A Study of Exotic Compound Nuclear Systems and Subsequent Fragment Emission Using Skyrme Energy Density Formalism

Abstract

In this thesis, the formation and subsequent decay mechanisms of compound nuclear systems induced via heavy-ion reactions have been studied at the low-energy regime. For this analysis, the nucleus-nucleus interaction potential derived using the semiclassical SEDF approach is considered as a tool to estimate the fusion barrier characteristics, which are used as input to calculate the fusion cross-sections witih the Wong formula (and its extended version) for incident energies lying across the Coulomb barrier. Additionally, the influence of different density distribution functions and approximations employed within the SEDF approach has been studied in view of the fusion barrier characteristics and the fusion crosssections. For comparative analysis, the phenomenological potentials, like Prox77, Pox88 and Woods-Saxon etc., are considered and analyzed the corresponding influence in nuclear fusion dynamics. Further, to study the subsequent decay mechanisms of the formed compound nucleus (CN), the mass and charge distributions of excited CN have been examined within the framework of collective clusterization approach of Dynamical Cluster-decay Model (DCM). The model based on the Quantum Mechanical Fragmentation Theory (QMFT). In the fusion-fission dynamics of heavy-ion induced reactions, the role of deformations (to octupole β3 deformation) and corresponding optimum orientations has also been investigated. In view of above, the present thesis is divided into eight chapters, which are briefly described as: Chapter 1 begins with the basic understandings related to the subatomic particles and their interactions with the other nuclei, taken place at the low-energy regime (beam energy ≤ 15 MeV/nucleon). In the present thesis to study the nucleus-nucleus interactions, the heavy-ion (with mass and charge numbers ≥ to that of 42 He nucleus) reactions are taken into consideration. Later, the theoretical models developed to study the heavy-ion collisions are discussed. Also, a description regarding the relevance of deformations and orientations degrees of freedom in nuclear fusion-fission dynamics is discussed. The motivation of this work is to study the formation and subsequent decay mechanisms of compound nuclear systems using Skyrme Energy Density Formalism and phenomenological model. iii iv In Chapter 2, the formalisms used to derive the nucleus-nucleus interaction potential on the basis of the semiclassical SEDF approach and the phenomenological model are discussed. The mathematical formulations defining the repulsive Coulomb and centrifugal potentials are discussed for the spherical-spherical, spherical-deformed and deformed-deformed pairs of colliding nuclear partners. Further, the fusion barrier characteristics (barrier position RB, barrier height VB and barrier curvature ¯hωB) extracted from the total interaction potential, obtained by combining nuclear, Coulomb and centrifugal potentials, are used as input terms to calculate the fusion cross-sections. To estimate the fusion cross-sections as a function of center of mass energies, the Wong formula and its extended version are employed. In order to study the mass and charge distribution of compound nuclear systems, the expressions for the fragmentation potential and preformation probability obtained within the collective clusterization approach are illustrated. The Appendixes A and B are given to detail the curvature radii of deformed surfaces. In the following Chapters, the results and calculations are discussed. In Chapter 3, different density approximations such as frozen, sudden and modified sudden are employed within the Skyrme Energy Density Formalism and compared with the phenomenological relaxed-density approach for Ni-based reactions. These approximations give different ways in which individual densities of projectile and target can be added for obtaining compound nucleus density. On the basis of this, the corresponding influence of above mentioned density approximations has been analyzed in view of the fusion barrier characteristics and subsequently on the fusion cross-sections (σfus) for 18O, 40Ca, 58Ni and 132Sn+58Ni reactions. The fusion cross-sections obtained using extended ℓ-summed Wong model are compared with the available experimental data across the Coulomb barrier energies for the 58Ni-based reactions. In Chapter 4, the role of three-parameter Fermi (3pF) and three-parameter Gaussian (3pG) density functions in the fusion dynamics has been explored in comparison to the two-parameter Fermi (2pF) employed within the semiclassical SEDF approach. For the case of the three-parameterized density functions (3pF and 3pG), an additional parameter ‘w’ influences the tail and nearby region, and hence the barrier characteristics get modified accordingly. In view of this, the role of 2pF, 3pF and 3pG density functions has been analyzed by calculating the fusion barrier height VB (and barrier position RB) for a variety of nuclear reactions with the mass-asymmetry spread from symmetric to asymmetric reaction partners, v and the results are compared with the available experimental data. In addition to this, the fusion cross-sections for 58Ni-based reactions are calculated using extended ℓ-summed Wong model and the collective effect of VB, RB and ¯hωB (barrier height, position and curvature respectively) for the use of above mentioned density distributions has been examined. The ℓmax-values have been obtained using the sharp cut-off model for above barrier energies and extrapolated for below barrier energies. In Chapter 5, the relevance of deformation and orientation degrees of freedom has been explored for the synthesis of heavy and superheavy nuclei. In view of this, the octupole deformation (β3) which distorts the spherically symmetric or quadrupole deformed (β2) nuclei into a pear shape has been taken into account. The influence of octupole deformed nuclei on the optimum (or uniquely fixed) orientations obtained for the ‘elongated’ and ‘compact’ fusion configurations of these nuclei has been analysed and discussed in comparison to that of the quadrupole deformed nuclei. Also, to investigate the effect of β3-deformation in reference to that of β2, a systematic analysis has been done for the the soft-pear shape nuclei with small β3-deformations and rigid-pear shape nuclei with strong β3-deformation. Additionally, the ‘+’ and ‘−’ sign effects of β3-deformation have been discussed. The analysis done in this chapter is exercised using the SEDF and phenomenological based potentials. As an extension of above analysis, Chapter 6 is devoted to investigate the significance of deformation and associated optimum/uniquely fixed orientations for the formation of compound nuclei via cold and hot fusion reactions. The proposed set of optimum orientations corresponding to β3-deformed nuclei, discussed in the earlier chapter, is utilized to understand the respective influence on the fusion barrier characteristics and fusion cross-sections for 16O and 48Ca-induced reactions. In these reactions, β3-deformed nuclei are taken as targets belonging to different mass-regions of the Periodic Table. The above analysis is exercised for around 200 spherical-plus-β3 deformed pairs of colliding nuclear partners. The results are compared with the available experimental data for 16O+150Sm (β22 = 0.205, β32 = -0.055) reaction. In Chapter 7, the disintegration of light and heavy-mass isotopes of Thorium i.e. 222,224,226,228,230Th∗ compound nucleus have been discussed using the SEDF and phenomenological potentials within the collective clusterization approach of QMFT. In this analysis, the significance of octupole deformations and corresponding cold optimum orientations has been explored in terms of the fragmentation potential and preformation probability. The vi obtained results are discussed in comparison with the quadrupole deformation of decaying fragments. Additionally, the mass- and charge-distributions of considered isotopes of Th are compared with the experimentally obtained yield profiles. At the end, in Summary chapter, all the results discussed in the above chapters on the basis of Skyrme Energy Density Formalism, in comparison with the phenomenological models, are summarized. The future scope of the work done in the present thesis is discussed briefly.