Reaction dynamics in clustered nuclear systems

Abstract

This work is concerned with the theoretical study of nuclear reactions between light charged ions at incident energies around and below the reactants Coulomb barrier, with a focus on the energy range of astrophysical interest for Big Bang and quiescent stellar processes. The main goal of the analysis is to investigate the sensitivity of nuclear reaction dynamics, and more specifically the cross-section predictions, to the description of the structure of each reactant, and in particular to clustering phenomena. The case of the 6Li + p -> 3He + 4He reaction was investigated explicitly, treating the process as a direct deuteron transfer in first- or second-order distorted-wave Born approximation (DWBA) and through a coupled reaction channels (CRC) approach. The penetrability of the Coulomb barrier in the initial state was also analysed phenomenologically from available experimental data, and studied theoretically taking into account the 6Li ground-state deformation. Chapter 1 of this thesis treats some phenomenological aspects of the class of nuclear reactions of interest, both taking place in vacuum (``bare-nuclei'') or immersed in an external medium. The tools developed in this chapter, in spite of (and thanks to) their simplicity, allow to understand the main features of the non-resonant sub-Coulomb reaction cross-section, providing analytical expressions that can be compared to the results of more advanced computations to discuss their qualitative meaning and implications. Section 1.2 includes a quantitative analysis on the electron screening anomalies observed in the 6Li + p -> 3He + 4He reaction. Chapter 2 is a dissertation on some characteristics of the static structure of an isolated nucleus, with a focus on clustered systems. In particular, section 2.2 presents the formalism of overlap functions, which are important for treating direct transfer reactions and encode the required information to represent reactants within a cluster model. Section 2.3 instead is dedicated to the explicit computation of the root-mean-square radius and the electric quadrupole moment of a nucleus described as a bound state of several clusters. Chapter 3 reviews the theory of direct transfer reactions that is later employed in the practical calculations shown in chapter 4. In particular, the discussion is focused on the formalism of first- and second-order DWBA and of CRC approaches. Chapter 4 is concerned with the study of the 6Li + p -> 3He + 4He reaction, treated as the direct transfer of either a structureless deuteron or a generic p+n system, through the whole sub-Coulomb energy range and up to the resonance corresponding to the second 5/2- state of 7Be (namely, at centre-of-mass incident energies between few keV to about 1.5 MeV). The excitation function of the process is explicitly evaluated within a fully quantum framework and without adjusting the calculation parameters on transfer experimental data. Different descriptions of the reactants structure are considered in the evaluation of the cross-section. First- and second-order DWBA calculations are employed to study the role of the system ground state in the initial and final partition, and in particular the model adopted for the transferred particle internal structure, and the corresponding strength of clustered configurations. Virtual excitations in the relative motion between core and transferred systems, which can account for a dynamical deformation of the reactants during the reaction, are investigated in a preliminary calculation using a CRC scheme. The physical ingredients required to perform the calculations are also discussed here. Chapter 5 presents an investigation on the quadrupole deformation of the ground state of 6Li, described within a di-cluster model. Such deformation is required to explain the measured electric quadrupole moment of 6Li, and induces tensor components in the interaction of 6Li with other particles, breaking the angular symmetry of the Coulomb barrier. Previous semi-classical calculations are here improved and expanded, and employed to evaluate and compare the impact of the classical and quantum-mechanical cluster model on the Coulomb-barrier penetrability within a scattering process.