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 pocket, and its minimal value are crucially important for the interpretation experimental data. Within our approach we found a good agreement with the experimental data for the S-factor of the fusion reaction 12C+12C, which has no a pronounced maximum for this system.
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 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.
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…
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…
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…
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…
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…
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…
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+…
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…
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.
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…
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…
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…
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 wit…
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.
Classical mechanics and Time Dependent Hartree-Fock (TDHF) calculations of heavy ions collisions are performed to study the rotation of a deformed nucleus in the Coulomb field of its partner. This reorientation is shown to be independent on charges and relative energy of the partners. It only depends upon the deformations and inertias. TDHF calculations predict an increase by 30% of the induced rotation due to quantum effects while the nuclear contribution seems negligible. This reorientation modifies strongly the fusion cross-section around the barrier for light deformed nuclei on heavy colli…
A novel quantum dynamical model based on the dissipative quantum dynamics of open quantum systems is presented. It allows the treatment of both deep-inelastic processes and quantum tunneling (fusion) within a fully quantum mechanical coupled-channels approach. Model calculations show the transition from pure state (coherent) to mixed state (decoherent and dissipative) dynamics during a near-barrier nuclear collision. Energy dissipation, due to irreversible decay of giant-dipole excitations of the interacting nuclei, results in hindrance of quantum tunneling.
We discuss the effect of the coupling to the break-up channel on the total fusion involving a halo nucleus with a heavy target. We show that there is a competition between the hindrance arising from this coupling, mostly at above barrier energies, and the enhancement which ensues at sub-barrier energies owing to the static effect of the extended matter distribution and the coupling to the soft modes.
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…
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-…
A microscopic mean-field description of heavy ion collisions is performed in the framework of the time dependent Hartree-Fock theory using a Skyrme energy density functional. A good agreement with experiments is obtained on the position of the fusion barriers for various total masses and mass asymmetries. The excitation function of the 16O+208Pb is overestimated by about 16% above the barrier. Transfer below the barrier is studied in 16O+208Pb central collisions. Heavier systems are considered to study their fusion hindrance. We also compute collision times of the 238U+238U system. The latter …
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…
We demonstrate that when two colliding nuclei approach each other, their quantum vibrations are damped near the touching point. We show that this damping is responsible for the fusion hindrance phenomena measured in the deep sub-barrier fusion reactions. To show those, we for the first time apply the random-phase-approximation (RPA) method to the two-body $^{16}$O + $^{16}$O and $^{40}$Ca + $^{40}$Ca systems. We calculate the octupole transition strengths for the two nuclei adiabatically approaching each other. The calculated transition strength drastically decreases near the touching point, s…
Background: The tensor interaction is known to play an important role in the nuclear structure studies of exotic nuclei. However, most microscopic studies of low-energy nuclear reactions neglect the tensor force, resulting in a lack of knowledge concerning the effect of the tensor force on HIC...... Purpose: The theoretical study of the influence of the tensor force on heavy-ion interaction potentials is required to further our understanding of the microscopic mechanisms entailed in fusion dynamics. Method: The full Skyrme tensor force is implemented into the static Hartree-Fock and dynamic de…
The Pauli exclusion principle induces a repulsion between composite systems of identical fermions such as colliding atomic nuclei. Our goal is to study how heavy-ion fusion is impacted by this "Pauli repulsion". We propose a new microscopic approach, the density-constrained frozen Hartree-Fock method, to compute the bare potential including the Pauli exclusion principle exactly. Pauli repulsion is shown to be important inside the barrier radius and increases with the charge product of the nuclei. Its main effect is to reduce tunnelling probability. Pauli repulsion is part of the solution to th…
we assessed Wong's formula for its angular momentum $\ell$-summation and "barrier modification" effects at sub-barrier energies in the dominant fusion-evaporation and capture (equivalently, quasi-fission) reaction cross-sections. For use of the multipole deformations (up to $β_4$) and (in-plane, $Φ$=0$^0$) orientations-dependent proximity potential in fusion-evaporation cross-sections of $^{58}$Ni+$^{58}$Ni, $^{64}$Ni+$^{64}$Ni and $^{100}$Mo, known for fusion hindrance phenomenon in coupled-channels calculations, and the capture cross-sections of $^{48}$Ca+$^{238}$U, $^{244}$Pu and $^{248}$Cm…
A hybrid model where the tunneling probability is estimated based on both sudden and adiabatic approaches has been proposed to understand the heavy ion fusion phenomena at deep sub-barrier energies. It is shown that under certain approximations, it amounts to tunneling through two barriers: one while overcoming the normal Coulomb barrier (which is of sudden nature) along the radial direction until the repulsive core is reached and thereafter through an adiabatic barrier along the neck degree of freedom while making transition from a di-nuclear to a mono-nuclear regime through shape relaxation.…
The Time-dependent Hartree-Fock (TDHF) theory is applied to the study of heavy ion collisions at energies around the Coulomb barrier. The competition between fusion and nucleon transfer mechanisms is investigated. For intermediate mass systems such as 16O+208Pb, proton transfer favors fusion by reducing the Coulomb repulsion. A comparison with sub-barrier transfer experimental data shows that pairing correlations are playing an important role in enhancing proton pair transfer. For heavier and more symmetric systems, a fusion hindrance is observed due to the dominance of the quasi-fission proce…
[Background] Reactions with stable beams have demonstrated a strong interplay between nuclear structure and fusion. Exotic beam facilities open new perspectives to understand the impact of neutron skin, large isospin, and weak binding energies on fusion. Microscopic theories of fusion are required to guide future experiments. [Purpose] To investigate new effects of exotic structures and dynamics in near-barrier fusion with exotic nuclei. [Method] Microscopic approaches based on the Hartree-Fock (HF) mean-field theory are used for studying fusion barriers in $^{40-54}$Ca+$^{116}$Sn reactions fo…
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 tunneling of composite systems, where breakup may occur during the barrier penetration process is considered in connection with the fusion of halo-like radioactive, neutron- and proton-rich nuclei on heavy targets. The large amount of recent and new data clearly indicates that breakup hinders the fusion at near and below the Coulomb barrier energies. However, clear evidence for the halo enhancements, seems to over ride the breakup hindrance at lower energies, owing, to a large extent, to the extended matter density distribution. In particular we report here that at sub-barrier energies the…
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…
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…
[Background] While the tensor interaction has been shown to significantly affect the nuclear structure of exotic nuclei, its influence on nuclear reactions has only recently been investigated. The primary reason for this neglect is the fact that most studies of nuclear dynamics do not include the tensor force at all in their models. Indeed, only a few Skyrme parametrizations consider the tensor interaction in parameter determination. With modern research facilities extending our ability to probe exotic nuclei, a correct description of nuclear dynamics and heavy-ion fusion is vital to both supp…
The evaporation residue yields from compound nuclei $^{220}$Th formed in the $^{16}$O+$^{204}$Pb, $^{40}$Ar+$^{180}$Hf, $^{82}$Se+$^{138}$Ba, $^{124}$Sn+$^{96}$Zr reactions are analyzed to study the entrance channel effects by comparison of the capture, fusion and evaporation residue cross sections calculated by the combined dinuclear system (DNS) and advanced statistical models. The difference between evaporation residue (ER) cross sections can be related to the stages of compound nucleus formation or/and at its surviving against fission. The sensitivity of the both stages in the evolution of…
Fusion data for $^{16}$O+$^{16}$O are analyzed by coupled-channels calculations. It is shown that the calculated cross sections are sensitive to the couplings to the $2^+$ and $3^-$ excitation channels even at low energies, where these channels are closed. The sensitivity to the ion-ion potential is investigated by applying a conventional Woods-Saxon potential and the M3Y+repulsion potential, consisting of the M3Y double-folding potential and a repulsive term that simulates the effect of the nuclear incompressibility. The best overall fit to the data is obtained with a M3Y+repulsion potential …
The fusion excitation function is the important quantity in planning experiments for the synthesis of superheavy elements. Its values seem to be determined by the experimental study of the hindrance to complete fusion by the observation of mass, angular and energy distributions of the fissionlike fragments. There is ambiguity in establishment of the reaction mechanism leading to the observed binary fissionlike fragments. The fissionlike fragments can be produced in the quasifission, fast fission, and fusion-fission processes which have overlapping in the mass (angular, kinetic energy) distribu…
Universal empirical coupled channel calculations for capture cross sections in synthesis of superheavy nuclei
Guangxi Normal University（广西师范大学）；Guangxi Key Laboratory of Nuclear Physics and Technology（广西核物理与技术重点实验室）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Hunan Normal University（湖南师范大学）；Yangzhou University（扬州大学）；China Institute of Atomic Energy（中国原子能科学研究院）；Sun Yat-sen University（中山大学）；University of Chinese Academy of Sciences（中国科学院大学）
