We analyze if the nucleon structure of the $alpha$ decaying nucleus can be visible in the experimental bremsstrahlung spectra of the emitted photons which accompany such a decay. We develop a new formalism of the bremsstrahlung model taking into acco
unt distribution of nucleons in the $alpha$ decaying nuclear system. We conclude the following: (1) After inclusion of the nucleon structure into the model the calculated bremsstrahlung spectrum is changed very slowly for a majority of the $alpha$ decaying nuclei. However, we have observed that visible changes really exist for the $^{106}{rm Te}$ nucleus ($Q_{alpha}=4.29$ MeV, $T_{1/2}$=70 mks) even for the energy of the emitted photons up to 1 MeV. This nucleus is a good candidate for future experimental study of this task. (2) Inclusion of the nucleon structure into the model increases the bremsstrahlung probability of the emitted photons. (3) We find the following tendencies for obtaining the nuclei, which have bremsstrahlung spectra more sensitive to the nucleon structure: (a) direction to nuclei with smaller $Z$, (b) direction to nuclei with larger $Q_{alpha}$-values.
A high precision method to determine fusion in the capture of $alpha$-particles by nuclei is presented. For $alpha$-capture by $^{40}{rm Ca}$ and $^{44}{rm Ca}$, such an approach gives (1) the parameters of the $alpha$--nucleus potential and (2) fusi
on probabilities. This method found new parametrization and fusion probabilities and decreased the error by $41.72$ times for $alpha + ^{40}{rm Ca}$ and $34.06$ times for $alpha + ^{44}{rm Ca}$ 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, Wongs 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 $alpha + ^{40}{rm Ca}$ and $alpha + ^{44}{rm Ca}$, 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 $alpha + ^{46}{rm Ca}$ is predicted for future experimental tests. The role of nuclear deformations in calculations of the fusion probabilities is analyzed.
