Fusion Barrier Research Articles

Dynamical nucleus-nucleus potential at short distances

The dynamical nucleus-nucleus potentials for fusion reactions 40Ca+40Ca, 48Ca+208Pb and 126Sn+130Te are studied with the improved quantum molecular dynamics (ImQMD) model together with the extended Thomas-Fermi approximation for the kinetic energies of nuclei. The obtained fusion barrier for 40Ca+40Ca is in good agreement with the extracted fusion barrier from the measured fusion excitation function, and the depth of the fusion pockets are close to the results of time-dependent Hartree-Fock calculations. The energy dependence of fusion barrier is also investigated. For heavy fusion system, the fusion pocket becomes shallow and almost disappears for symmetric systems and the obtained potential at short distances is higher than the adiabatic potential.

Near-barrier fusion and barrier distribution ofNi58+Fe54

Near- and sub-barrier fusion cross sections have been measured for the system {sup 58}Ni+{sup 54}Fe, and the fusion barrier distribution has been extracted. The measured cross sections cover the range from approx =1 mub up to around 500 mb. Close analogies are found between the extracted barrier distribution and the available data on {sup 58}Ni+{sup 60}Ni, indicating the dominating influence of complex surface vibrations on the fusion of {sup 58}Ni+{sup 54}Fe. The present data on {sup 58}Ni+{sup 54}Fe are well reproduced by standard coupled-channels calculations in the measured energy range, including quadrupole and octupole phonons in both colliding nuclei.

Suppression of fusion by breakup: Resolving the discrepancy between the reactions ofBe9withPb208andBi209

Complete fusion cross sections for $^{9}\mathrm{Be}$ incident on $^{208}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ have been measured at energies greater than the fusion barrier to investigate the large differences in their reported complete fusion cross sections. Relative $\mathit{xn}$ and fission cross sections are in good agreement. Thus, it is concluded that the differences arise from errors in absolute normalization in the previous measurements. The present measurements show that the above-barrier complete fusion cross sections for the reactions of $^{9}\mathrm{Be}$ with $^{209}\mathrm{Bi}$ and $^{208}\mathrm{Pb}$ are very similar, which resolves the previously observed anomaly. Complete fusion for the reaction of $^{9}\mathrm{Be}$ with $^{209}\mathrm{Bi}$ is found to be suppressed by $~32%$ compared to the expectations of a single-barrier penetration model, which is in close agreement with the value previously determined for the reaction with $^{208}\mathrm{Pb}$.

Dependence of barrier distribution and fusion-fission process on entrance channel

The entrance barrier distributions for the heavy systems 48Ti, 54Cr, 56Fe, 64Ni, 70Zn, 76Ge and 86Kr + 208Pb have been extracted from excitation functions for quasi-elastic scattering at backward angles. The entrance barrier heights for these systems are presented. The fusion probability for the system 64Ni + 154Sm has been obtained from the measurement of evaporation residues. It is shown that the fusion barrier shifts to high energies corresponding to barrier heights at an equatorial side of the prolate nucleus 154Sm.

Reaction dynamics of weakly bound nuclei at near-barrier energies

The above-barrier suppression of complete fusion in reactions with weakly bound stable nuclei displays a strong correlation with their breakup threshold. Simplistically, this observation suggests that suppression of complete fusion is due to the direct breakup of the weakly bound partner, prior to reaching the barrier. However, new measurements of breakup at energies below the fusion barrier show that breakup following transfer, rather than direct breakup, is the dominant mechanism. The insights into the physical mechanisms of breakup from these measurements, in conjunction with theoretical developments, are being used to obtain an understanding of the relationship between sub-barrier breakup and suppression of complete fusion.

Competition between fusion-fission and quasifission processes in 32S+ 184W reaction

The angular distributions of fission fragments for the 32S+ 184W reaction at center-of-mass energies of 118.8, 123.1, 127.3, 131.5, 135.8, 141.1 and 144.4 MeV were measured. The fragment angular anisotropies are found by extrapolating the fission angular distributions. The measured fission cross sections are decomposed into fusion-fission, quasifission and fast-fission contributions by the dinuclear system model. The hindrance to complete fusion at small collision energies increases due to the increase of quasifission events and it is explained by the elongated shape of the dinuclear system which is formed in collisions with small orientation angles to the beam direction. An increase of the hindrance to complete fusion at large beam energies is explained by the dependence of the quasifission and intrinsic fusion barriers of dinuclear system on its angular momentum. In this reaction the contributions of fusion-fission and quasifission fragments are comparable.

Elastic and quasielastic barrier distributions for light neutron-rich nuclei: The role of neutron stripping channels

Recent interest in the elastic and quasielastic barrier distributions of systems involving weakly bound light projectiles has concentrated on the influence of coupling to breakup. We show that, for light neutron-rich radioactive beams, single-neutron stripping also has an important effect on the calculated barrier distribution. We also show that the recent suggestion that for such systems the quasielastic barrier distribution will not be exactly equivalent to the true fusion barrier distribution seems to hold true, although in the particular case investigated here the discrepancy in the barrier peak position, $0.25$ MeV, is considerably smaller than that found experimentally for the $^{6}\mathrm{Li}+^{144}\mathrm{Sm}$ system, $1.5$ MeV, where breakup is considered to be most important.

Effects of weakly coupled channels on quasielastic barrier distributions

Heavy-ion collisions often produce fusion barrier distributions with structures displaying a fingerprint of couplings to highly collective excitations. Similar distributions can be obtained from large-angle quasielastic scattering, although in this case, the role of the many weak direct-reaction channels is unclear. For $^{20}\mathrm{Ne}+^{90}\mathrm{Zr}$, we have observed the barrier structures expected for the highly deformed neon projectile; however, for $^{20}\mathrm{Ne}+^{92}\mathrm{Zr}$, we find significant extra absorption into a large number of noncollective inelastic channels. This leads to smearing of the barrier distribution and a consequent reduction in the ``resolving power'' of the quasielastic method.

Interpretation of quasi-elastic barrier distributions for weakly bound systems

We verify that quasi-elastic (elastic$+$inelastic) backscattering barrier distributions for weakly-bound systems do not strictly correspond to fusion barrier distributions, but rather to a reaction threshold distribution, as proposed by Zagrebaev [Phys. Rev. C 78, 047602 (2008)] in a recent paper concerning very heavy systems.

Barrier distributions for weakly bound systems

We discuss the use of reduced fusion cross sections in the derivation of fusion barrier distributions. We show that the elimination of static effects associated with system sizes and optical potentials obtained by the recently introduced fusion functions can be extended to barrier distributions. This can be a useful tool for systematic studies of breakup coupling effects in fusion processes.

Breakup coupling effects on near-barrier quasi-elastic scattering ofLi6,7onSm144

Excitation functions of quasi-elastic scattering at backward angles have been measured for the $^{6,7}\mathrm{Li}+^{144}\mathrm{Sm}$ systems at near-barrier energies, and fusion barrier distributions have been extracted from the first derivatives of the experimental cross sections with respect to the bombarding energies. The data have been analyzed in the framework of continuum discretized coupled-channel calculations, and the results have been obtained in terms of the influence exerted by the inclusion of different reaction channels, with emphasis on the role played by the projectile breakup.

Fusion dynamics of symmetric systems near barrier energies

Within the framework of the improved isospin-dependent quantum molecular dynamics (ImIQMD) model, the fusion dynamics of symmetric reaction systems are investigated systematically. Calculations show that the number of nucleon transfer in the neck region is appreciably dependent on the incident energies, but strongly on the reaction systems. A comparison of the neck dynamics is performed for the symmetric reactions $^{58}\mathrm{Ni}+^{58}\mathrm{Ni}$ and $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$ at energies in the vicinity of the Coulomb barrier. An increase of the ratios of the neutron to proton in the neck region at initial collision stage is observed and obvious for the latter system, which reduces the fusion barrier of two colliding nuclei. The distribution of the dynamical fusion barriers and the fusion excitation functions are calculated and compared with the available experimental data.

THE EFFECT OF SURFACE NUCLEON DENSITY ON THE TOTAL POTENTIAL OF DI-NUCLEAR SYSTEMS

The effect of the density of the surface nucleons on the calculation of the total potential in reactions where the participant nuclei are on the stability line and at least one of the participant nuclei is rich in neutrons has been studied. The results obtained by the analysis of the 16 O +209 Bi , 16 O +144 Nd , and 16 O +144 Sm reactions using the Hartree–Fock calculations of the neutron and the proton densities show a decrease of about 0.67, 0.53, and 0.45 MeV of the fusion barrier height in comparison to the corresponding values obtained when the nuclear density is taken to be proportional to the nuclear charge. It is shown that this decrease is due to the variation of the ratio of the density of neutrons to that of the protons in outer regions of the nuclear densities of 209 Bi , 144 Nd , and 144 Sm nuclei.

Fusion enhancement in the reactions of neutron-rich nuclei

The neutron-rich fusion reactions are investigated systematically using the improved isospin dependent quantum molecular dynamics model. By studying the systematic dependence of fusion barrier on neuron excess, we find the enhancement of the fusion cross sections for neutron-rich nuclear reactions that give the lowered static Coulomb barriers. The calculated fusion cross sections agree quantitatively with the experimental data. We further discuss the mechanism of the fusion enhancement of the cross sections for neutron-rich nuclear reactions by analyzing the dynamical lowering of the Coulomb barrier that is attributed to the enhancement of the N / Z ratio at the neck region.

Improved determination of the fusion barrier distribution

The usual formula employed to estimate the barrier distribution in fusion reactions contains a systematic error. The origin of this error is related to the numerical approximation of the second derivative appearing in the expression of the barrier distribution. We show how to approximately correct for this systematic error. Previous determinations of the uncertainties in the barrier distribution, that did not include this error, could be severely underestimated. Furthermore, we find that minimization of the total error leads to an optimal energy grid at which the fusion cross section data should be taken.

The effect of difference between neutron and proton density distributions on the nuclei fusion barrier in a double folding model

The basic parameters (height, radius, and curvature) of the atomic nuclei fusion barrier are compared for the cases where the proton and neutron density distributions are identical and where they are different. As the difference exceeds 11%, it must be taken into consideration, especially for neutron-deficient and neutron-rich nuclides.

Nucleon–nucleon interactions in the double folding model for fusion reactions

Nucleus–nucleus potentials are determined in the framework of double folding model for M3Y–Reid and M3Y–Paris effective nucleon–nucleon (NN) interactions. Both zero-range and finite-range exchange parts of NN interactions are considered in the folding procedure. In this paper the spherical projectile-spherical target system 16O+208Pb is selected for calculating the barrier energies, fusion cross sections and barrier distributions with the density-independent and density-dependent NN interactions on the basis of M3Y–Reid and M3Y–Paris NN interactions. The barrier energies become lower for Paris NN interactions in comparison with Reid NN interactions, and also for finite-range exchange part in comparison with zero-range exchange part. The density-dependent NN interactions give similar fusion cross sections and barrier distributions, and the density-independent NN interaction causes the barrier distribution moving to a higher position. However, the density-independent Reid NN interaction with zero-range exchange part gives the lowest fusion cross sections. We find that the calculated fusion cross sections and the barrier distributions are in agreement with the experimental data after renormalization of the nuclear potential due to coupled-channel effect.

Energetics of (dis)assembly of the ternary SNARE complex

Energetics of (dis)assembly of the ternary SNARE complex

Heavy-ion fusion cross sections and barrier distributions for 12C, 16O, 28Si and 35Cl on 92Zr

The fusion excitation functions and barrier distributions for the fusion of 12C, 16O, 28Si and 35Cl on 92Zr have been calculated using one-dimensional barrier penetration model, taking scattering potential as the sum of Coulomb and proximity potential. Calculated results are compared with experimental data and CC calculations using code CCFULL. At and above the barrier the computed cross sections match well with the experimental data, whereas below the barrier, calculations with nuclear surface tension coefficient improved by Reisdorf in the proximity potential give good fit. Reduced reaction cross sections for the systems have also been described.

132Sn+96Zrreaction: A study of fusion enhancement/hindrance

Capture-fission cross sections were measured for the collision of the massive nucleus {sup 132}Sn with {sup 96}Zr at center-of-mass energies ranging from 192.8 to 249.6 MeV in an attempt to study fusion enhancement and hindrance in this reaction involving very neutron-rich nuclei. Coincident fission fragments were detected using silicon detectors. Using angle and energy conditions, deep inelastic scattering events were separated from fission events. Coupled-channels calculations can describe the data if the surface diffuseness parameter, a, is allowed to be 1.10 fm instead of the customary 0.6 fm. The measured capture-fission cross sections agree moderately well with model calculations using the dinuclear system model. If we use this model to predict fusion barrier heights for these reactions, we find the predicted fusion hindrance, as represented by the extra push energy, is greater for the more neutron-rich system, lessening the advantage of the lower interaction barriers with neutron-rich projectiles.