Heavy-ion Fusion Reactions Research Articles

Indirect Study of the16O+16O Fusion Reaction Toward Stellar Energies by the Trojan Horse Method

The 16 O+ 16 O fusion reaction is important in terms of the explosive oxygen burning process during late evolution stage of massive stars as well as understanding of the mechanism of low-energy heavy-ion fusion reactions. We aim to determine the excitation function for the most major exit channels, α + 28 Si and p + 31 P, toward stellar energies indirectly by the Trojan Horse Method via the 16 O( 20 Ne , α 28 Si) α and 16 O( 20 Ne , p 31 P) α three-body reactions. We report preliminary results involving reaction identification, and determination of the momentum distribution of α - 16 O intercluster motion in the projectile 20 Ne nucleus.

Analysis of fusion dynamics of colliding systems involving stable, loosely bound and halo nuclei

This article analyzed the fusion dynamics of stable nuclei, loosely bound nuclei and halo nuclei within the view of coupled channel approach and the energy dependent Woods–Saxon potential model (EDWSP model). The different projectiles ( and are bombarded onto common spherical target isotope ( wherein target isotope exhibits inelastic surface excitations as dominant mode of coupling. The fusion dynamics of reactions, wherein there is no signature of fusion suppression at above barrier energies, are adequately explained by both theoretical approaches in domain of Coulomb barrier. In case of reactions, the couplings of inelastic surface excitations of colliding systems remove the discrepancies between below barrier fusion data and expectations of one-dimensional barrier penetration model. However, at above barrier energies, the fusion excitation function data are suppressed in comparison to the theoretical predictions of both approaches. Interestingly, this suppression of above barrier fusion data is minimized by the present model calculation by a factor of 7% with respect to a value reported in literature. Within the view of the EDWSP model calculations, the above barrier fusion data of reaction are hindered by a factor of 25% and by a factor of 17% for reaction which is smaller than a value as pointed out in literature. The observed sub-barrier fusion dynamics of and reactions are reasonably described by the coupled channel model and the EDWSP model. Furthermore, the applicability of the EDWSP model has been tested for exploration of the fusion of reaction and hence due to barrier modification effects, the EDWSP model successfully explains the observed fusion enhancement of reaction. The present calculations clearly indicate that different theoretical approaches (coupled channel formulation and EDWSP model) induce similar kinds of barrier modification effects in the heavy ion fusion reactions.

Configuration transition effect in heavy-ion fusion reactions with deformed nuclei

Fusion reactions of 16O + 24Mg are investigated with the three-dimensional time-dependent Hartree-Fock (TDHF) method. The resultant fusion excitation functions show some novel features that are beyond the current understandings and the predictions of various theoretical models. We will demonstrate that these phenomena cannot be explained by a density rearrangement effect but by the configuration transition mechanism in the dynamical process.

Nuclear dynamical octupole deformation in heavy-ion reactions

Within the quantum molecular dynamics (QMD) model, the dynamical octupole deformation is studied as a function of the central distance between the projectile and target in the approaching process of heavy-ion fusion reactions. The dependence of the maximum dynamical octupole deformations on the incident energies is also investigated. The dynamical octupole deformations can be observed during the approaching process, and the maximum dynamical octupole deformations become more significant with decreasing incident energies. The distributions of the proton and neutron centers in the projectile and target are also investigated, respectively. In the approaching process of heavy-ion fusion reactions, the separation between proton centers for two nuclei is larger than that between neutron centers because of the strong Coulomb potential.

Effects of intrinsic degrees of freedom in enhancement of sub-barrier fusion excitation function data and energy-dependent one-dimensional barrier penetration model

We have analyzed the role of barrier modification effects (barrier height, barrier position, barrier curvature) introduced due to the energy-dependent Woods–Saxon potential model (EDWSP model) and the coupled channel model on the sub-barrier fusion dynamics of $$ {}_{16}^{32,36} {\text{S}} + {}_{40}^{90,96} {\text{Zr}} $$ reactions. The influence of inelastic surface excitations of colliding pairs and multi-neutron transfer channels is found to be a dominant mode of couplings. The coupling of relative motion of colliding nuclei to these dominant intrinsic degrees of freedom leads to a substantially large fusion enhancement at below-barrier energies over the expectations of one-dimensional barrier penetration model. The coupled channel calculations based upon static Woods–Saxon potential must include the internal nuclear structure degrees of freedom of colliding nuclei for complete description of experimental data. On the other hand, theoretical calculations based upon the EDWSP model along with Wong formula provide a complete description of sub-barrier fusion enhancement of various heavy-ion fusion reactions. In EDWSP model calculations, significantly larger values of diffuseness parameter ranging from a = 0.98 fm to a = 0.85 fm are required to address the observed sub-barrier fusion enhancement of $$ {}_{16}^{32,36} {\text{S}} + {}_{40}^{90,96} {\text{Zr}} $$ reactions. Furthermore, within the context of EDWSP model, it is possible to achieve an agreement with the experimental fusion cross-sectional data within 10 %. For four heavy-ion fusion reactions, only at 4 fusion data points out of 90 fusion data points deviates exceeding 5 %, while 86 fusion data points lie within 5 % and hence the EDWSP model is able to account the above-barrier portion of the fusion cross-sectional data within 5 % with a probability greater than 90 %.

Microscopic analysis of fusion hindrance in heavy nuclear systems

Background: Heavy-ion fusion reactions involving heavy nuclei at energies around the Coulomb barrier exhibit fusion hindrance, where the probability of compound nucleus formation is strongly hindered compared with that in light- and medium-mass systems. The origin of this fusion hindrance has not been well understood from a microscopic point of view. Purpose: Analyze the fusion dynamics in heavy systems by a microscopic reaction model and understand the origin of the fusion hindrance. Method: We employ the time-dependent Hartree-Fock (TDHF) theory. We extract nucleus--nucleus potential and energy dissipation by the method combining TDHF dynamics of the entrance channel of fusion reactions with one-dimensional Newton equation including a dissipation term. Then, we analyze the origin of the fusion hindrance using the properties of the extracted potential and energy dissipation. Results: Extracted potentials show monotonic increase as the relative distance of two nuclei decreases, which induces the disappearance of an ordinary barrier structure of the potential. This is different from those in light- and medium-mass systems and from density-constraint TDHF calculations. Extracted friction coefficients show sizable energy dependence and universal value of their magnitude, which are rather similar to those in light- and medium-mass systems. Using these properties, we analyze the origin of the fusion hindrance and find that contribution of the increase in potential to the extra-push energy is larger than that of the accumulated dissipation energy in most systems studied in this article. Conclusions: By the analysis of the origin of the fusion hindrance, we conclude that, as the system becomes heavier, the dynamical increase in potential at small relative distances plays a more important role than the dissipation during the fusion reaction for understanding the origin of the fusion hindrance.

Semimicroscopic modeling of heavy-ion fusion reactions with multireference covariant density functional theory

Semimicroscopic modeling of heavy-ion fusion reactions with multireference covariant density functional theory

Cross sections for the production of superheavy nuclei

Production and studying properties of superheavy (SH) nuclei meet significant experimental difficulties owing to extremely low cross sections of their formation in heavy ion fusion or multinucleon transfer reactions. Accurate predictions of these cross sections along with the corresponding excitation functions are quite desirable for planning and performing experiments of such kind. Study of these cross sections (their dependence on projectile–target combination and energy dependence) gives us an opportunity to investigate complicated dynamics of low-energy heavy ion collisions as well as decay properties of excited SH nuclei.

Dynamical Dipole mode in heavy-ion fusion reactions in the 192Pb mass region

The dynamical dipole mode was investigated in the mass region of the 192Pb compound nucleus, by using the 40Ca + 152Sm and 48Ca + 144Sm reactions at Elab=11 and 10.1 MeV/nucleon, respectively. Both fusion-evaporation and fission events were studied simultaneously for the first time. Our results for evaporation and fission events (preliminary) show that the dynamical dipole mode survives in reactions involving heavier nuclei than those studied previously.

Effects of intrinsic degrees of freedom in enhancement of sub-barrier fusion excitation function data

This paper is mainly focused on the limitations of energy independent Woods–Saxon potential and the applicability of energy dependent Woods–Saxon potential (EDWSP) model in conjunction with one-dimensional Wong formula for description of the heavy-ion fusion reactions. The effects of neutron transfer channels and inelastic surface vibrations of colliding nuclei in the enhancement of sub-barrier fusion excitation function data, in the various heavy-ion fusion reactions, have been investigated within the framework of energy independent one-dimensional barrier penetration model, the EDWSP model and the coupled channel code CCFULL. In certain projectile-target combinations, the influences of multi-neutrons transfer between reactants are found to be dominating over the coupling to low lying surface vibrational states. Furthermore, the effects of these dominant degrees of freedom can be simulated by introducing the energy dependence in real part of nucleus–nucleus potential.

Mapping from quasi-elastic scattering to fusion reactions

The fusion barrier distribution has provided a nice representation for the channel coupling effects on heavy-ion fusion reactions at energies around the Coulomb barrier. Here we discuss how one can extract the same representation using the so called sum-of-differences (SOD) method with quasi-elastic scattering cross sections. In contrast to the conventional quasi-elastic barrier distribution, the SOD barrier distribution has an advantage in that it can be applied both to non-symmetric and symmetric systems. It is also the case that the correspondence to the fusion barrier distribution is much better than the quasi-elastic barrier distribution. We demonstrate its usefulness by studying $^{16}$O+$^{144}$Sm, $^{58}$Ni+$^{58}$Ni, and $^{12}$C+$^{12}$C systems.

Microscopic study of noncentral effects in heavy-ion fusion reactions with spherical nuclei

Fusion reactions of $^{16}\mathrm{O}+^{16}\mathrm{O},^{40}\mathrm{Ca}+^{40}\mathrm{Ca}$, and $^{40}\mathrm{Ca}+^{90}\mathrm{Zr}$ have been investigated by using the three-dimensional (3D) time-dependent Hartree-Fock approach with and without density constraint. The interaction potentials and effective mass parameters are studied. It is found that both the nucleus-nucleus interaction potentials and the effective mass parameters of these systems depend on the impact parameter. Such noncentral effects on fusion cross sections are also investigated. It is shown that the noncentral effect can reduce the fusion cross sections significantly when the incident energy is just above the barrier, while it becomes weaker with the increasing incident energy and can be totally neglected when the energy is up to twice as much as the barrier height in these spherical colliding systems.

Systematic study ofO16-induced fusion with the improved quantum molecular dynamics model

The heavy-ion fusion reactions with $^{16}\mathrm{O}$ bombarding on $^{62}\mathrm{Ni},^{65}\mathrm{Cu},^{74}\mathrm{Ge},^{148}\mathrm{Nd},^{180}\mathrm{Hf},^{186}\mathrm{W},^{208}\mathrm{Pb},^{238}\mathrm{U}$ are systematically investigated with the improved quantum molecular dynamics model. The fusion cross sections at energies near and above the Coulomb barriers can be reasonably well reproduced by using this semiclassical microscopic transport model with the parameter sets SkP* and IQ3a. The dynamical nucleus-nucleus potentials and the influence of Fermi constraint on the fusion process are also studied simultaneously. In addition to the mean field, the Fermi constraint also plays a key role for the reliable description of the fusion process and for improving the stability of fragments in heavy-ion collisions.

Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure

Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly-bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, they are all characterized by large sizes and complex topologies, in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory. To describe complex superfluid many-fermion systems, we introduce an adaptive pseudo-spectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver {\madnesshfb} is benchmarked against a two-dimensional coordinate-space solver {\hfbax} based on B-spline technique and three-dimensional solver {\hfodd} based on the harmonic oscillator basis expansion. Several examples are considered, including self-consistent HFB problem for spin-polarized trapped cold fermions and Skyrme-Hartree-Fock (+BCS) problem for triaxial deformed nuclei. The new {\madnesshfb} framework has many attractive features when applied to nuclear and atomic problems involving many-particle superfluid systems. Of particular interest are weakly-bound nuclear configurations close to particle drip lines, strongly elongated and dinuclear configurations such as those present in fission and heavy ion fusion, and exotic pasta phases that appear in the neutron star crust.

Microscopic dynamics simulations of heavy-ion fusion reactions induced by neutron-rich nuclei

The heavy-ion fusion reactions induced by neutron-rich nuclei are investigated with the improved quantum molecular dynamics (ImQMD) model. With a subtle consideration of the neutron skin thickness of nuclei and the symmetry potential, the stability of nuclei and the fusion excitation functions of heavy-ion fusion reactions $^{16}$O+$^{76}$Ge, $^{16}$O+$^{154}$Sm, $^{40}$Ca+$^{96}$Zr and $^{132}$Sn+$^{40}$Ca are systematically studied. The fusion cross sections of these reactions at energies around the Coulomb barrier can be well reproduced by using the ImQMD model. The corresponding slope parameter of the symmetry energy adopted in the calculations is $L \approx 78$ MeV and the surface energy coefficient is $g_{\rm sur}=18\pm 1.5$ MeVfm$^2$. In addition, it is found that the surface-symmetry term significantly influences the fusion cross sections of neutron-rich fusion systems. For sub-barrier fusion, the dynamical fluctuations in the densities of the reaction partners and the enhanced surface diffuseness at neck side result in the lowering of the fusion barrier.

Study of angular momentum variation due to entrance channel effect in heavy ion fusion reactions

A systematic investigation of the properties of hot nuclei may be studied by detecting the evaporated particles. These emissions reflect the behavior of the nucleus at various stages of the deexcitation cascade. When the nucleus is formed by the collision of a heavy nucleus with a light particle, the statistical model has done a good job of predicting the distribution of evaporated particles when reasonable choices were made for the level densities and yrast lines. Comparison to more specific measurements could, of course, provide a more severe test of the model and enable one to identify the deviations from the statistical model as the signature of other effects not included in the model. Some papers have claimed that experimental evaporation spectra from heavy-ion fusion reactions at higher excitation energies and angular momenta are no longer consistent with the predictions of the standard statistical model.In order to confirm this prediction we have employed two systems, a mass-symmetric (31P+45Sc) and a mass-asymmetric channel (12C+64Zn), leading to the same compound nucleus 76Kr* at the excitation energy of 75 MeV. Neutron energy spectra of the asymmetric system (12C+64Zn) at different angles are well described by the statistical model predictions using the normal value of the level density parameter a = A/8 MeV−1. However, in the case of the symmetric system (31P+45Sc), the statistical model interpretation of the data requires the change in the value of a = A/10 MeV−1. The delayed evolution of the compound system in case of the symmetric 31P+45Sc system may lead to the formation of a temperature equilibrated dinuclear complex, which may be responsible for the neutron emission at higher temperature, while the protons and alpha particles are evaporated after neutron emission when the system is sufficiently cooled down and the higher g-values do not contribute in the formation of the compound nucleus for the symmetric entrance channel in case of charged particle emission.

Classical simulations of heavy-ion fusion reactions and weakly-bound projectile breakup reactions

Heavy-ion collision simulations in various classical models are discussed. Heavy-ion reactions with spherical and deformed nuclei are simulated in a classical rigid-body dynamics (CRBD) model which takes into account the reorientation of the deformed projectile. It is found that the barrier parameters not only on the initial orientations of the deformed nucleus, but also on the collision energy and the moment of inertia of the deformed nucleus. Maximum reorientation effect occurs at near- and below-barrier energies for light deformed nuclei. Calculated fusion cross-sections for 24Mg + 208Pb reaction are compared with a static-barrier-penetration model (SBPM) calculation to see the effect of reorientation. Heavy-ion reactions are also simulated in a 3-stage classical molecular dynamics (3S-CMD) model in which the rigid-body constraints are relaxed when the two nuclei are close to the barrier thus, taking into account all the rotational and vibrational degrees of freedom in the same calculation. This model is extended to simulate heavy-ion reactions such as6Li + 209Bi involving the weakly-bound projectile considered as a weakly-bound cluster of deuteron and 4He nuclei, thus, simulating a 3-body system in 3S-CMD model. All the essential features of breakup reactions, such as complete fusion, incomplete fusion, no-capture breakup and scattering are demonstrated.

Recent developments in heavy-ion fusion reactions

In this review the main advances in heavy-ion fusion research that have taken place over the last decade are addressed. During this period, experimental studies have been extended to deep subbarrier energies to reveal the unexpected phenomenon of fusion hindrance. The coupled-channels descriptions have been refined to include the effects of nucleon transfer and to account for the fusion hindrance in terms of the ion-ion potential in the strongly overlapping region. Substantial progress has been made in time-dependent Hartree-Fock theory to the point that this approach now can make parameter-free predictions of heavy-ion fusion excitation functions. As several heavy-ion fusion reactions are of crucial importance in late-stage giant-star evolution, these reactions continue to be studied with better experimental and theoretical tools in order to provide improved input to astrophysical models. The effects of loosely bound valence nucleons on the fusion cross sections are the focus of a number of experimental studies involving radioactive beams, which have only recently become available. And finally, as the active field of synthesizing superheavy elements relies on heavy-ion fusion to reach the nuclei of interest, it is important to understand the fusion dynamics that plays a crucial role in both the “cold-fusion” and “hot-fusion” approaches to the superheavy island of stability. Also this area has seen significant progress in several different approaches to the problem of predicting the cross sections for formation and survival of these rare nuclei.

Probable Projectile-Target Combinations for the Synthesis of Super Heavy Nucleus 286112

The fusion cross sections for the reactions of all the projectile-target combinations found in the cold valleys of 286 112 have been studied using scattering potential as the sum of Coulomb and proximity potential, so as to predict the most probable projectile-target combinations in heavy ion fusion reactions for the synthesis of super heavy nucleus 286 112. While considering the nature of potential pockets and half lives of the colliding nuclei, the systems 82 Ge + 204 Hg, 80 Ge + 206 Hg and 78 Zn + 208 Pb found in the deep cold valley region and the systems 48 Ca+ 238 U, 38 S+ 248 Cm and 44 Ar+ 242 Pu in the cold valleys are predicted to be the better optimal projectile-target combinations for the synthesis of super heavy nucleus 286 112.

Analysis of heavy-ion fusion reactions at extreme sub-barrier energies using the proximity formalism

The recent measured values of the fusion excitation functions of the heavy-ion colliding systems ${}^{28}$Si${+}^{100}$Mo, ${}^{58}$Ni${+}^{54}$Fe, and ${}^{64}$Ni${+}^{64}$Ni are investigated using the original version of the proximity formalism. The fusion cross sections are calculated based on the coupled-channels approach, including couplings to the low-lying ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states in both target and projectile nuclei. The comparison between the calculated and the measured values of the fusion excitation functions indicates that the potential Prox.77 needs to be modified considerably at sub-barrier energies. In the present study, the role of the surface energy coefficient $\ensuremath{\gamma}$ and also the temperature $T$ of the compound nucleus in nuclear potential and fusion cross section has been explored for our colliding systems. Moreover, the mutual and the multiphonon excitations of the lowest ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states are considered in the coupled-channels calculations. It is demonstrated that the potential Prox.77 with these corrective effects can reproduce the experimental data of the fusion cross section, the $S$ factor and the logarithmic derivative for fusion reactions ${}^{28}$Si${+}^{100}$Mo, ${}^{58}$Ni${+}^{54}$Fe, and ${}^{64}$Ni${+}^{64}$Ni with good accuracy especially at below-barrier energies.