Enhancement Of Fusion Cross Sections Research Articles

Microscopic study of fusion reactions with a weakly bound nucleus: Effects of deformed halo

We present a microscopic study on the fusion reactions C14,15+Th232 by emphasizing the effect of deformed halo structure on reaction dynamics within the framework of time-dependent density functional theory. The internuclear potentials are obtained by using the density-constraint frozen Hartree-Fock approach and then are adopted to calculate the fusion cross sections of C14,15+Th232, taking all the orientations of deformed reactants into account. Our microscopic calculations not only reproduce the enhancement of fusion cross sections at sub-barrier energies without any adjustable parameters, but also reveal the underlying mechanism of this enhancement, which is driven by the deformed halo structure of C15. More interestingly, by performing particle number projection based on the wave functions from time-dependent Hartree-Fock simulation, we find that the one-neutron transfer probabilities are more sensitive to the orientations of C15 than Th232, indicating the notable effects of halo structure on the reaction dynamics.Received 30 August 2022Accepted 17 November 2022DOI:https://doi.org/10.1103/PhysRevC.107.L011601©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear density functional theoryNuclear reactionsUnstable nuclei induced nuclear reactionsNuclear Physics

Theoretical study of dynamic effects on fusion cross sections for reactions S32,34,36+Pb204,206,208

The universal fusion function prescription and the empirical coupled-channel (ECC) model are used to analyze the dynamic effects on fusion cross sections for reactions $^{32,34,36}\mathrm{S}+^{204,206,208}\mathrm{Pb}$. An examination of the reduced fusion functions shows that the total dynamic effects on fusion cross sections in $^{36}\mathrm{S}+^{204,206,208}\mathrm{Pb}$ are almost the same as those in $^{34}\mathrm{S}+^{204,206,208}\mathrm{Pb}$. Furthermore, at sub-barrier energies of the reactions $^{32,34,36}\mathrm{S}+^{208}\mathrm{Pb}$, the largest enhancement of reduced fusion function is observed in the reaction $^{32}\mathrm{S}+^{208}\mathrm{Pb}$. Then the enhancement of fusion cross sections due to couplings to inelastic excitation channels and neutron transfer channels with positive $Q$ values is investigated by using the ECC model. The results show that the experimental data of the reactions $^{34,36}\mathrm{S}+^{204,206,208}\mathrm{Pb}$ and $^{32}\mathrm{S}+^{208}\mathrm{Pb}$ are reproduced well by the ECC model. In addition, it can be found that the effect of coupling to positive $Q$-value neutron transfer channels is necessary to reproduce the sub-barrier fusion data of the reaction $^{32}\mathrm{S}+^{208}\mathrm{Pb}$. Furthermore, for the two reactions $^{32}\mathrm{S}+^{204}\mathrm{Pb}$ and $^{32}\mathrm{S}+^{206}\mathrm{Pb}$, the effects of coupling to positive $Q$-value neutron transfer channels are predicted to be significant. The fusion cross sections for these two reactions are also predicted.

Analysis of fusion excitation functions of 11Be+209Bi and 15C+232Th reaction through quantum diffusion approach

We have studied the fusion of 11 Be with 209 Bi and 15 C with 232 Th in the energy region around the barrier within the framework of quantum diffusion approach and have found enhancement in fusion cross-section in deep sub-barrier region and a very minor suppression in the above barrier energy region with respect to the corresponding experimental observations. The fusion cross-section is found to be slightly increased for reactions involving 11 Be and 15 C nuclei in comparison to those involving the stable 10 Be and 12 C isotopes, respectively.

Systematic analysis of the effect of a positiveQ-value neutron transfer in fusion reactions

The experimental data of fusion cross sections for the different projectile and target nuclei systems are systematically analyzed. In order to explore the positive $Q$-value neutron transfer (PQNT) effect we systematically analyze their fusion functions F($x$) as a function of $x$, which reduces the barrier height, radius, and curvature of fusion systems. From the comparison of F($x$)s among them, it is found that after neutron transfer when the deformation of interacting nuclei increases largely, the enhancement of fusion cross sections can be observed at energies below the Coulomb barrier due to the PQNT effect. However, even if the fusion systems show the PQNT values, the fusion cross sections are almost the same due to the small deformation of interaction nuclei after neutron transfer. Many experiments need to be systematically done for this research.

Why the complete fusion of weakly bound nuclei is enhanced at sub-barrier energies and suppressed above the barrier?

In this paper we explain the reasons for the systematic behaviour of enhancement of the complete fusion cross section of weakly bound systems at sub-barrier energies and its suppression above the barrier, when compared with predictions from calculations which do not take into account breakup and transfer channels. The methodology used is the study of dynamic polarization potentials. At above barrier energies the net polarization potential due to direct breakup is dominant and repulsive, consequently fusion is suppressed. At sub-barrier energies, the enhancement of fusion cross section is consistent with recent experimental observations that nucleon transfer leading to breakup is dominant compared to direct breakup and produces attractive polarization potential.

Transfer/Breakup Channel Couplings in Sub-barrier Fusion Reactions

With the recent availability of state-of-the-art radioactive ion beams, there has been a renew interest in the investigation of nuclear reactions with heavy ions near the Coulomb barrier. The role of inelastic and transfer channel couplings in fusion reactions induced by stable heavy ions can be revisited. Detailed analysis of recent experimental fusion cross sections by using standard coupled-channel calculations is first discussed. Multi-neutron transfer effects are introduced in the fusion process below the Coulomb barrier by analyzing 32S+90,96Zr as benchmark reactions. The enhancement of fusion cross sections for 32S+96Zr is well reproduced at sub-barrier energies by NTFus code calculations including the coupling of the neutrontransfer channels following the Zagrebaev semi-classical model. Similar effects for 40Ca+90Zr and 40Ca+96Zr fusion excitation functions are found. The breakup coupling in both the elastic scattering and in the fusion process induced by weakly bound stable projectiles is also shown to be crucial. In the second part of this work, full coupled-channel calculations of the fusion excitation functions are performed by using the breakup coupling for the more neutron-rich reaction and for the more weakly bound projectiles. We clearly demonstrate that Continuum-Discretized Coupled-Channel calculations are capable to reproduce the fusion enhancement from the breakup coupling in 6Li+59Co.

Microscopic sub-barrier fusion calculations for the neutron star crust

Fusion of very neutron-rich nuclei may be important to determine the composition and heating of the crust of accreting neutron stars. Fusion cross sections are calculated using time-dependent Hartree-Fock theory coupled with density-constrained Hartree-Fock calculations to deduce an effective potential. Systems studied include ${}^{16}$O+${}^{16}$O, ${}^{16}$O+${}^{24}$O, ${}^{24}$O+${}^{24}$O, ${}^{12}$C+${}^{16}$O, and ${}^{12}$C+${}^{24}$O. We find remarkable agreement with experimental cross sections for the fusion of stable nuclei. Our simulations use the SLy4 Skyrme force that has been previously fit to the properties of stable nuclei, and no parameters have been fit to fusion data. We compare our results to the simple S\~ao Paulo static barrier penetration model. For the asymmetric systems ${}^{12}$C+${}^{24}$O or ${}^{16}$O+${}^{24}$O we predict an order of magnitude larger cross section than those predicted by the S\~ao Paulo model. This is likely due to the transfer of neutrons from the very neutron rich nucleus to the stable nucleus and dynamical rearrangements of the nuclear densities during the collision process. These effects are not included in potential models. This enhancement of fusion cross sections, for very neutron rich nuclei, can be tested in the laboratory with radioactive beams.

Effect of neutron rearrangement on subbarrier fusion reactions

Abstract The role of neutron transfer is investigated in the fusion process near and below the Coulomb barrier within the empirical channel coupling approach. The possibility of neutron transfer with positive Q-values considerably increases the barrier penetrability. The enhancement of fusion cross sections for 58Ni + 64Ni, 32S + 64Ni, 40Ca + 48Ca, and 40Ca + 124Sn is well reproduced at subbarrier energies by the empirical channel coupling approach including the coupling to the neutron-transfer channels. The predictions of the fusion cross sections for several combinations of colliding nuclei are also proposed which may shed additional light on the effect of neutron transfer in fusion processes. A huge enhancement of deep subbarrier fusion probability was found for light neutron-rich weakly bound nuclei. This may be quite important for astrophysical primordial and supernova nucleosynthesis.

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.

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.

Structure effects and dynamics in fusion reactions of light weakly bound nuclei

The study of fusion in collision around the Coulomb barrier, induced by radioactive or stable weakly bound nuclei, has been the subject of many experiments in the last years. From a semiclassical point of view, direct processes like break-up or transfer may be favoured by the low binding energies and one might also expect suppressed fusion cross section due to the competition with the break-up. However, according to the Coupled Channel calculations (CC), it is well known that the presence of strong open reaction channels can be responsible for a fusion cross-section enhancement with respect to the single barrier penetration calculations and the break-up should be included in such calculations. In order to further investigate on this topic, the 6Li+64Zn collision has been studied at several energies around the Coulomb barrier, to extract the total fusion and the total reaction cross sections and to study the energy dependence of the optical model potential.

Multi-neutron transfer coupling in sub-barrier32S +90,96Zr fusion reactions

The role of neutron transfers is investigated in the fusion process below the Coulomb barrier by analyzing 32S+90Zr and 32S+96Zr as benchmark reactions. A full coupled-channel calculation of the fusion excitation functions has been performed for both systems by using multi-neutron transfer coupling for the more neutron-rich reaction. The enhancement of fusion cross sections for 32S+96Zr is well reproduced at sub-barrier energies by NTFus code calculations including the coupling of the neutron-transfer channels following the Zagrebaev semiclassical model. We found similar effects for 40Ca+90Zr and 40Ca+96Zr fusion excitation functions.

Fusion, elastic and total reaction cross sections in the collision6Li+64Zn

The structure of the weakly bound nuclei is expected to influence the fusion mechanism at energies around and below the Coulomb barrier. In fact direct channels may be favoured with respect to fusion by the low binding energies, while Coupling of the break-up channel can be responsible for a fusion cross-section enhancement. In this context the {sup 6}Li+{sup 64}Zn collision has been studied at several energies around the Coulomb barrier. The fusion cross section was measured by using an activation technique where the radioactive evaporation residues produced in the reaction were identified by the X-ray emission which follows their electron capture decay. The elastic scattering angular distributions were analyzed within the Optical Model and total reaction cross-sections were deduced from optical model calculations. (authors)

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.

Suppression of complete fusion in theLi6+Sm144reaction

Complete fusion excitation function for the $^{6}\mathrm{Li}+^{144}\mathrm{Sm}$ reaction has been measured at near barrier energies by the activation technique. Coupled-channel calculations show an enhancement in fusion cross section at energies below the barrier compared to the one-dimensional barrier penetration model calculation, but they overpredict it in the entire energy range compared to the experimental data. Reduced fusion cross sections for the present system at energies normalized to the Coulomb barrier were also found to be systematically lower than those with strongly bound projectiles forming a similar compound nucleus. These two observations conclusively show that the complete fusion cross section, at above barrier energies, is suppressed by $~32%$ in the $^{6}\mathrm{Li}+^{144}\mathrm{Sm}$ reaction. Reanalyses of existing fusion data for $^{7}\mathrm{Li}+^{165}\mathrm{Ho}$ and $^{7}\mathrm{Li}+^{159}\mathrm{Tb}$ also show a suppression compared to those with strongly bound projectiles, which contradicts earlier conclusions. The fusion suppression factor seems to exhibit a systematic behavior with respect to the breakup threshold of the projectile and the atomic number of the target nucleus.

Effects of breakup of weakly bound projectile and neutron transfer on fusion reactions around Coulomb barrier

The excitation functions of quasielastic and elastic scattering at backward angles have been measured for the systems of 16 O+ 152 Sm, 6,7 Li+ 208 Pb and 32 S+ 90,96 Zr. The barrier distributions are extracted from these measured excitation functions and compared with the corresponding fusion barrier distributions. Except some details, the barrier distributions derived from the data of fusion and quasielastic/elastic scattering are almost the same for the tightly bound reaction systems. For the reaction systems with weakly bound projectile, the barrier distributions extracted from quasielastic scattering are obviously different from the fusion barrier distributions. However, the barrier distributions extracted from the excitation functions of the quasielastic scattering plus breakup are almost the same as the one extracted from the complete fusion data. This result means that barrier distribution not only bears the information of nuclear structures but also contains the knowledge of reaction mechanisms. Our results show that the complete fusion of the weakly bound projectile with heavy target is suppressed at the above barrier energies as compared with the model predictions. In addition, the measured barrier distribution of 32 S+ 96 Zr is broaden and extends to lower energy than in the case of 32 S+ 90 Zr due to the coupling of neutron transfer with positive Q-values, which result in a significant enhancement of fusion cross sections at the subbarrier energies.

Threshold anomaly in the19F+208Pbsystem

Angular distributions of elastic scatterings for the ${}^{19}\mathrm{F}{+}^{208}\mathrm{Pb}$ system were measured at six energies around the Coulomb barrier. By means of a phenomenological optical model analysis, it is found that the real and imaginary potentials show a pronounced energy dependence. The real parts of potentials extracted from the fusion data are similar to those from the elastic data. A comparison with the neighboring systems of ${}^{16}\mathrm{O}{+}^{208}\mathrm{Pb}$ and ${}^{16}\mathrm{O}{+}^{209}\mathrm{Bi}$ reveals that the effects of the ${}^{19}\mathrm{F}$ deformations in the entrance channel play an important role in the fusion reaction. Based on the deformed and energy dependent barrier penetration model, the calculation results of the fusion cross sections and mean-square spin distribution agree with the experimental data well. Furthermore, it is indicated that the enhancement of fusion cross sections is attributed to the dynamic polarization effects around the barrier, and to the static deformation effects further below the barrier.

Collectivity against nucleon transfer in sub-barrier fusion of12C+194,198Pt

In order to determine the relative importance of the role played by inelastic excitations and transfer channels of the colliding nuclei, in near-barrier fusion enhancement, the fusion cross sections have been measured for 12 C+ 194,198 Pt in the energy range of 0.9≤E/V B ≤1.2. Additional data of quasielastic and nucleon(s)-exchange cross sections have also been measured at an energy of 1.2V B . The strength of transfer form factors required for the simplified coupled-channels calculations has been obtained from the transfer reaction measurements using a semiclassical approach and calculations based on complex WKB approximations. Coupled-reaction-channels calculations have been performed to explain the complete data set that included fusion, quasielastic, and transfer cross sections. The dominant contributions to the enhancement of fusion cross section compared to a one-dimensional barrier-penetration model arise from coupling to inelastic channels. It has been shown for the first time that the lighter isotope ( 194 Pt) of a given nuclide that has a relatively larger collectivity (β λ ) and a larger neutron separation energy compared to the heavier isotope ( 198 Pt), exhibits larger enhancement of fusion cross section. The experimental fusion-barrier distributions were obtained from fusion and quasielastic scattering data.

One- and two-nucleon transfer in the28Si+68Zn system at energies below the Coulomb barrier

Excitation functions for one- and two-nucleon transfer in {sup 28}Si + {sup 68}Zn system have been measured at energies below the Coulomb barrier. The experiment was carried out by detecting the forward recoiling targetlike nuclei using the recoil mass separator, HIRA. With a pulsed beam, the time-of-flight of the recoils was measured and used to resolve the M/q ambiguity. This enabled the determination of the two-nucleon transfer yields. The role of one- and two-nucleon transfer in the sub-barrier fusion cross-section enhancement has been investigated. It turns out that the coupling of the positive Q-value two-neutron transfer channel results in a significant contribution to the enhancement. Coupling to both the transfer and the inelastic channels is able to explain the observed enhancement. {copyright} {ital 1997} {ital The American Physical Society}

Fusion of 59Co with light projectiles at near barrier energies

Fusion cross sections have been measured for the 14N, 16O+59Co systems at bombarding energies from 32 to 56 MeV. Total transfer cross sections to excited states were simultaneously measured for the stripping of one proton and stripping of one neutron channels in the 14N induced reactions, and their upper limits for other transfer channels could be estimated. The elastic-scattering angular distribution was measured at Elab = 40 MeV for the 16O+59Co system. The effects of collective properties of the nuclei, included in the Wong model or the alternative approach of coupling inelastic channels, were found to be too small to explain the large sub-barrier fusion cross section enhancement. In order to perform simplified coupled-channel calculations involving transfer channels, a semiclassical formalism was used to derive the transfer form factors. Within the uncertainties of the calculations, the behavior of the sub-barrier fusion could be understood in terms of the coupling of charged-particle transfer channels, particularly the stripping of multi-nucleons, which act as doorways to fusion. An alternative approach, the liquid drop model, which accounts for the neck formation, also leads to satisfactory and compatible results.