the fundamental relation .:Edrri=drrn in the semi-classical theory (SCT) holds with good accuracy in the case of proton bombardment. A quantum mechanical expression for the reorientation effect in the Coulomb excitation is also derived in the second order approximation. Among those terms which are contained in the excitation cross section, a term, which is proportional to the product of the wave number of the projectile and the quadrupole moment of the first excited state, is the most effective one for the reorientation. Though comparison of our re­ sults with those obtained by the SCT has not yet been made, analysis of experimental data seems to indicate inadequacy of the application of the SCT in higher order approximations.