Fusion-Fission and Associated Nuclear Structure Effects at Low Energies

Abstract

The work presented in this thesis deals with the formation and decay of variety of nuclear systems formed in heavy ion reactions using `-summed Wong formula and dynamical cluster decay model (DCM) respectively. The study is done using two types of nuclear interaction potentials; one is obtained from proximity theorem and other via Skyrme Energy Density Formalism (SEDF). A non-statistical model DCM is based on collective clusterization approach and is used to account for the decay of hot and rotating nuclei formed in low energy heavy ion collisions. The main advantage of DCM over other statistical model is that it contains the structural information of the decaying nucleus via the relative preformation probability of the decaying fragments, before penetrating the interaction barrier. It is relevant to mention here that the temperature, angular momentum, deformations and orientation effects of the reaction partners and decaying products are dully incorporated respectively in Wong and DCM approach. The thesis comprises of seven chapters, a brief account of which is discussed below. Chapter 1, presents the general introduction of the present work which includes the status of the experimental and theoretical developments to understand the dynamics of fusion-fission and associated nuclear structure effects. To study the formation and decay of nuclear systems, the precise and systematic understanding of various nucleus-nucleus interaction potentials is essential, a brief account of such interactions is summarized in this chapter. Beside this, the role of angular momentum, entrance channels, deformations and orientations, fusion hindrance etc. have been discussed. Chapter 2 gives the details of the methodology used, the dynamical clusterdecay model (DCM) based on the Quantum Mechanical Fragmentation Theory (QMFT) for binary fragmentation, which find its basis in the collective mass transfer process. The process of binary decay like neutron evaporation, -decay, cluster decay, fission fragments etc is treated in two steps: In first step the quantum mechanical preformation probability of the cluster in the mother nucleus is evaluated and the second step accounts for the penetration of the cluster through the interaction barrier. In this model the preformation probability of all possible clusters within the mother nucleus is calculated by solving stationary Schrodinger equation in mass asymmetry ( ) coordinate. The role of temperature dependence of the proximity potential, Coulomb interaction potential, rotational energy and binding energies is briefly discussed. Details of the Skyrme energy density formalism (SEDF), used to calculate the interaction potential between the two colliding nuclei is also described. Finally the Wong’s formula and its extended version are also described in brief. In Chapter 3, the dependence of fusion-fission process on Skyrme forces is analyzed by using the dynamical cluster-decay model (DCM) and the `-summed extended-Wong model. An extensive study on 132Sn+64Ni!196Pt reaction is carried out, where the nuclear proximity potential is obtained by using the semiclassical extended Thomas Fermi (ETF) approach in Skyrme Energy Density Formalism (SEDF) under Frozen density approximation. The DCM gives an excellent fit to the measured fusion-evaporation residue (ER) and the fission cross-sections at below and above-barrier energies, with ER data needing “barrier lowering” at below-barrier energies for each Skyrme force, an in built property of DCM, and the fission crosssections show a contribution of quasi-fission (qf) at the above-barrier two/ three highest energies, depending on the type of Skyrme force. Calculations are illustrated for three Skyrme forces GSkI, SSk and SIII. Another interesting result is that there is a change of fission mass distribution from a predominantly asymmetric to symmetric one with decrease in the N/Z ratio of compound nucleus, independent of the choice of nuclear interaction potential, which gives an opportunity to address the isospin effects in Pt nucleus. Within `-summed extended-Wong model we observe that the GSkI and SSk forces fit the total fusion cross-section data almost exactly, whereas SIII force needs “barrier modification” in order to fit the data at below-barrier energies. This happens because the isospin and neutron-proton asymmetry nature of GSkI and SSk forces is different from that of the SIII force, and that the centerof- mass energy Ec,m, dependence of the barrier height for SIII (and Blocki et al.) force differs strongly (by a constant amount of 7 MeV) as compared to those for GSKI and SSk forces. In this chapter, the role of deformations and orientations is investigated by employing a variety of Skyrme forces such as SIII, GSkI and SSK within energy density formalism (EDF) approach. Beside this the fusion probability is estimated using `-summed Wong formula (or equivalently Hill-Wheeler method) and exclusive role of above mentioned Skyrme forces is dully addresed. In Chapter 4, we have studied the role of deformations and orientations by using different proximity potentials to analyse the persistence of entrance channel effect in the decay of 190Pt compound nucleus formed by using 132Sn+58Ni and 126Sn+64Ni reactions. The inclusion of deformations significantly effects the fragmentation profile of 190Pt compound nucleus with in the framework of DCM. Moreover, the decay pattern of Pt nuclei formed using stable 124Sn beam is also investigated. For both entrance channels i.e. 132Sn+58Ni and 126Sn+64Ni, the fragmentation potential and preformation probability of decaying fragments is almost identical at comparable center-of-mass energies (Ec.m.), suggesting that the decay of 190Pt is perhaps independent of it’s formation effects. In order to check for the persistence of entrance channel independence in the decay of Pt compound nucleus, various versions of nuclear proximity potentials and different values of level density parameter are employed in the calculations and the signature of entrance channel independence seem to sustain throughout. It is also observed that with inclusion of deformation effects up to quadrupole ( 2) with in the optimum orientation approach, the structure of potential energy surfaces changes significantly. The 132Sn+58Ni reaction is also studied using four proximity potentials i.e. Prox 1977, Prox 1988, mod-Prox 1988 and Denisov 2002 with in the framework of `-summed extended-Wong model for addressing the fusion hindrance phenomena. We find that Prox 77 and Prox 88 fit the total fusion cross-section data only at above barrier energies whereas Denisov 2002 underestimate the data at all energies due to its least sensitiveness towards asymmetry and isospin. So a stronger nuclear interaction potential mod-Prox 1988 that accounts for isospin effect and asymmetry of the colliding nuclei is employed, which fits the data with smooth variation of `max(Ec.m.). Our calculations indicate that the isospin and asymmetry of colliding nuclei also play an important role in the fusion dynamics particularly at below barrier region. In previous chapters, the decay patterns of Pt compound nuclei formed using radioactive and stable beams are analysed, by employing various nuclear interaction potentials calculated using EDF as well as available nuclear proximity potentials. In Chapter 5, the effect of deformation and orientation on barrier height and barrier position is studied using different types of proximity potentials for some 52 colliding nuclei with mass asymmetry parameter in range of 0 to 0.96. Various proximity potentials like Prox 77, Prox 88, Prox 00, Bass 80 and Denisov DP are used to extract barrier characteristics. These potentials cover a wide range of barrier and have different isospin and asymmetry dependence. With the inclusion of deformations, the barrier height and barrier position gets modified along with a significant change in the curvature of interaction potential. In order to study the possible effect of these deformation and orientation dependent proximity potentials, an effort is made in the framework of Wong formula to address O-, Ca- and Ni- based reactions in medium mass region in reference to available data on fusion cross-sections across the Coulomb barrier. For 16O- and 48Ca-based reactions, Prox 77 gives better comparison with experimental data as compared to other potentials around the Coulomb barrier energies whereas for 64Ni-based reactions Prox 88 seems a better option. At energies above the Coulomb barrier Bass 80 and Denisov DP compete with each other. The angular dependence of cross-section is also studied. In summary, it is observed that deformation and orientation degree of freedom play a significant role in reaction dynamics of chosen set of heavy ion reactions. Upto now, the role of nuclear shape of colliding and decaying fragments is ad- dresses using proximity pocket formulas as well as the EDF based Skyrme approach. Although the barrier profile calculated using proximity and EDF based nuclear interaction looks similar, but the latter approach seem to have merit over the earlier one. The main advantage of using the Skyrme approach is that the hamiltonian used in microscopic EDF approach consists of two terms namely: spin-orbit dependent and spin-orbit independent interaction potentials, which otherwise is not possible while using phenomenological models i.e. proximity potentials. Hence, in Chapter 6, a systematic study of the spin-orbit density dependent interaction potential is carried out, with spherical as well as deformed choices of nuclei, for a variety of near-symmetric and asymmetric colliding nuclei leading to various isotopes of compound nucleus Yb , using the semiclassical extended-Thomas Fermi formulation (ETF) of the Skyrme energy density formalism (SEDF). We observe that the spinorbit density interaction barrier-height (VJB) and barrier-position (RJB) increase systematically with increase in number of neutrons in either the projectile or target, for spherical systems. On allowing deformation effects with optimum orientations, the barrier-height increases systematically with enhanced magnitude as compared to the spherical case, in going from 156Yb to 172Yb nuclear systems formed via near-symmetric Ni+Mo or asymmetric O+Sm colliding nuclei, except that for the oblate-shaped nuclei, the barrier height and barrier distribution does not follow the usual trend. The temperature does not change the behavior of spin-orbit density dependent (VJ ) and independent (VP ) interaction potentials, except for some minor modifications in the magnitude. The orientation degree of freedom also plays an important role in modifying the barrier characteristics and hence produce a large effect on the fusion cross section. The fusion excitation function of compound nuclei 160,164Yb formed in different incoming channels, seem to suggest that the new forces GSkI and KDE0v1 respond better than the old SIII force. The fusion cross-sections are also predicted for few other isotopes of Yb . Beside this, the decay pattern of hot and rotating 172Yb* compound nucleus, formed in two entrance channels 124Sn+48Ca and 132Sn+40Ca, is studied using the dynamical cluster-decay model. Finally, in chapter 7, the summary and significance of the work of this thesis and the scope for possible extension of present work is discussed.