We have already measured the ER excitation function of $^{48}$Ti + $^{138}$Ba reaction around the Coulomb barrier. While a detailed report of measurement of ER excitation function of $^{48}$Ti + $^{138}$Ba is available in literature, the present paper compares it with other channels forming the same compound nucleus. The experiment was performed at IUAC, New Delhi for lab energies from 189.3 to 234.4 MeV, where the ER cross sections show an abrupt fall beyond 160.03 MeV. The decrease in ER cross section is attributed to non compound nuclear reaction such as quasi-fission (QF). A comparison with statistical model code PACE 4 also shows significant deviation of the experimental data from theoretical predictions. When this reaction is compared with $^{86}$Kr + $^{100}$Mo and $^{64}$Ni + $^{122}$Sn forming the same compound nucleus $^{186}Pt^{*}$, the symmetric systems show more ERs than the asymmetric one and it is against the general trend. Preliminary study predict the influence of deformation and isospin asymmetry in the abrupt fall of ER cross section than that of the symmetric systems. A detailed theoretical analysis of the systems are in progress and will be published shortly.
The fusion hindrance, which is also denominated by the term extra-push, is studied on mass-symmetric systems by the use of the liquid drop model with the two-center parameterization. Following the idea that the fusion hindrance exists only if the liquid drop barrier (saddle point) is located at the inner side of the contact point after overcoming the outer Coulomb barrier, the reactions in which two barriers are overlapped with each other are determined. It is shown that there are many systems where the fusion hindrance does not exist for the atomic number of projectile or target nucleus $Z\le…
The relationship between the threshold energy for a deep sub-barrier fusion hindrance phenomenon and the energy at which the regime of interaction changes (the turning-off of the nuclear forces and friction) in the sub-barrier capture process, is studied within the quantum diffusion approach. The quasielastic barrier distribution is shown to be a useful tool to clarify whether the slope of capture cross section changes at sub-barrier energies.
The two-step model for fusion reactions of massive systems is briefly reviewed.By the use of fusion probabilities obtained by the model and of survival probabilities obtained by the new statistical code, we predict residue cross sections for 48Ca+actinide systems leading to superheavy elements with Z=114, 116 and 118.
We present the first attempt of systematically investigating the effects of shell correction energy for a dynamical process, which includes fusion, fusion-fission and quasi-fission processes. In the superheavy mass region, for the fusion process, shell correction energy plays a very important role and enhances the fusion probability when the colliding partner has a strong shell structure. By analyzing the trajectory in three-dimensional coordinate space with the Langevin equation, we reveal the mechanism of the enhancement of the fusion probability caused by `cold fusion valleys'. The temperat…
We propose a new mechanism to explain the unexpected steep falloff of fusion cross sections at energies far below the Coulomb barrier. The saturation properties of nuclear matter are causing a hindrance to large overlap of the reacting nuclei and consequently a sensitive change of the nuclear potential inside the barrier. We report in this letter a good agreement with the data of coupled-channels calculation for the {64}Ni+{64}Ni combination using the double-folding potential with M3Y-Reid effective N-N forces supplemented with a repulsive core that reproduces the nuclear incompressibility for…
The roles of nuclear deformation and neutron transfer in sub-barrier capture process are studied within the quantum diffusion approach. The change of the deformations of colliding nuclei with neutron exchange can crucially influence the sub-barrier fusion. The comparison of the calculated capture cross section and the measured fusion cross section in various reactions at extreme sub- barrier energies gives us information about the fusion and quasifission.
We present the first attempt of the systematical investigation about the effects of shell correction energy for dynamical processes, which include fusion, fusion-fission and quasi-fission processes. In the superheavy mass region, for the fusion process, the shell correction energy plays a very important role and enhances the fusion probability, when the colliding partner has strong shell structure. By analyzing the trajectory in the three-dimensional coordinate space with a Langevin equation, we reveal the mechanism of the enhancement of the fusion probability caused by shell effects.
The fusion hindrance in heavy ion collisions is studied in the framework of the two-center liquid drop model. It appears that the neck and the radial degrees of freedom might both be hampered by an inner potential barrier on their path between the contact configuration to the compound nucleus. Heavy ion reactions with and without the two kinds of fusion hindrance are classified through systematic calculations. It is found that the number of reactions without radial fusion hindrance is much smaller than that without neck fusion hindrance, and for both kinds of fusion hindrance the number of rea…
We systematically evaluate the potential energy at the touching configuration for heavy-ion reactions using various potential models. We point out that the energy at the touching point, especially that estimated with the Krappe-Nix-Sierk (KNS) potential, strongly correlates with the threshold incident energy for steep fall-off of fusion cross sections observed recently for several systems at extremely low energies. This clearly indicates that the steep fall-off phenomenon can be attributed to the dynamics after the target and projectile touch with each other, e.g., the tunneling process and th…
The coupled-channels technique is applied to analyze recent fusion data for $^{48}$Ca+$^{48}$Ca. The calculations include the excitations of the low-lying $2^+$, $3^-$ and $5^-$ states in projectile and target, and the influence of mutual excitations as well as the two-phonon quadrupole excitations is also investigated. The ion-ion potential is obtained by double-folding the nuclear densities of the reacting nuclei with the M3Y+repulsion effective interaction but a standard Woods-Saxon potential is also applied. The data exhibit a strong hindrance at low energy compared to calculations that ar…
We analyse the origin of the unexpected deep sub-barrier heavy-ion fusion hindrance in 64Ni+100Mo and 28Si+64Ni recations. Our analysis is based on the improved coupled-channels approach, implemented by means of the finite element method. With the aid of the Woods-Saxon potential the experimental cross sections and the S-factors of these reactions are remarkably well reproduced. We found that the account on the non-diagonal matrix elements of the coupling matrix, traditionally neglected in the conventional coupled-channels approaches in setting the left boundary conditions inside the potential…
We analyze the fusion data for $^{16}$O+$^{208}$Pb using coupled-channels calculations. We include couplings to the low-lying surface excitations of the projectile and target and study the effect of the ($^{16}$O,$^{17}$O) one-neutron pickup. The hindrance of the fusion data that is observed at energies far below the Coulomb barrier cannot be explained by a conventional ion-ion potential and defining the fusion in terms of ingoing-wave boundary conditions (IWBC). We show that the hindrance can be explained fairly well by applying the M3Y double-folding potential which has been corrected with a…
A new framework is proposed for the study of collisions between very heavy ions which lead to the synthesis of Super-Heavy Elements (SHE), to address the fusion hindrance phenomenon. The dynamics of the reaction is studied in terms of collective degrees of freedom undergoing relaxation processes with different time scales. The Nakajima-Zwanzig projection operator method is employed to eliminate fast variable and derive a dynamical equation for the reduced system with only slow variables. There, the time evolution operator is renormalised and an inhomogeneous term appears, which represents a pr…
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 ene…
Measurements of fusion cross-sections of 7Li and 12C with 198Pt at deep sub-barrier energies are reported to unravel the role of the entrance channel in the occurrence of fusion hindrance. The onset of fusion hindrance has been clearly observed in 12C + 198Pt system but not in 7Li + 198Pt system, within the measured energy range. Emergence of the hindrance, moving from lighter (6,7Li) to heavier (12C,16O) projectiles is explained employing a model that considers a gradual transition from a sudden to adiabatic regime at low energies. The model calculation reveals a weak effect of the damping of…
Background: Studies of low-energy fusion of light nuclei are important in astrophysical modeling, with small variations in reaction rates having a large impact on nucleosynthesis yields. Due to the lack of experimental data at astrophysical energies, extrapolation and microscopic methods are needed to model fusion probabilities. Purpose: To investigate deep sub-barrier $^{12}$C+$^{12}$C fusion cross sections and establish trends for the $S$ factor. Method: Microscopic methods based on static Hartree-Fock (HF) and time-dependent Hartree-Fock (TDHF) mean-field theory are used to obtain $^{12}$C+…
A steeper fall of fusion excitation function, compared to the predictions of coupled-channels models, at energies below the lowest barrier between the reaction partners, is termed as deep sub-barrier fusion hindrance. This phenomenon has been observed in many symmetric and nearly-symmetric systems. Different physical origins of the hindrance have been proposed. This work aims to study the probable effects of direct reactions on deep sub-barrier fusion cross sections. Fusion (evaporation residue) cross sections have been measured for the system $^{19}$F+$^{181}$Ta, from above the barrier down t…
Adiabatic fusion potentials, extended well into compound nucleus region, are calculated for a number of reactions within the static Hartree-Fock method with the Skyrme SkM* interaction. The calculated fusion barriers agree quite well with the data, in spite of considerable errors in reaction Q values. This suggests some error cancellation, possibly with the relative kinetic energy term. Calculated berrier heights are consistent with the idea of fusion hindrance in tip collisions. Adiabatic potentials differ considerably from the results of the frozen density approximation. We briefly discuss r…
Inertial confinement fusion hotspots and cluster Coulomb explosion plasmas may develop a positive net electric charge. The Coulomb barrier penetrability and the rate of nuclear fusion reactions at ultra-low energies ($\lesssim 10$ keV) are altered by such an environment. These effects are here studied via the screening potential approach. Approximate analytical results are developed by evaluating the average screening potential for some scenarios of interest. It is found that fusion is hindered for reactions between thermal fuel nuclei, while an enhancement is expected for secondary and "beam-…
The hindrance phenomenon of heavy-ion fusion cross sections at deep subbarrier energies often accompanies a maximum of an astrophysical $S$ factor at a threshold energy for fusion hindrance. We argue that this phenomenon can naturally be explained when the fusion excitation function is fitted with two potentials, with a larger (smaller) logarithmic slope at energies lower (higher) than the threshold energy. This analysis clearly suggests that the astrophysical $S$ factor provides a convenient tool to analyze the deep subbarrier hindrance phenomenon, even though the $S$ factor may have a strong…
We demonstrate the damping of quantum octupole vibrations near the touching point when two colliding nuclei approach each other in the mass-asymmetric $^{208}$Pb + $^{16}$O system, for which the strong fusion hindrance was clearly observed. We, for the first time, apply the random-phase approximation method to the heavy-mass asymmetric di-nuclear system to calculate the transition strength $B$(E3) as a function of the center-of-mass distance. The obtained $B$(E3) strengths are substantially damped near the touching point, because the single-particle wave functions of the two nuclei strongly mi…
A new model is proposed for fusion mechanisms of massive nuclear systems where so-called fusion hindrance exists. The model describes two-body collision processes in an approaching phase and shape evolutions of an amalgamated system into the compound nucleus formation. It is applied to $^{48}$Ca-induced reactions and is found to reproduce the experimental fusion cross sections extremely well, without any free parameter. Combined with the statistical decay theory, residue cross sections for the superheavy elements can be readily calculated. Examples are given.
Fusion-evaporation cross-sections σevr in reactions known for fusion hindrance phenomenon in coupled-channels calculations at below-barrier energies, are studied in terms of the dynamical cluster-decay model (DCM) of one of us (RKG) and Collaborators and the Wong formula extended by us, both based on proximity potential, by using the concept of "barrier modification" at sub-barrier energies, first advocated by Misicu and Esbensen for M3Y potential. The DCM is shown to contain the "barrier lowering" as its inbuilt characteristic, and the same is found essential, and introduced empirically, in t…
Fusion reactions relevant for the carbon and oxygen burning cycles in highly evolved stars are investigated in a standard approach to fusion. We employ the double folding method to evaluate the ion-ion interactions with Gogny-D1 and M3Y-Paris $n-n$ effective forces. The cross-section evaluation do not indicate a possible hindrance even at the lowest energies under the barrier. Reaction rates at temperatures relevant for the stellar processes are estimated and compared to the traditional and modern extrapolation formulas.
To describe fusion hindrance observed in fusion reactions at extremely low incident energies, I propose a novel extension of the standard CC model by introducing a damping factor that describes a smooth transition from sudden to adiabatic processes. I demonstrate the performance of this model by systematically investigating various deep sub-barrier fusion reactions. I extend the standard CC model by introducing a damping factor into the coupling matrix elements in the standard CC model. I adopt the Yukawa-plus-exponential (YPE) model as a basic heavy ion-ion potential, which is advantageous fo…
Fusion data for $^{48}$Ca+$^{96}$Zr are analyzed by coupled-channels calculations. Puzzling features of a previous analysis are eliminated by applying a potential that has a shallow pocket in the entrance channel. Thus the observed $S$ factor for fusion, which develops a maximum at low energy, can be reproduced fairly well. The high-energy data can also be accounted for but that requires the use of a weak, short-ranged imaginary potential that absorbs the incoming flux near the location of the minimum of the potential pocket. Predictions of the fusion hindrance in other Ca+Zr systems are made …
A statistical model description of heavy ion induced fusion-fission reactions is presented where shell effects, collective enhancement of level density, tilting away effect of compound nuclear spin and dissipation are included. It is shown that the inclusion of all these effects provides a consistent picture of fission where fission hindrance is required to explain the experimental values of both pre-scission neutron multiplicities and evaporation residue cross-sections in contrast to some of the earlier works where a fission hindrance is required for pre-scission neutrons but a fission enhanc…
Numerical simulation on nuclear collisions are performed using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory (Cb-TDHFB) in the three-dimensional coordinate space. Comparing results of the Cb-TDHFB and the conventional time-dependent Hartree-Fock (TDHF) calculations, we study effects of the pairing correlation on fusion reaction of $^{22}$O+$^{22}$O, $^{52}$Ca+$^{52}$Ca, and $^{22}$O+$^{52}$Ca, using the Skyrme SkM$^*$ functional and a contact-type pairing energy functional. Although current results are yet preliminary, they may suggest that the pairing correlation could hin…
We introduce a new microscopic approach to calculate the dependence of fusion barriers and cross-sections on isospin dynamics. The method is based on the time-dependent Hartree-Fock theory and the isoscalar and isovector properties of the energy density functional (EDF). The contribution to the fusion barriers originating from the isoscalar and isovector parts of the EDF is calculated. It is shown that for non-symmetric systems the isovector dynamics influence the sub-barrier fusion cross-sections. For most systems this results in an enhancement of the sub-barrier cross-sections, while for oth…
Within the framework of the dinuclear system (DNS) model, the fusion reactions leading to the compound nuclei 274Hs and 286Cn are investigated. The fusion probability as a function of DNS excitation energy is studied. The calculated results are in good agreement with the available experimental data. The obtained results show that the fusion probabilities are obviously enhanced for the reactions located at high place in potential energy surface, although these reactions may have small values of mass asymmetry. It is found that the enhancement is due to the large potential energy of the initial …
In this theoretical study, we establish an interrelationship between the nucleon-nucleon interaction potential and the nuclear fusion reaction cross-sections at low energies. The axially deformed self-consistent relativistic mean field with non-linear NL3$^*$ force is used to calculate the density distribution of the projectile and target nuclei for fusion. The Wong formula is used to estimate the fusion cross-section and barrier distribution from the nucleus-nucleus optical potential for Ni-based systems, which are known for fusion hindrance phenomena. The results of the application of the so…
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 co…
A realistic microscopically-based quantum approach to the competition between fusion and quasi-fission in a heavy fusing system is applied to several reactions leading to $^{256}$No. Fusion and quasi-fission are described in terms of a diffusion process of nuclear shapes through a dynamical collective potential energy landscape which is initially diabatic and gradually becomes adiabatic. The microscopic ingredients of the theory are obtained with a realistic two-center shell model based on Woods-Saxon potentials. The results indicate that (i) the diabatic effects play a very important role in …
The fusion probability in "hot" fusion reactions leading to the synthesis of super-heavy nuclei is investigated systematically. The quasi-fission barrier influences the formation of the super-heavy nucleus around the "island of stability" in addition to the shell correction. Based on the quasi-fission barrier height obtained with the Skyrme energy-density functional, we propose an analytical expression for the description of the fusion probability, with which the measured evaporation residual cross sections can be reproduced acceptably well. Simultaneously, some special fusion reactions for sy…
Fusion reactions with a weakly bound projectile are studied using the double-folding model along with a repulsive interaction modifying term. Using this modified potential, including nuclear matter incompressibility effects, the fusion reaction cross sections and suppression parameters are calculated for 9Be +209Bi,208Pb,29Si and 27Al reactions. The results show that applying these effects at energies near the Coulomb barrier improves the agreement between the calculated and experimental cross sections, and modifies the mean values of the suppression parameter.
A variety of phenomena connected with the formation of a dinuclear complex is observed in the heavy ion collisions at low energies. The dinuclear system model allows us to analyze the experimental data and to interpret them by comparison of the partial capture, fusion and evaporation residue cross sections measured for the different reactions leading to the same compound nucleus. The comparison of theoretical and experimental values of the mass and angular distributions of the reaction products gives us a detailed information about reaction mechanism forming the observed yields. The observed v…
Chances of synthesis of transactinide nuclei in cold fusion reactions (one-neutron-out) reactions using radioactive beams are evaluated. Because intensities of radioactive beams are in most of the cases significantly lower than the ones of the stable beams, reactions with the highest radioactive beam intensities for the particular elements are considered. The results are compared with the recent ones obtained by Loveland who investigated the same nuclei.
Molecular dynamics in 2-D accompanied by granular model provides an opportunity to investigate binding between nuclei particles and its properties that arises during collision in a fusion reaction. A fully classical approach is used to observe the influence of initial angle of nucleus orientation to the product yielded by the reaction. As an example, a simplest fusion reaction between 1H2 and 1H3 is observed. Several products of the fusion reaction have been obtained, even the unreported ones, including temporary 2He4 nucleus.
Recently measured high precision data of fusion excitation function have enabled a detailed study on the effects of nuclear collective excitations on fusion reactions. Using such highly accurate data of the $^{16}$O + $^{144,148}$Sm reactions, we discuss the anharmonic properties of collective phonon excitations in $^{144,148}$Sm nuclei. It is shown that subbarrier fusion reactions are strongly affected by the anharmonic effects and thus offer an alternative method to extract the static quadrupole moments of phonon states in a spherical nucleus.
The Skyrme energy-density functional approach has been extended to study the massive heavy-ion fusion reactions. Based on the potential barrier obtained and the parameterized barrier distribution the fusion (capture) excitation functions of a lot of heavy-ion fusion reactions are studied systematically. The average deviations of fusion cross sections at energies near and above the barriers from experimental data are less than 0.05 for 92% of 76 fusion reactions with $Z_1Z_2<1200$. For the massive fusion reactions, for example, the $^{238}$U-induced reactions and $^{48}$Ca+$^{208}$Pb the captur…
Relativistic mean field calculations suggest that the charge and matter deformations significantly differ in some of the unstable neutron and proton rich nuclei. We discuss the effects of the difference on the fusion reactions induced by them at energies near and below the Coulomb barrier by taking the $^{19,25,37}$Na + $^{208}$Pb reactions as examples. We also discuss whether one can probe the difference by the so called fusion barrier distribution analysis.
The isotopic dependence of the complete fusion (capture) cross section is analyzed in the reactions $^{130,132,134,136,138,140,142,144,146,148,150}$Xe+$^{48}$Ca with stable and radioactive beams. It is shown for the first time that the very neutron-rich nuclei $^{186-191}$W can be reached with relatively large cross sections by complete fusion reactions with radioactive ion beams at incident energies near the Coulomb barrier. A comparison between the complete fusion and fragmentation reactions for the production of neutron-rich W and neutron-deficient Rn isotopes is performed.
Collective reaction paths for fusion reactions, $^{16}$O+$α$ $\rightarrow$ $^{20}$Ne and $^{16}$O+$^{16}$O $\rightarrow$ $^{32}$S, are microscopically determined, on the basis of the adiabatic self-consistent collective coordinate (ASCC) method. The collective path is maximally decoupled from other intrinsic degrees of freedom. The reaction paths turn out to deviate from those obtained with standard mean-field calculations with constraints on quadrupole and octupole moments. The potentials and inertial masses defined in the ASCC method are calculated along the reaction paths. The sub-barrier f…
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 para…
A modified Woods-Saxon potential model is proposed for a unified description of the entrance channel fusion barrier and the fission barrier of fusion-fission reactions based on the Skyrme energy-density functional approach. The fusion excitation functions of 120 reactions have been systematically studied. The fusion (capture) cross sections are well described with the calculated potential and an empirical barrier distribution. Incorporating a statistical model (HIVAP code) for describing the decay of the compound nucleus, the evaporation residue (and fission) cross sections of 51 fusion-fissio…
The Skyrme energy density functional has been applied to the study of heavy-ion fusion reactions. The barriers for fusion reactions are calculated by the Skyrme energy density functional with proton and neutron density distributions determined by using restricted density variational (RDV) method within the same energy density functional together with semi-classical approach known as the extended semi-classical Thomas-Fermi method. Based on the fusion barrier obtained, we propose a parametrization of the empirical barrier distribution to take into account the multi-dimensional character of real…
In recent several years, the tensor force, one of the most important components of the nucleon-nucleon force, has been implemented in time-dependent density functional theories and it has been found to influence many aspects of low-energy heavy-ion reactions, such as dissipation dynamics, sub-barrier fusions, low-lying vibration states of colliding partners. Especially, the effects of tensor force on fusion reactions have been investigated from the internuclear potential to fusion cross sections systematically. In this work we present a mini review on the recent progresses on this topic. Consi…
Describing fusion reactions between ^{16}O and ^{154}Dy and, between ^{16}O and ^{144}Sm by the $sd-$ and $sdf-$ interacting boson model, we show that heavy-ion fusion reactions are strongly affected by anharmonic properties of nuclear surface vibrations and nuclear shape, and thus provide a powerful method to study details of nuclear structure and dynamics.
We overview the current status of theoretical approaches for heavy-ion fusion reactions at subbarrier energies. We particularly discuss theoretical challenges in the coupled-channels approach, that include i) a description of deep subbarrier hindrance of fusion cross sections, ii) the role of nuclear dissipation, iii) fusion of unstable nuclei, and iv) an interplay between fusion and multi-nucleon transfer processes. We also present results of a semi-microscopic approach to heavy-ion fusion reactions, that combines the coupled-channels approach with state-of-the-art microscopic nuclear structu…
Within the dinuclear system model, unknown neutron-deficient isotopes Np, Pu, Am, Cm, Bk, Cf, Es, Fm are investigated in $^{40}$Ca, $^{36,40}$Ar, $^{32}$S, $^{28}$Si,$^{24}$Mg induced fusion-evaporation reactions and multinucleon transfer reactions with radioactive beams $^{59}$Cu,$^{69}$As,$^{90}$Nb,$^{91}$Tc, $^{94}$Rh, $^{105,110}$Sn, $^{118}$Xe induced with $^{238}$U near Coulomb barrier energies. The production cross sections of compound nuclei in the fusion-evaporation reactions and fragments yields in the multinucleon transfer reactions are calculated within the model. A statistical app…
The fusion reaction of a halo nucleus 11Be on 208Pb is described by a three-body direct reaction model. A time-dependent wave packet approach is applied to a three-body reaction problem. The wave packet approach enables us to obtain scattering solutions without considering the three-body scattering boundary conditions. The time evolution of the wave packet also helps us to obtain intuitive understanding of the reaction dynamics. The calculations indicate a decrease of the fusion probability by the presence of the halo neutron.
In heavy-ion fusion reactions involving a well deformed nucleus, one often assumes that the orientation of the target nucleus does not change during the reaction. We discuss the accuracy of this procedure by analyzing the excitation function of the fusion cross section and the fusion barrier distribution in the reactions of $^{154}$Sm target with various projectiles ranging from $^{12}$C to $^{40}$Ar. It is shown that the approximation gradually looses its accuracy with increasing charge product of the projectile and target nuclei because of the effects of finite excitation energy of the targe…
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 …
