Study of the Difference between the Spin-Orbit Potentials of 3He and t by the Resonating Group Method

Scattering experiments of 3He and triton (t) have been extensively performed using the polar ized beams and analyses of these data by the optical potentials have given us rich information on the spin-orbit (t. s) potentials of these pro jectiles. However, the obtained parameters of the l· s potentials fot 3He and those for tare found to be fairly different from each other. The l' s potentials for 3He obtained by Birmingham group 1) have very small diffuseness parameter (aso"='O.2 fm) and the radius parameter for the l· s potential rs~ is somewhat larger than that for the central potential. On the other hand, the l· s potential for t obtained by Los Alamos group2) are deeper at least twice than are expected by the folding model. Typically V so ( t) / V so ( 3He) = 2 ~ 3, rso(t) / rso('He) =O.8~O.9 and aso(t) / aso('He) =3~4. It is therefore quite interesting to study micro scopically how difference can be derived between the l· s potentials of 3He and t. In this paper we report the results of the study of the difference between the l· s potentials of 3He and t; the equivalent local l· s potentials are obtained from the non-local potentials of the resonating group method (RGM) by the use of the WKB approx imation. The procedure to derive the l· s potential for composite projectiles by the RGM is explained in detail in Ref. 3). Since the nuclear force between two nucleons is isospin invariant, the difference between the l' s potentials of 3He and t arises only from the difference in the Coulomb forces for these two projectiles. Stronger Coulomb force for 3He causes smaller local momentum for this projectile compared with that for t at the same incident energy. The smaller the local momentum is, the larger the exchange contributions in the Wigner transforms of the RGM non-local potentials are. As is explained in Ref. 3), the l' s potential comes not only from the two-nucleon spin-orbit interaction directly but also from the two-nucleon central interaction and the kinetic energy as a