Sub-barrier Fusion Cross Sections Research Articles

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.

Nucleus-nucleus potential with shell-correction contribution and deep sub-barrier fusion of heavy nuclei

It is suggested that the full nucleus-nucleus potential consists of the macroscopic and shell-correction parts. The deep sub-barrier fusion hindrance takes place in a nucleus-nucleus system with a strong negative shell-correction contribution to the full heavy-ion potential, while a strong positive shell-correction contribution to the full potential leads to weak enhancement of the deep sub-barrier fusion cross section.

Energy dependence of potential barriers and its effect on fusion cross sections

Couplings between relative motion and internal structures are known to affect fusion barriers by dynamically modifying the densities of the colliding nuclei. The effect is expected to be stronger at energies near the barrier top, where changes in density have longer time to develop than at higher energies. Quantitatively, modern TDHF calculations are able to predict realistic fusion thresholds. However, the evolution of the potential barrier with bombarding energy remains to be confronted with the experimental data. The aim is to find signatures of the energy dependence of the barrier by comparing fusion cross-sections calculated from potentials obtained at different bombarding energies with the experimental data. This comparison is made for the $^{40}$Ca+$^{40}$Ca and $^{16}$O+$^{208}$Pb systems. Fusion cross-sections are computed from potentials calculated with the density-constrained TDHF method. The couplings decrease the barrier at low-energy in both cases. A deviation from the Woods-Saxon nuclear potential is also observed at the lowest energies. In general, fusion cross-sections around a given energy are better reproduced by the potential calculated at this energy. The coordinate-dependent mass plays a crucial role for the reproduction of sub-barrier fusion cross-sections. Effects of the energy dependence of the potential can be found in experimental barrier distributions only if the variation of the barrier is significant in the energy-range spanned by the distribution. It appears to be the case for $^{16}$O+$^{208}$Pb but not for $^{40}$Ca+$^{40}$Ca. These results show that the energy dependence of the barrier predicted in TDHF calculations is realistic. This confirms that the TDHF approach can be used to study the couplings between relative motion and internal degrees of freedom in heavy-ion collisions.

Fusion at near-barrier energies within the quantum diffusion approach

The nuclear deformation and neutron-transfer process have been identified as playing a major role in the magnitude of the sub-barrier fusion (capture) cross sections. There are a several experimental evidences which confirm the importance of nuclear deformation on the fusion. The influence of nuclear deformation is straightforward. If the target nucleus is prolate in the ground state, the Coulomb field on its tips is lower than on its sides, that then increases the capture or fusion probability at energies below the barrier corresponding to the spherical nuclei. The role of neutron transfer reactions is less clear. The importance of neutron transfer with positive Q-values on nuclear fusion (capture) originates from the fact that neutrons are insensitive to the Coulomb barrier and therefore they can start being transferred at larger separations before the projectile is captured by target-nucleus. Therefore, it is generally thought that the sub-barrier fusion cross section will increase because of the neutron transfer. The fusion (capture) dynamics induced by loosely bound radioactive ion beams is currently being extensively studied. However, the long-standing question whether fusion (capture) is enhanced or suppressed with these beams has not yet been answered unambiguously. The study of the fusion reactions involving nuclei at the drip-lines has led to contradictory results.

Spin-density contribution in the optical potential of openj-shell nuclei

The energy-dependent real and imaginary parts of the optical potential of some twenty pairs of spin-unsaturated, open $j$-shell nuclei are calculated in the energy density model, using the complex Skyrme III energy density. The calculated potentials, without any renormalization, reproduce the experimental data on elastic scattering cross sections of all the pairs of nuclei studied. The contribution of the spin density terms, of the Skyrme III energy density, toward such potentials and toward the corresponding elastic scattering cross sections and sub-barrier fusion cross sections are investigated.

Confronting measured near- and sub-barrier fusion cross sections for20O+12C with a microscopic method

Recently measured fusion cross sections for the neutron-rich system ${}^{20}$O+${}^{12}$C are compared to dynamic, microscopic calculations using time-dependent density functional theory. The calculations are carried out on a three-dimensional lattice and performed both with and without a constraint on the density. The method has no adjustable parameters, and its only input is the Skyrme effective nucleon-nucleon interaction. While the microscopic density constrained time-dependent Hartree-Fock calculations lie closer to the experimental data than standard fusion systematics, they underpredict the experimental data significantly.

Adiabatic internuclear potentials obtained by energy variation with the internuclear-distance constraint

We propose a method to obtain adiabatic internuclear potentials via energy variation with the intercluster-distance constraint. The adiabatic $^{16}$O + $^{16,18}$O potentials obtained by the proposed method are applied to investigate the effects of valence neutrons in $^{16}$O + $^{18}$O sub-barrier fusions. Sub-barrier fusion cross sections of $^{16}$O + $^{18}$O are enhanced more compared to those of $^{16}$O + $^{16}$O because of distortion of valence neutrons in $^{18}$O.

Near-Barrier Fusion ofSn+NiandTe+NiSystems: Examining the Correlation between Nucleon Transfer and Fusion Enhancement

The fusion excitation functions for radioactive (132)Sn + (58)Ni and stable (130)Te + (58,64)Ni were measured at energies near the Coulomb barrier. The coupling of transfer channels in heavy-ion fusion was examined through a comparison of Sn + Ni and Te + Ni systems, which have large variations in the number of positive Q-value nucleon transfer channels. In contrast with previous experimental comparisons, where increased sub-barrier fusion cross sections were observed in systems with positive Q-value neutron transfer channels, the reduced excitation functions were equivalent for the different Sn + Ni and Te + Ni systems. The present results suggest a dramatically different influence of positive Q-value transfer channels on the fusion process for the Sn + Ni and Te + Ni systems.

Fusion of 6Li with 152Sm: Role of projectile breakup versus target deformation

Abstract Complete fusion cross sections for 6 Li + 152 Sm reaction have been measured at beam energies ( E lab = 20 – 40 MeV ) near the Coulomb barrier. The sub-barrier fusion cross sections were found to be systematically larger than those for 6 Li + 144 Sm, as expected from the deformed shape of the 152 Sm nucleus. The coupled-channels (CC) calculations including both projectile and target couplings overpredict the experimental fusion cross sections at above barrier energies. Reduced fusion cross sections for the present system at above barrier energies are found to be smaller compared to those with tightly-bound projectiles forming similar compound nuclei and also to those predicted using proximity potential. These observations along with the comparison of derived barrier distributions conclude that the complete fusion cross sections at energies above the Coulomb barrier are suppressed by 28 ± 4 % . A large cross section measured for incomplete fusion indicates that the above suppression is due to the loss of incident flux caused by projectile breakup. Thus the effect of both target deformation and projectile breakup are found to coexist.

Fusion and transfer reactions around the Coulomb barrier for 28Si+90,94Zr systems

Fusion excitation functions and transfer probabilities were measured for 28Si+90,94Zr systems around the Coulomb barrier, using the recoil mass separator, Heavy Ion Reaction Analyzer (HIRA) at Inter University Accelerator Centre (IUAC), New Delhi. The aim of these experiments was the study of coupling effects of inelastic and transfer channels on the sub-barrier fusion cross section enhancement. The experimental fusion cross sections were found to be strongly enhanced as compared to one dimensional barrier penetration model (1-d BPM) predictions in both the cases. The trend of data could be easily reproduced theoretically using coupled channels code CCFULL in the case of 28Si+90Zr but the observed enhancement could not be explained in the case of 28Si+94Zr, which may be attributed to the coupling of multinucleon transfer channels as both isotopes have similar collective strengths. The transfer probabilities in the case of 94Zr were found to be substantially higher than for 90Zr in the sub-barrier region.

Consistent description of hindrance in sub-barrier fusion ofCa48withS36,Ca48, andZr96

Recent fusion reaction data for the systems ${}^{36}\mathrm{S}+{}^{48}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, and ${}^{96}\mathrm{Zr}+{}^{48}\mathrm{Ca}$ are analyzed within the coupled-channel formalism. The heavy-ion entrance channel potential is calculated employing an improved double-folding prescription. The nonlocal kernel arising from the knock-on exchange component of the effective $N\ensuremath{-}N$ interaction is localized within the lowest order of the Perey-Saxon approach, including full recoil. The single-particle densities entering the folding integrals are prescribed according to the density matrix expansion method. The investigation is more elaborated because each case is tested with four different types of $N\ensuremath{-}N$ effective forces: The two standard parametrizations of the density-independent M3Y force (Reid and Paris) and two parametrizations of the density-dependent Gogny force (D1S and D1N). A consistent description of all three reactions is achieved by keeping fixed the nuclear structure input for $^{48}\mathrm{Ca}$. The inclusion of 2${}^{+}$ and 3${}^{\ensuremath{-}}$ phonon states in the coupled-channel calculation, within an energy excitation window identical for all three reactions explains better the hindrance in extreme sub-barrier fusion cross sections. The interactions providing the best fit to the data are not pointing to a possible maximum in the astrophysical $S$ factor, thereby confirming the conclusion reached by the Legnaro group for these cases.

Multinucleon transfer reactions for theSi28+Zr90,94systems in the region below and near the Coulomb barrier

Measurements on multinucleon transfer reactions for $^{28}\mathrm{Si}+^{90,94}\mathrm{Zr}$ systems were performed at sub- and near-barrier energies. The fact that $^{90}\mathrm{Zr}$ has a closed neutron shell ($N$ $=$ 50) and $^{94}\mathrm{Zr}$ has four neutrons outside the closed shell, allows us to investigate the effects of shell closure and pairing correlation on multinucleon transfer mechanism. The experiment was performed with pulsed $^{28}\mathrm{Si}$ beam using the Heavy Ion Reaction Analyzer (HIRA) at Inter University Accelerator Centre (IUAC), New Delhi. Based on the $Q$-value considerations, it turned out that pickup channels were neutron transfer whereas stripping channels were proton transfer. For the $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ system, the values of the slope parameter for two-neutron pickup turned out to be less than that for one-neutron pickup. The values of the slope parameter were almost the same for two-, three-, and four-neutron pickup channels in the case of the $^{28}\mathrm{Si}+^{94}\mathrm{Zr}$ system. The transfer probabilities in the case of the $^{28}\mathrm{Si}+^{94}\mathrm{Zr}$ system were much larger than those for the $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ system, further supporting the fact that there is a correlation between the transfer channels and sub-barrier fusion cross-section enhancement. An odd-even staggering was observed in the extracted transfer probabilities at the barrier radius implying the role of pairing correlation in transfer reactions.

Sub-barrier fusion ofS36+Ni64and other medium-light systems

Sub-barrier fusion cross sections of $^{36}\mathrm{S}$ $+$ $^{64}\mathrm{Ni}$ have been measured down to $\ensuremath{\simeq}$$3$ $\ensuremath{\mu}$b. The logarithmic slope of the fusion excitation function has a steep rise in the barrier region with decreasing energy and saturates at lower energies. The data can be reproduced within the coupled-channels model using a Woods-Saxon potential with a large diffuseness. The slope saturation is analogous to what has been observed for $^{36}\mathrm{S}$, $^{48}\mathrm{Ca}$ $+$ $^{48}\mathrm{Ca}$, while for heavier systems the slope increases steadily below the barrier.

Near-barrier fusion ofS32+Zr90,96: The effect of multi-neutron transfers in sub-barrier fusion reactions

Fusion excitation functions have been measured for the first time with rather good accuracy for $^{32}\mathrm{S}+^{90}\mathrm{Zr}$ and $^{32}\mathrm{S}+^{96}\mathrm{Zr}$ near and below the Coulomb barrier. The sub-barrier cross sections for $^{32}\mathrm{S}+^{96}\mathrm{Zr}$ are much larger than for $^{32}\mathrm{S}+^{90}\mathrm{Zr}$. A coupled-channels calculation considering the inelastic excitations is capable of describing sub-barrier enhancement only for $^{32}\mathrm{S}+^{90}\mathrm{Zr}$. The unexplained part for $^{32}\mathrm{S}+^{96}\mathrm{Zr}$ is found to be correlated with the positive-$Q$-value intermediate neutron transfers in this system. The comparison with $^{40}\mathrm{Ca}+^{96}\mathrm{Zr}$ suggests that couplings to the positive-$Q$-value neutron transfer channels may play a role in the sub-barrier fusion enhancement. Multi-neutron transfers are taken into account in Zagrebaev's semiclassical model to explain the discrepancies of the sub-barrier fusion cross sections for $^{32}\mathrm{S}+^{96}\mathrm{Zr}$.

Channel coupling effects on the fusion excitation functions forSi28+Zr90,94in sub- and near-barrier regions

Fusion excitation functions and angular distributions of evaporation residues (ERs) have been measured for $^{28}\mathrm{Si}+^{90,94}\mathrm{Zr}$ systems around the Coulomb barrier using the recoil mass spectrometer, Heavy Ion Reaction Analyzer (HIRA). For both systems, the experimental fusion cross sections are strongly enhanced compared to the predictions of the one-dimensional barrier penetration model (1-d BPM) below the barrier. Coupled channels formalism has been employed to theoretically explain the observed sub-barrier fusion cross section enhancement. The enhancement could be explained by considering the coupling of the low-lying inelastic states of the projectile and target in the $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ system. In the sub-barrier region, the measured fusion cross sections for $^{28}\mathrm{Si}+^{94}\mathrm{Zr}$ turned out to be about an order of magnitude higher than the ones for the $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ system, which could not be explained by coupling to inelastic states alone. This observation indicates the importance of multinucleon transfer reaction channels with positive $Q$ values in the sub-barrier fusion cross section enhancement, because $^{90,94}\mathrm{Zr}$ are believed to have similar collective strengths. This implies that no strong isotopic dependence of fusion cross sections is expected as far as the couplings to collective inelastic states are concerned. In addition, the role of projectile and multiphonon couplings in the enhancement has been explored.

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.

Sub-barrier fusion hindrance in medium-light systems

The fusion excitation functions of 48Ca + 48Ca and 36S + 64Ni have been measured down to very low energies, where the phenomenon known as fusion “hindrance” should show up, extending previous measurements which were limited to rather large near-barrier cross sections. Both systems show a steady decrease of the sub-barrier fusion cross sections with no pronounced change of slope. The logarithmic slopes of the two fusion excitation functions have a steep rise in the barrier region with decreasing energy and then level off in both cases. A close analogy with the case of 36S + 48Ca, a system with a positive Q-value for fusion ( Q f u s ), that was measured recently, is pointed out.

Survey of heavy-ion fusion hindrance for lighter systems

A survey of heavy-ion fusion cross sections at extreme sub-barrier energies has been carried out for lighter systems with positive $Q$ values. A general parametrization is proposed, which describes excitation functions for a wide range of light systems at low energies. This parametrization is then applied to a calculation of excitation functions and $S$ factors for the system $^{16}\mathrm{O}+^{16}\mathrm{O}$, which has recently been investigated with various other theoretical approaches. It is suggested that this parametrization is useful for estimating sub-barrier fusion cross sections with exotic neutron-rich partners which cannot be studied in the laboratory.

Dynamical analysis on heavy-ion fusion reactions near Coulomb barrier

The shell correction is proposed in the improved isospin dependent quantum molecular dynamics (ImIQMD) model, which plays an important role in heavy-ion fusion reactions near Coulomb barrier. By using the ImIQMD model, the static and dynamical fusion barriers, dynamical barrier distribution in the fusion reactions are analyzed systematically. The fusion and capture excitation functions for a series of reaction systems are calculated and compared with experimental data. It is found that the fusion cross sections for neutron-rich systems increase obviously, and the strong shell effects of two colliding nuclei result in a decrease of the fusion cross sections at the sub-barrier energies. The lowering of the dynamical fusion barriers favors the enhancement of the sub-barrier fusion cross sections, which is related to the nucleon transfer and the neck formation in the fusion reactions.

Effects of anharmonic vibration on large-angle quasi-elastic scattering ofO16+Sm144

We study the effects of double octupole and quadrupole phonon excitations in the $^{144}\mathrm{Sm}$ nucleus on quasi-elastic $^{16}\mathrm{O}+^{144}\mathrm{Sm}$ scattering at backward angles. To this end, we use the coupled-channels framework, taking into account explicitly the anharmonicities of the vibrations. We use the same coupling scheme as that previously employed to explain the experimental data of sub-barrier fusion cross sections for the same system. We show that the experimental data for the quasi-elastic cross sections are well reproduced in this way, although the quasi-elastic barrier distribution has a distinct high energy peak which is somewhat smeared in the experimental barrier distribution. We also discuss the effects of proton transfer on the quasi-elastic barrier distribution. Our study indicates that the fusion and quasi-elastic barrier distributions for this system cannot be accounted for simultaneously with the standard coupled-channels approach.