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

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=20N=20. To provide deeper insight into the physics of nuclei with the new magic number N=26N=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.