Dynamics of Fusion-Fission and Related Phenomena at Low Energies

Abstract

The aim of present work is to study the possible decay modes of different nuclear systems at low energies. In the process, issues related to fine-structure/ sub-structure of fission fragments, shell effects, angular momentum, deformation and orientation effects, etc., are investigated. The role of deformations in cluster radioactivity (CR) have also been studied extensively. The Dynamical Cluster-decay Model (DCM) is used to study the decay of heavy nuclear systems formed in heavy ion reactions. It is relevant to mention here that the contribution of angular momentum, nuclear deformations and orientations are included in DCM. For all the systems studied in this thesis, DCM results find nice comparisons with the experimental data over a wide range of energies. The DCM with angular momentum (`)=0 and temperature (T)=0 approximations is used to investigate the role of deformation in CR. The thesis is divided into seven chapters. Chapter 1 contains the general introduction to present work. An overview of current research status of fusion-fission and related aspects is given. Beside this, a brief account of low energy nuclear reactions is explained where emphasis is laid on deeper understanding of compound nuclear systems. The role of nuclear shapes i.e. the effects of deformation and orientation on formation and decay of a nuclear system is discussed. 1 2 Chapter 2 gives the details of the methodology used in this thesis. The DCM which is used to calculate the decay properties such as decay cross sections, kinetic energies, etc., has been discussed in detail. In DCM, besides the temperature and angular momentum effects in the decay of excited compound nuclei, the deformation and orientation effects of decay products are also taken care of. The DCM is based on the Quantum Mechanical Fragmentation Theory (QMFT), and hence a brief overview of the same is also given. The method of calculating the fragmentation potentials, the collective potentials, and kinetic energy part of the Hamiltonian are discussed, together with the solution of the stationary Schr¨odinger wave equation. The details are given for the effects of deformed and oriented nuclei in the proximity, Coulomb and angular momentum potentials. The DCM is used to study the decay of hot and rotating compound nucleus formed in heavy ion reactions, whereas DCM with T=0, `=0 approximations, known as Preformed Cluster Decay Model (PCM), is used to study the ground state decay of nuclei, the cluster radioactivity, in trans-lead region. In Chapter 3, the decay of 202Pb formed in 48Ca + 154Sm reaction at different center-of-mass energies is studied using the dynamical cluster-decay model (DCM) for spherical fragments. The calculated results show an excellent agreement with experimental data for the fusion-evaporation residue cross-section ER together with the fusion-fission cross-section FF , and the competing, non-compound-nucleus quasi-fission cross-section QF . Also the prediction of two fission windows, the symmetric fission (SF) and the near symmetric fission (nSF) whose contribution is more at lower incident energies, suggests the presence of a fine structure effect in the 3 fusion-fission of 202Pb . The nSF window (responsible for quasi-fission (QF) process) is shown to be due to the presence of shell-effects (magic shells) in the mass distribution of 48Ca + 144Sm !202Pb !A1+A2 reaction. As a further verification of this result, no QF component has been observed in the decay of 192Pb formed in 48Ca + 144Sm reaction in agreement to experimental observation. In Chapter 4, the decay of Pt isotopes 176,182,188,196Pt formed by 64Ni+112Sn, 64Ni+118Sn, 64Ni+124Sn and 132Sn +64Ni reactions has been studied using the Dynamical Cluster-decay model (DCM). The interesting aspect of this study is that, the data for evaporation residue (ER) and fusion-fission cross-sections is available on either side of Coulomb barrier energy. Here we observe that different isotopes of Pt display different decay patterns. With the increase in number of neutrons, i.e., with the increase of N/Z ratio of CN, the characteristics of the emitted light particles (the ER) change and the fission mass distribution changes from a symmetric fragmentation to an asymmetric fragmentation. The DCM based ER cross-section find nice comparison with experimental data, whereas, the fiss calculations show a significant contribution of quasi-fission ( qf ) at the highest one or two energies. Then the total fusion cross-sections/ ( ER+ fission+ qf ) calculated on DCM fit the data nicely for all the four isotopes of Pt over a wide range of energies. Specifically, other model calculations, like the BPM, CCFULL and DC-TDHF, are available for the 132Sn+64Ni!196Pt reaction and the DCM results are found better than these predictions, in particular at sub-barrier energies. In Chapter 5, the dynamical cluster-decay model is used for the first time to 4 study the decay of odd-mass nuclear systems 213Fr (with N=126) and 217Fr (with N=130) formed in 19F+194,198Pt reactions with spherical as well as quadrupole ( 2) deformations having ”optimal” orientations of hot (compact) configurations. As 213Fr is more fissile than 217Fr , so fiss is more for 213Fr over the entire measured energy range as compared to that for the less fissile 217Fr . Interestingly, the calculated fission distributions for both 213Fr and 217Fr are symmetric for spherical nuclei and asymmetric for 2 deformation included. The role of deformations in the decay of 213Fr and 217Fr nuclear systems can be assessed from the comparative behavior of mass fragmentations. The measured anomaly in fission anisotropy reported in case of 213Fr can be understood in terms of either the possible role of magic N=126 shell of the compound nucleus or the presence of a non-compound nucleus (nCN) component, like the quasi-fission (qf), in fission cross-section. For quadrupole deformed and ”optimal” oriented fragments, the calculated fission crosssections (as well as the evaporation residue cross-sections) match the data nearly exactly, leaving no room for the nCN, qf component in fission cross-sections. Therefore, measured anomaly in the fission anisotropy for 213Fr can be due to the role of magic shell i.e N=126. As the fragmentation process for spherical and or 2 deformations is almost identical for 213Fr and 217Fr , nothing conclusive can be said about the role of magic shell N=126. However, it will be of interest to include further the higher multipole deformations and ”generalized orientations” in the decay process of these nuclei in order to establish the explicit role of N=126 in the decay of 213Fr nucleus, if any. In Chapter 6, we have used the Preformed Cluster Model (PCM) of Gupta and 5 collaborators, to study the role of deformations/orientations in all the measured cluster-decays, including the very recent experiments for the decay of 14C and 15N from 223Ac and 34Si from 238U. It has been observed that 2 alone with optimal orientations is good enough to fit the experimental decay half-life times T1/2 for majority of measured clusters-decays. However higher multi-pole deformation effects seems essential for 14C decays of 221Fr, 221−224,226Ra, and 225Ac. Because the PCM treats the cluster-decay process as the tunnelling of a preformed cluster, the deformations and orientations of nuclei modify both the preformation probability P0 and tunnelling probability P, and hence the decay half-life, considerably. It has been established through this study that the deformation and orientation effects are extremely desirable, in addition to the shell and Q-value effects. Finally, in chapter 7, we summarize the results of this work and give a brief outlook.