The effect of projectile shape on cross sections and momentum distributions of fragments from heavy ion reactions is studied. We propose a new approach that implements the underlying symmetries of each isotope with a few parameters directly in the density. Various densities and their nuclear structure are then analyzed in the reactions of $^{12}$C and $^{11}$Li, $^{11}$Be, and $^{11}$C on a carbon target.

The main results obtained during the last ten years in the framework of the method of hyperspherical functions are reviewed. New developments of the mathematical formalism of the method are presented. The main results on the application of the method in the theory of many-particle reactions are given. The results of application of the method of hyperspherical functions in the investigation of collective excited states of light nuclei, and also of elastic and inelastic cross sections for reactions with ions are reviewed. An approach to the solution of the Coulomb problem in a hyperspherical basis is described, and a method for taking into account simultaneously the nuclear and Coulomb interactions is formulated. The main results of the application of the method of hyperspherical functions for the study of the structure of multiquark systems are presented. A review of results on the development of the hyperspherical approach to the solution of the Faddeev equations is given.

Within the analytic folding model analytic expressions are found for potentials in the system of interacting heavy ions. A simple parametrization is proposed for the distribution densities of matter in light nuclei calculated in the hyperspherical-function method. The potentials are calculated numerically with the use of finite-range effective forces for the systems4He+4He,4He+6Li,4He+12C,4He+16O,6Li+6Li,6Li+12C,6Li+16O,12C+12C,12C+16O,16O+16O.

The interaction potential of heavy ions4He,6Li,12C and16O is constructed in the folding model. The density distribution of nuclear matter for these nuclei is calculated in the framework of the hyperspherical function method. For the calculation of the folding potentials we have employed the Skyrme nucleon-nucleon forces. The influence of several effects on the results of calculations is studied: the role of the three-body forces of the nucleon-nucleon interaction, dependence of the folding potential on the mass numbers of the colliding nuclei and the possibility of observing the monopole resonance in the ion inelastic scattering. Using our folding potential as a real part of the optical potential we have calculated the differential cross section of elastic scattering of6Li from12C at laboratory energy of lithium ionsT L =90.0 MeV. Reasonable agreement with experiment is obtained.

Consideration is given to the properties of light nuclei in the method of hyperspherical functions with central realistic potentials. In general, the following set of parameters can be described satisfactorily for the nuclei: binding energy, excitation energy of monopole resonance, RMS radius, elastic and inelastic form factors. The detailed reproduction of the relevant data for each nucleus necessitates the solution of the inverse problem and requires that the corresponding nucleon-nucleon potential (which will probably vary from nucleus to nucleus) be found.

The complication effects in the highly-excited state structure (impurity of the complex configurations of the 2p2h type) of the (γ, n), (e, e′) and (Μ−, γ) nuclear reactions with the40Ca nucleus have been studied in terms of the ph-approximation including the following effects: (a) the presence of states of the two particles — two holes type, (b) rigidity loss by nucleus in excited state.

The paper deals with the photonucleon energy spectra for two branches of the giant resonance (T< andT>) on the basis of the microscopic theory of the pre-equilibrium decay. The first stage of the reaction is described by the wave function obtained by matrix diagonalization based on particle-hole configurations (T< andT>). The densities of the intermediate complex statesJ = = 1− (T< andT>) are calculated with the Saxon-Woods potential. Specific calculations have been made for the nuclei of60Ni and90Zr.