Angular Momentum Limitations in Heavy Ion-Induced Fusion Reactions Leading to CALCIUM-40 and CALCIUM-42.

Cross sections for the fusion of ^ {28}Si + ^{12} C from 4.6 to 9.4 MeV/nucleon and ^ {30}Si + ^{12} C from 5.2 to 8.3 MeV/nucleon have been measured. The bombarding energy covered in these experiments extends from the intermediate to high energy regimes of the fusion excitation function where the fusion cross section is known for most heavy ion-induced reactions to be decreasing. The decrease in the high energy fusion cross section is understood to be caused by a limitation imposed on the fusing system by the maximum angular momentum (l_ {rm cr}) the system can sustain. The mechanisms which determine the l_ {rm cr} for a particular projectile -target combination, or entrance channel, are however, not understood. It has been found that the characteristics of the entrance channel, rather than those of the compound nuclei ^{40}Ca and ^{42}Ca, determine the l_{rm cr} for the ^{28}Si + ^ {12}C and ^{30} Si + ^{12}C systems, respectively. The experiments were carried out with the time of flight apparatus at the Holifield Heavy Ion Research Facility at Oak Ridge National Laboratory. Beams of ^{28}Si and ^{30 }Si ions were used to bombard ^ {12}C targets and complete or partial angular distributions for the heavy reaction products with atomic numbers from 24 to 40 were obtained at 6.4, 7.8, and 9.4 MeV/nucleon for ^{28} Si + ^{12}C and 5.2, 5.7, 6.4, 7.5 and 8.3 MeV/nucleon for ^ {30}Si + ^{12} C. Charge and mass identification, combined with a kinematic analysis of the velocity distributions for individual isotopes, allowed separation of the yields from compound nucleus evaporation residues and nonfusion processes. A comparison of the l_ {rm cr} obtained for ^ {28}Si + ^{12} C (l_{rm cr} = 22h) and ^{30}Si + ^{12}C (l _{rm cr} = 24h) to the other entrance channels which lead to the compound nuclei ^{40,42}Ca clearly show an entrance channel limit imposed in the ^{28,30 }Si + ^{12}C systems. This is also consistent with previous measurements made of back-angle deeply inelastic (orbiting) reactions, which imply that the fusion and orbiting systems share the same angular momentum limit. It has been found, based on fusion measurements for a number of different projectile -target combinations, that there is a wide range for the maximum angular momentum sustainable in the system that may depend on the entrance channel mass asymmetry.