Collective Clusterization in Ground and Excited States of Nuclear Systems at Low Energies

Abstract

The aim of the present work is to carry out a comprehensive theoretical study of the decay paths of nuclear systems formed in heavy ion reactions alongwith the decay of ground state trans-lead nuclei exhibiting the phenomenon of cluster radioactivity. The reaction dynamics of hot and rotating, heavy compound systems is studied within the framework of Dynamical Cluster-decay Model (DCM) which is based on collective clusterization approach. The deformation and orientation effects of the reaction partners and decay products are explicitly included along with temperature and angular momentum contribution in this model. The ground state cluster decay of radioactive nuclei have been undertaken within the Preformed Cluster-decay Model (PCM), again having deformation and orientation effects of daughter and cluster nuclei included in it. The thesis is organized into the following seven chapters. Chapter 1 gives a brief account of available experimental and theoretical attempts made to understand the reaction dynamics of hot and rotating nuclei, and the phenomenon of cluster radioactivity. An extensive study of formation and decay of compound nucleus (CN) and noncompound nucleus (nCN) processes is described. Beside this, the role of deformations and orientations of nuclei, entrance channel ef- 1 2 fects, barrier modification, and fission fragment anisotropies in the fusion-fission process have been discussed. Chapter 2 gives relevant details of the Preformed Cluster-decay Model (PCM) and the Dynamical Cluster-decay Model (DCM). PCM is applied to study the spontaneous cluster radioactivity process and DCM is applied to investigate the decay of hot and rotating compound nucleus (CN) formed in heavy ion reactions. It is important to note here that DCM is an extension of PCM which finds its basis in Quantum mechanical fragmentation theory (QMFT). Within this formulism, the fragmentation potential is calculated as sum of temperature dependent binding energies, Coulomb interaction, proximity potential and rotational energy. The deformation and orientation effects are duly incorporated in PCM as well as in DCM. The DCM treats the CN decay of light particles LPs, intermediate mass fragments IMFs, heavy mass fragments HMFs and the asymmetric or near-symmetric fission AF, and symmetric fission SF on equal footings, in contrast to statistical models which follow different formalisms for different processes. In Chapter 3, the entrance channel effects in the decay of 215Fr nucleus, formed in 11B+204Pb and 18O+197Au reactions, is studied by using the dynamical clusterdecay model (DCM). The observed decay is mainly via fusion-fission, with data collected for both the fission excitation functions and fission fragment anisotropies. In agreement with experimental data and conclusions based on statistical code PACE2, for fission excitation functions, DCM calculations also show no contribution of the quasi-fission component in fission cross-sections for both the reaction channels, mea3 sured at incident center-of-mass energy spread on either side of the Coulomb barrier. Also, the fission fragment anisotropies, calculated on DCM for the first time, are found consistent with experimental data for both the reaction channels, confirming the entrance channel independence in the decay of 215Fr . In addition to this, the decay paths of other Fr-isotopes namely, 213Fr (with neutron number N = 126) and 217Fr (with N = 130), formed in 19F + 194,198Pt reactions, are studied as collective clusterization process, for emissions of both the light particles (LPs) and fission fragments, within the DCM. The role of magic N = 126 shell of the compound nucleus (CN) or the presence of a noncompound nucleus (nCN) component, like the quasi-fission (qf), in fission cross-sections are investigated. A small hump or shoulder is seen in fragment preformation yields for the deformed case ( 2 or 2- 4) in both the systems due to a deformed closed shell around Z2 = 36 and spherical magic shell around Z1 = 50, which for 213Fr (N = 126) decay is somewhat more pronounced as compared to 217Fr (N = 130). In Chapter 4, the excitation functions for both the evaporation residue and fission have been calculated for 10B + 209Bi and 11B + 209Bi reactions forming compound systems 219,220Ra , using the dynamical cluster-decay model (DCM) with effects of deformations and orientations of nuclei included in it. In addition to this, the excitation functions for complete fusion (CF) are obtained by summing the fission cross-sections, neutron evaporation and charged particle evaporation residue cross-sections produced through the xn and pxn (x = 2, 3, 4) emission channels for the 219Ra system at various incident centre-of-mass energies. Experimentally the CF cross-sections are suppressed and the observed suppression is attributed to the 4 low binding energy of 10,11B which breaks up into charged fragments. The reported complete fusion (CF) and incomplete fusion (ICF) excitation functions for the 219Ra system are found to be nicely fitted by the calculations performed in the framework of DCM, without invoking significant contribution from quasi-fission. Although DCM has been applied for a number of compound nucleus decay studies in recent past, the same is tested here in reference to ICF and subsequent decay processes along with the CF process. In Chapter 5, the decay of hot and rotating compound nucleus 241Pu formed in the reaction 9Be + 232Th around the Coulomb barrier ( 42.16 MeV), at energies ranging from 37 - 48 MeV, is studied using the dynamical cluster-decay model (DCM) with effects of static and dynamic deformations included. With the inclusion of dynamical deformations both the preformation probability P0 and the tunneling probability P, and hence the cross-sections, change considerably. The only parameter of the model, namely the neck length parameter, varies smoothly with excitation energy or temperature of the system both at above-and below-barrier energies, whose value depends strongly on the limiting angular momentum, which in turn depends on the use of sticking and non-sticking moment of inertia. The relative effect of static and dynamic deformations on neck length parameter R is also studied, which indicate the reaction time scale for both static and dynamic choices of deformation. Beside this the exclusive role of angular momentum and “barrier modification” effects at sub-barrier energies are also addressed. In Chapter 6, we have studied nine cases of spontaneous emission of 14C clusters 5 in the ground-state decays of the same number of parent nuclei from the trans-lead region, specifically from 221Fr to 226Th, using the Preformed Cluster Model (PCM) of Gupta and collaborators, with choices of spherical, quadrupole deformation ( 2) alone, and higher multipole deformations ( 2, 3, 4) with cold “compact” orientations c of decay products. The calculated 14C cluster decay half-life times are found to be in nice agreement with experimental data only for the case of higher-multipole deformations ( 2- 4) and c orientations of cold elongated configurations. In other words, compared to an earlier study of clusters heavier than 14C, where the inclusion of 2 alone, with “optimum” orientations, was found to be enough to give the best comparison with data, here for 14C cluster decay the inclusion of higher-multipole deformations (up to hexadecapole), together with c orientations, is found essential on the basis of PCM. Interestingly, whereas both the penetration probability and assault frequency work simply as scaling factors, the preformation probability is strongly influenced by the order of multipole deformations, and orientations of nuclei. The possible role of Q value and angular-momentum effects are also considered in reference to 14C cluster radioactivity. Finally, in chapter 7, conclusions are summarized and an outlook of our work is presented.