Fusion Barrier Research Articles

Fusion mechanism in fullerene-fullerene collisions: The deciding role of giant oblate-prolate motion

We provide answers to long-lasting questions in the puzzling behavior of fullerene-fullerene fusion: Why are the fusion barriers so exceptionally high and the fusion cross sections so extremely small? An ab initio nonadiabatic quantum molecular-dynamics (NA-QMD) analysis of C60 + C60 collisions reveals that the dominant excitation of an exceptionally “giant” oblate-prolate mode plays the key role in answering both questions. From these microscopic calculations, a macroscopic collision model is derived, which reproduces the NA-QMD results. Moreover, it predicts analytically fusion barriers for different fullerene-fullerene combinations in excellent agreement with experiments.

On the role of deformed Coulomb potential in fusion using energy density formalism

Using the Skyrme energy density formalism, the effect of deformed Coulomb potential on fusion barriers and fusion cross-sections is studied. Our detailed study reveals that the fusion barriers as well as fusion probabilities depend on the shape deformation (due to deformed Coulomb potential) of the colliding nuclei. However, this dependence due to deformed Coulomb potential is found to be very weak.

Complete dissociation of the HIV-1 gp41 ectodomain and membrane proximal regions upon phospholipid binding

The envelope glycoprotein gp41 mediates the process of membrane fusion that enables entry of the HIV-1 virus into the host cell. Strong lipid affinity of the ectodomain suggests that its heptad repeat regions play an active role in destabilizing membranes by directly binding to the lipid bilayers and thereby lowering the free-energy barrier for membrane fusion. In such a model, immediately following the shedding of gp120, the N-heptad and C-heptad helices dissociate and melt into the host cell and viral membranes, respectively, pulling the destabilized membranes into juxtaposition, ready for fusion. Post-fusion, reaching the final 6-helix bundle (6 HB) conformation then involves competition between intermolecular interactions needed for formation of the symmetric 6 HB trimer and the membrane affinity of gp41's ectodomain, including its membrane-proximal regions. Our solution NMR study of the structural and dynamic properties of three constructs containing the ectodomain of gp41 with and without its membrane-proximal regions suggests that these segments do not form inter-helical interactions until the very late steps of the fusion process. Interactions between the polar termini of the heptad regions, which are not associating with the lipid surface, therefore may constitute the main driving force initiating formation of the final post-fusion states. The absence of significant intermolecular ectodomain interactions in the presence of dodecyl phosphocholine highlights the importance of trimerization of gp41's transmembrane helix to prevent complete dissociation of the trimer during the course of fusion.

Impact of Reaction Cross Section on the Unified Description of Fusion Excitation Function

A systematics of over 300 complete and incomplete fusion cross section data points covering energies beyond the barrier for fusion is presented. Owing to a usual reduction of the fusion cross sections by the total reaction cross sections and an original scaling of energy, a fusion excitation function common to all the data points is established. A universal description of the fusion exci- tation function relying on basic nuclear concepts is proposed and its dependence on the reaction cross section used for the cross section normalization is discussed. The pioneering empirical model proposed by Bass in 1974 to describe the complete fusion cross sections is rather successful for the incomplete fusion too and provides cross section predictions in satisfactory agreement with the observed universality of the fusion excitation function. The sophisticated microscopic transport DYWAN model not only reproduces the data but also predicts that fusion reaction mechanism disappears due to weakened nuclear stopping power around the Fermi energy.

Breakup following interactions with light targets: Investigating new methods to probe nuclear physics input to the cosmological lithium problem.

A well known issue with concordance cosmology is the cosmological lithium problem, where models of Big Bang Nucleosynthesis indicate abundances of 7 Li three to four times larger than values inferred via spectroscopic measurements of metal-poor halo stars [1]. Since the source of this discrepancy remains unclear [2], it is vital to fully understand the nuclear reactions that affect the production of 7 Li during the Big Bang [3]. At the Australian National University, experimental equipment and analysis techniques have been developed for nuclear reaction studies at energies near the fusion barrier, exploiting large solid angle detectors to enable the investigation of breakup without a priori assumption of the breakup kinematics. The extension to reactions of astrophysical interest may help shed light on these reactions. Recent experiments, using these new techniques, have provided a complete picture of the breakup mechanisms of light nuclei in collisions with heavy targets [4]. The present work focuses on obtaining a complete picture of breakup mechanisms of 7 Li following interactions with 27 Al. It has been found that breakup is almost exclusively triggered by nucleon transfer between the colliding partners, to a larger extent than was found for heavier targets. The findings of these experiments, as well as progress towards extensions to astrophysically relevant reactions, such as d + 7 Be [5] will be presented.

One neutron transfer reaction in the9Be+89Y system

One neutron transfer cross sections from the interaction of 9 Be with 89 Y have been measured at energies greater than the fusion barrier. The present measured 1n-transfer cross sections saturate at well above energies in comparison with the available experimental data at lower energies. Results of Coupled Reaction Channels Calculations (CRC) show very good agreement with the present measured cross sections.

Dynamical approach to heavy ion-induced fission

Deep inelastic collisions (DICs) can compete strongly with fusion in collisions of heavy nuclei. However, standard coupled-channels calculations do not take DIC processes into account. As a result, calculations have been shown to overestimate the fusion cross-sections, resulting in a discrepancy between experimental data and theoretical calculations, particularly at energies above the fusion barrier. To investigate this discrepancy, we conducted a series of experiments using the ANU 14UD tandem accelerator and the CUBE 2-body fission spectrometer to examine the competition between transfer/DIC and fusion. In particular, fusion-fission and 3-body fission yields have been extracted for 34 S + 232 Th and 40 Ca + 232 Th systems. This work shows that the transfer-fission probability is enhanced relative to fusion-fission for 40 Ca + 232 Th, when compared to 34 S+ 232 Th. It is suggested that the enhancement of this DIC process in 40 Ca + 232 Th is linked to an increase in the density overlap of the colliding nuclei as a function of the charge product and contributes to fusion hindrance.

Three-stage classical molecular dynamics model for simulation of heavy-ion fusion

A three-stage Classical Molecular Dynamics (3S-CMD) approach for heavy-ion fusion is developed. In this approach the Classical Rigid-Body Dynamics simulation for heavy-ion collision involving light deformed nucleus is initiated on their Rutherford trajectories at very large initial separation. Collision simulation is then followed by relaxation of the rigid-body constrains for one or both the colliding nuclei at distances close to the barrier when the trajectories of all the nucleons are obtained in a Classical Molecular Dynamics approach. This 3S-CMD approach explicitly takes into account not only the long range Coulomb reorientation of the deformed collision partner but also the internal vibrational excitations of one or both the nuclei at distances close to the barrier. The results of the dynamical simulation for 24 Mg+208 Pb collision show significant modification of the fusion barrier and calculated fusion cross sections due to internal excitations.

Effect of pairing on transfer and fusion reactions

In the present contribution, the effect of pairing on nuclear transfer and fusion reactions close to the Coulomb barrier is discussed. A Time-Dependent Hartree-Fock + BCS (TDHF+BCS) microscopic theory has been developed to incorporate pairing. One- and two-particle transfer probabilities can be obtained showing the importance of pairing. The calculated transfer probabilities are compared to the recent experimental results obtained for the $^{96}$Zr+$^{40}$Ca. Reactions involving the $^{18}$O with lead isotopes are also presented, that are also of current experimental interest. Finally, a study of the fusion barrier height predicted with the TDHF+BCS theory is compared to the experimental values for the $^{40,44,48}$Ca+$^{40}$Ca reactions.

Fusion Hindrance and Quadrupole Collectivity in Collisions of A≃50 Nuclei: The Case of48Ti +58Fe

The fusion excitation function of 48 Ti + 58 Fe has been measured in a wide energy range around the Coulomb barrier, covering 6 orders of magnitude of the cross sections. We present here the preliminary re- sults of this experiment, and a full comparison with the near-by system 58 Ni + 54 Fe where evidence of fusion hindrance shows up at relatively high cross sections. The sub-barrier cross sections of 48 Ti + 58 Fe are much larger than those of 58 Ni + 54 Fe. Significant differences are also observed in the logarithmic derivatives, astro- physical S-factors and fusion barrier distributions. The influence of low-energy nuclear structure on all these trends is pointed out and commented. Coupled-channels calculations using a Woods-Saxon potential are able to reproduce the experimental results for 48 Ti + 58 Fe. The logarithmic derivative of the excitation function is very nicely fit, and no evidence of hindrance is observed down to around 1 μb. The fusion barrier distribution is rather wide, flat and structureless. It is only in qualitative agreement with the calculated distribution.

A new technique to determine fusion barrier heights using proximity potentials

We develop a new technique to calculate fusion barrier heights of any fixed target reaction series. We calculate the barrier heights for the fusion reactions of 119 Sn and 197 Au targets using this technique. This technique is simple and very useful for estimating the fusion barrier heights for those reactions for which empirical values are not available. A formula is derived by performing theoretical calculations using different versions of proximity potential. Using this formula, we can predict the barrier height for the fusion reaction of any projectile with 119 Sn or 197 Au target using the empirical barrier height for the fusion reaction of same projectile with 62 Ni target. In order to check the accuracy of this technique, the fusion parameters calculated by this new technique are compared with the fusion parameters calculated by using parameterized formulae presented in a systematic study conducted by using double folding model. the colliding nuclei. The separation between the two col- liding nuclei is related to the internuclear distance between the centers of the colliding nuclei through their nuclear radii. So we need accurate knowledge of nuclear radii. In the present study, we propose a new technique, which can be used to calculate the fusion barrier heights of any fixed target reaction series. For this study, we first compute barrier heights for X + 62 Ni, X + 119 Sn and X + 197 Au reaction series using different versions of proximity potential. Here, X projectile varies from 1 Ht o 59 Co. This study is carried out using proximity potentials PROX 77, PROX 88, PROX 2000, PROX 2000DP, PROX 2010 and MOD-PROX 88.

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.

Effect of projectile breakup on fission-fragment mass distributions in theLi6,7 + U238reactions

Background: Detailed studies on the effect of the breakup of weakly bound projectile on fission are scarce. Distinguishing the events of compound nuclear (CN) fission from the breakup or transfer induced fission to understand the properties of measured fission fragments is difficult but desirable.Purpose: To investigate the effect of projectile breakup and its breakup threshold energy on fission-fragment (FF) mass distributions and folding angle distributions for $^{6,7}\mathrm{Li} + ^{238}\mathrm{U}$ reactions and find out the differences in the properties of the fission events produced by complete fusion (CF) from the total fusion (TF).Methods: The FF mass and folding angle distributions have been measured at energies around the Coulomb barrier using gas detectors by time-of-flight technique. The results are compared with the ones involving tightly bound projectiles as well as predictions from systematics to bring out the effect of the breakup.Results: A sharp increase in the peak to valley (P:V) ratio of FF mass distribution with the decrease in bombarding energy for $^{6,7}\mathrm{Li} + ^{238}\mathrm{U}$ reactions is observed when all events are assumed to be CN fission. As the beam energy falls through the fusion barrier, the full width half maximum (FWHM) of the FF folding angle distribution is found to increase at sub-barrier energies, unlike the reactions involving tightly bound projectiles where a linear decrease in FWHM is expected. By selecting pure CN events from the scatter plot of the velocity components of the composite nuclei, the energy dependence of the deduced FWHM is found to be consistent with the ones involving tightly bound projectiles. Similarly, the P:V ratio obtained for the selected CN events is consistent with the theoretical calculations as well as the experimental data for the proton induced reaction forming similar CN.Conclusions: The presence of projectile breakup induced fission and a relatively low breakup threshold for $^{6}\mathrm{Li}$ compared to $^{7}\mathrm{Li}$ explains the observed differences in the energy dependence of the P:V ratio and the FWHM of FF folding angle distributions for CF and TF fission in the present reactions.

Proximity Approach to Study the Fusion Barriers for Proton and Helium Induced Reactions

By using various proximity potentials, the fusion barrier heights and positions are calculated for proton and helium induced reactions with targets in the mass range 51 ≤ A ≤ 130 and 12 ≤ A ≤ 233, respectively. The calculated fusion barriers are parameterized by using the relations RBPar = aX1 + b and VBPar = cX2, where X1 and X2 are A21/3 and , respectively. The values of the constants a, b and c are different for different versions of proximity potentials. We and that the parameterized forms derived by using Proximity 1977 yield values closer to the empirical data in proton as well as helium induced reactions and can be used further to estimate directly the barrier parameters for the fusion reactions of proton and helium with any target.

Parametrization of fusion barriers based on empirical data

Abstract Using the empirical/experimental fusion barrier heights and positions, we perform a systematic study for large number of reactions having projectile/target masses 6 ≤ A ≤ 238 and present new parameterized form for fusion barrier heights and positions. A comparison with other well known parameterized forms is also made.

Sub-barrier enhancement of fusion as compared to a microscopic method inO18+C12

Measurement of the energy dependence of the fusion cross-sec on at sub-barrier energies provides an important test for theoretical models of fusion. To extend the measurement of fusion cross-sections in the sub-barrier domain for the 18O+12C system. Use the new experimental data to confront microscopic calculations of fusion. Evaporation residues produced in fusion of 18O ions with 12C target nuclei were detected with good geometric efficiency and identified by measuring their energy and time-of-flight. Theoretical calculations with a density constrained time dependent Hartree-Fock (DC-TDHF) theory include for the first time the effect of pairing on the fusion cross-section. Comparison of the measured fusion excitation function with the predictions of the DC-TDHF calculations reveal that the experimental data exhibits a smaller decrease in cross-section with decreasing energy than is theoretically predicted. The larger cross-sections observed at the lowest energies measured indicate a larger tunneling probability for the fusion process. This larger probability can be associated with a smaller, narrower fusion barrier than presently included in the theoretical calculations.

Fusion barrier distributions inLi6,7+Bi209reactions from quasi-elastic and fusion excitation function measurements

Fusion barrier distributions have been obtained from the measurement of the quasi-elastic scattering excitation functions at a backward angle in the reactions of $^{6,7}\mathrm{Li}$ with $^{209}\mathrm{Bi}$. Comparisons have been carried out among barrier distributions, obtained from quasi-elastic scattering by considering elastic + inelastic and elastic + inelastic + [breakup(BU) and/or transfer] and also from fusion excitation function measurements. It has been observed that representations of barrier distributions obtained from elastic + inelastic + [breakup(BU) and/or transfer] and from fusion excitation functions are in good agreement showing the importance of the inclusion breakup channels for the correct fusion barrier representations in the $^{6,7}\mathrm{Li}+^{209}\mathrm{Bi}$ reactions. The observed discrepancy in the resultant barrier distributions with and without including breakup and/or transfer has been interpreted in terms of the capture barrier distribution. The results obtained from the continuum discretized coupled channels calculations also follow the fusion barrier distributions which have been obtained from the fusion excitation functions measurements. It has been observed that the inclusion of direct breakup $\ensuremath{\alpha}$ with the elastic and inelastic channels in quasi-elastic scattering play an important role in explaining consistently the fusion barrier distributions for both the $^{6,7}\mathrm{Li}+^{209}\mathrm{Bi}$ systems.

Systematic study of the isotopic behavior of the fusion cross section at energies near and below the fusion barrier using the proximity formalism

The isotopic behavior of the fusion cross sections and barrier curvature at energies near and below the barrier are explored using the proximity formalism. For this purpose, various versions of the proximity potentials are used to calculate the nuclear part of the interaction potential. Our study has been restricted to the isotopic systems which obey the condition of $0.5\ensuremath{\le}N/Z\ensuremath{\le}1.6$ for their compound nuclei. The obtained results show that the barrier curvature and the fusion cross section follow a similar behavior at near- and below-barrier energies. In fact, these quantities decrease nonlinearly (second order) with the addition of a neutron. In the present study, the energy dependence of the fusion cross sections is also discussed for the considered isotopic systems.

Fusion ofS32 + Zr94: Further exploration of the effect of the positiveQxnvalue neutron transfer channels

The effect of the positive $Q$-value neutron transfer (PQNT) channels on the subbarrier fusion process is still far from a clear understanding and hence is worth further investigation. To this end, we have measured the fusion excitation function for $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ at energies near and below the Coulomb barrier with rather good accuracy, and deduced the experimental fusion barrier distribution. The reaction system $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ is a good candidate for the evaluation of PQNT effect because it has multineutron transfer channels with positive ground-state ${Q}_{xn}$ values as well as the relatively weak low-lying ${3}^{\ensuremath{-}}$ vibrational state in $^{94}\mathrm{Zr}$. Our results show that the fusion cross sections of $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ are strongly enhanced at the lower-energy region. By means of a cross comparison of the $^{32}\mathrm{S}$,$^{40}\mathrm{Ca}+^{90,94,96}\mathrm{Zr}$ systems, further evidence is given that the positive ${Q}_{xn}$-value neutron transfer channels, rather than the strong low-lying ${3}^{\ensuremath{-}}$ vibrational state, bring about the additional subbarrier fusion enhancement. Relative to the coupled-channels results with couplings to the low-lying inelastic collective excitations, an unexpectedly large enhancement for the subbarrier fusion cross sections is observed in $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ compared to $^{32}\mathrm{S}+^{96}\mathrm{Zr}$. Some existing theoretical models have been discussed, but a good explanation cannot be achieved. Exact coupled-channels theory and more experiments on transfer reactions themselves are strongly desired to comprehensively understand the effect of transfer on fusion.

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.