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

Maydanyuk, Sergei and Zhang, Peng-Ming and Belchikov, Sergei V (2015) Quantum design using a multiple internal reflections method in a study of fusion processes in the capture of alpha-particles by nuclei. NUCLEAR PHYSICS A, 940. pp. 89-118. ISSN 0375-9474

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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 probabil- ities. This method found new parametrization and fusion probabilities and decreased the error by 41.72 times for α +40 Ca and 34.06 times for α +44 Ca 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+40 Ca and α+44 Ca, 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 +46 Ca is predicted for future experimental tests. The role of nuclear deformations in calculations of the fusion probabilities is analyzed. Keywords: alpha-capture, tunneling, multiple internal reflections, wave packet, fusion probabilities, coefficients of penetrability and reflection, sharp angular momentum cut off, magic neutron numbers, alpha-decay.

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