Quantum design using a multiple internal reflections method in a study of fusion processes in the capture of alpha-particles by nuclei

Abstract

A high precision method to determine fusion in the capture of α-particles by nuclei is presented. For α-capture by 40Ca and 44Ca, such an approach gives (1) the parameters of the α–nucleus potential and (2) fusion probabilities. This method found new parametrization and fusion probabilities and decreased the error by 41.72 times for α+Ca40 and 34.06 times for α+Ca44 in a description of experimental data in comparison with existing results. We show that the sharp angular momentum cutoff proposed by Glas and Mosel is a rough approximation, Wong's formula and the Hill–Wheeler approach determine the penetrability of the barrier without a correct consideration of the barrier shape, and the WKB approach gives reduced fusion probabilities. Based on our fusion probability formula, we explain the difference between experimental cross-sections for α+Ca40 and α+Ca44, which is connected with the theory of coexistence of the spherical and deformed shapes in the ground state for nuclei near the neutron magic shell N=20. To provide deeper insight into the physics of nuclei with the new magic number N=26, the cross-section for α+Ca46 is predicted for future experimental tests. The role of nuclear deformations in calculations of the fusion probabilities is analyzed.