Yu. M. Tchuvil’sky

Cluster states in atomic nuclei and cluster-decay processes

The relationship between decay properties of nuclei (primarily cluster properties) and cluster-decay characteristics is discussed. Both purely microscopic and microscopically substantiated semimicroscopic and semiempirical methods are considered. The current state of the proton-, α-, and cluster-radioactivity theory is presented.

Investigation of the radiative capture reaction t + α → 7Li + γ in the algebraic version of the resonating group method

The radiative capture reaction t + α → 7Li + γ is investigated in the framework of the algebraic version of the resonating group method at low energies. The Hasegawa-Nagata nucleon-nucleon potential is used in calculations. The lowest compatible with the Pauli exclusion principle wave functions of a translationally invariant shell model are adopted as the internal wave functions for α and t clusters. The obtained results are in reasonable agreement with the experimental data.

Alpha decay in electron surrounding

The influence of atomic electron shells on the constant of alpha decay of heavy and mediummass nuclei was considered in detail. A method for simultaneously taking into account the change in the potential-barrier shape and the effect of reflection of a diverging Coulomb wave in the classically allowed region was developed. The ratios of decay probabilities per unit time for a bare nucleus and the respective neutral atom were found for some alpha-decaying isotopes.

Description of the

The 3He(α, γ)7Be nuclear reaction, which is of great interest for modern nuclear astrophysics, is investigated. The astrophysical S-factor of the reaction is calculated using the algebraic version of the resonating group model. The results agree with current experimental data.

^{3}

A microscopic approach based on the algebraic version of the resonating group method was implemented by applying it to the radiative capture reaction 3He(α, γ)7Be. The astrophysical S-factor of the reaction and the branching ratio between the capture to the ground and the first excited states of the 7Be nucleus were calculated. A comparison of the theoretical results with the most recent experimental data was performed, and good agreement with these data was found. Advantages of the theoretical approach realized are indicated, and possible ways to refine upon it are outlined.

He(α, γ)

A class of A-nucleon (for even N = Z) Hamiltonians is found such that they admit, among others, solutions that can be exactly related to solutions to the problem of A/4 alpha particles in the sense that the respective eigenvalues of the two problems coincide and that the A-nucleon solutions can be constructed from the alpha-particle solutions within a procedure that follows from the resonating-group model. It is shown that an effective nuclear Hamiltonian close to a realistic one possesses these properties, the alpha-particle states in nuclei having basic properties of an alpha condensate and, frequently, a normal nuclear density. The statistics of alpha particles (and other composite bosons) proves to be different from Bose-Einstein and Fermi-Dirac statistics and from parastatistics.

^{7}

A method for studying cluster spectroscopic properties of nuclear fragmentation, such as spectroscopic amplitudes, cluster form factors, and spectroscopic factors, is developed on the basis of modern precision nuclear models that take into account the mixing of large-scale shell-model configurations. Alpha-cluster channels are considered as an example. A mathematical proof of the need for taking into account the channel-wave-function renormalization generated by exchange terms of the antisymmetrization operator (Fliessbach effect) is given. Examples where this effect is confirmed by a high quality of the description of experimental data are presented. By and large, the method in question extends substantially the possibilities for studying clustering phenomena in nuclei and for improving the quality of their description.

Be radiative capture reaction within the resonating group model

Three different approaches to taking into account exchange effects in heavy-ion collisions are studied. Within the first of them, the lowest eigenstates of the Hamiltonian are treated as forbidden states. In the second approach, the eigenstates of the normalization kernel of the resonating-group model that correspond to zero eigenvalues are treated as forbidden states. The third approach takes additionally into account semiforbidden states. The 16O + 16O system is considered. A hybrid approach that combines the methods of discrete and continuous mathematics is developed for calculating the widths of narrow resonance states. The resonance width calculated within the approach that takes into account semiforbidden states proves to be sharply different from the widths obtained within traditional approaches.

Microscopic interpretation of the results of new measurements for the 3He(α, γ)7Be reaction

States that exhibit the properties of an α-cluster or an α-binucleon condensate are studied in 1p-shell nuclei. The generalized Hamiltonian of the Elliott SU(3) model is used to classify these states and to calculate their spectra. The results of the calculations are found to be in good agreement with experimental data. States not observed so far in the cluster spectra of the 12C, 16O, 10Be, and 12Be nuclei are predicted.

Properties of alpha-particle solutions to the many-nucleon problem

The functional efficiency of various versions of the resonating group model (RGM) and its approximations for describing deep subbarrier resonances were studied. A number of approaches convenient for calculations of such states in RGM and the orthogonality conditions model (OCM) are proposed. A model that, on the one hand, is relatively simple to use and, on the other hand, produces a satisfactory description of resonance widths is found. The model seems to be promising for studying the α decay of heavy nuclei.