Mass parameters for the relative and neck motions in fusion reactions of symmetric systems $^{90}$Zr+$^{90}$Zr, $^{110}$Pd+$^{110}$Pd, and $^{138}$Ba+$^{138}$Ba are studied by means of a microscopic transport model. The shape of the nuclear system is determined by an equi-density surface obtained from the density distribution of the system. The relative and neck motions are then studied and the mass parameters for these two motions are deduced. The mass parameter for the relative motion is around the reduced mass when the reaction partners are at the separated configuration and increases with decrease of the distance between two reaction partners after the touching configuration. The mass parameter for the neck motion first decreases slightly up to the touching configuration and then increases with the neck width, and its magnitude is from less than tenth to several times more than the total mass of the system. The mass parameters obtained from the microscopic transport model are larger than the ones obtained from the hydrodynamic model and smaller than those obtained from the linear response function theory. The mass parameters for both motions depend on the reaction systems, but the one for the relative motion depends on the incompressibility of the EoS more obviously than that for neck motion.
The enhancement of the sub-barrier fusion cross sections was explained as the lowering of the dynamical fusion barriers within the framework of the improved isospin-dependent quantum molecular dynamics (ImIQMD) model. The numbers of nucleon transfer in the neck region are appreciably dependent on the incident energies, but strongly on the reaction systems. A comparison of the neck dynamics is performed for the symmetric reactions $^{58}$Ni+$^{58}$Ni and $^{64}$Ni+$^{64}$Ni at energies in the vicinity of the Coulomb barrier. An increase of the ratios of neutron to proton in the neck region at i…
The fission-fragments mass-yield of 236U is obtained by an approximate solution of the eigenvalue problem of the collective Hamiltonian that describes the dynamics of the fission process whose degrees of freedom are: the fission (elongation), the neck and the mass-asymmetry mode. The macroscopic-microscopic method is used to evaluate the potential energy surface. The macroscopic energy part is calculated using the liquid drop model and the microscopic corrections are obtained using the Woods-Saxon single-particle levels. The four dimensional modified Cassini ovals shape parametrization is used…
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…
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…
Despite the supposed simplicity of double-closed shell nuclei, conventional coupled-channels calculations, that include all of the known collective states of the target and projectile, give a poor fit to the fusion cross section for the $^{16}$O + $^{208}$Pb system. The discrepancies are highlighted through the experimental barrier distribution and logarithmic derivative, that are both well defined by the precise experimental fusion data available. In order to broaden our search for possible causes for this anomaly, we revisit this system and include in our calculations a large number of non-c…
We consider the prototypical deuterium-tritium fusion reaction. At intermediate initial kinetic energies (in the keV regime), a major bottle-neck of this reaction is the Coulomb barrier between the nuclei, which is overcome by tunneling. Here, we study whether the tunneling probability can be enhanced by an additional electromagnetic field, such as an x-ray free electron laser (XFEL). We find that this dynamical assistance should be feasible with present-day or near future technology.
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…
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…
An one dimensional adiabatic model has been proposed for fusion of loosely bound and halo light nuclei with various heavy targets. It is shown that fusion cross sections at near and sub-barrier energies can be explained using a simple WKB tunneling through an adiabatic barrier without invoking breakup coupling explicitly. The model has been applied successfully to explain fusion cross sections for several systems including recently measured $^{6}Li+^{198}Pt$ system (Phy. Rev. Lett. 103, 232702, 2009) where data exists well above and below the barrier and $^{8}He+^{197}Au$ system (Phy. Rev. Let…
A systematic analysis of the fusion cross sections around the Coulomb barrier energies with stable weakly bound ($^{6}$Li,$^{7}$Li,$^{9}$Be) and strongly bound $^{12}$C projectiles on various targets was performed by using neutron flow model and coupled channels approach. The analysis show that both the models are successful in explaining the near barrier fusion data. Further, it is also observed that the collective degrees of freedom as well as the neutron flow influence the near barrier fusion process involving weakly bound projectiles.
Using a theory of large amplitude collective motion, the adiabatic self-consistent collective coordinate method, we derive reaction path for the fusion process at sub-barrier energies. The collective Hamiltonian to describe the fusion process is constructed, based on the obtained reaction path and canonical variables. We study the reaction of N=Z stable nuclei, alpha+16O, 16O+16O, and alpha+12C. The results suggest that, after two nuclei touch, the reaction path is significantly deviated from the simple relative motion, which may affect the deep sub-barrier fusion cross section.
Using the random matrix model, we discuss the effect of couplings to non-collective states on the penetrability of a one dimensional potential barrier. We show that these non-collective excitations hinder the penetrability and thus smear the barrier distribution at energies above the barrier, while they do not affect significantly the penetrability at deep subbarrier energies. The energy dependence of the Q-value distribution obtained with this model is also discussed.
The mechanism of fusion hindrance, an effect preventing the synthesis of superheavy elements in the reactions of cold and hot fusion, is investigated using the Boltzmann-Uehling-Uhlenbeck equation, where Coulomb interaction is introduced. A strong sensitivity is observed both to the modulus of incompressibility of symmetric nuclear matter, controlling the competition of surface tension and Coulomb repulsion, and to the stiffness of the density-dependence of symmetry energy, influencing the formation of the neck prior to scission. The experimental fusion probabilities were for the first time us…
Descriptions of heavy-ion collisions at Fermi energies require to take into account in-medium dissipation and phase-space fluctuations. The interplay of these correlations with the one-body collective behaviour determines the properties (kinematics and fragment production) and the variety of mechanisms (from fusion to neck formation and multifragmentation) of the exit channel. Starting from fundamental concepts tested on nuclear matter, we build up a microscopic description which addresses finite systems and applies to experimental observables.
The surface energy is one of the fundamental properties nuclei, appearing in the simplest form of the semi-empirical mass formula. The surface enery has an influence on e.g. the shape of a nucleus and its ability to deform. This in turn could be expected to have an effect in fusion reactions around the Coulomb barrier where dynamical effects such as the formation of a neck is part of the fusion process. Frozen Hartree-Fock and Time-Dependent Hartree-Fock calculations are made for a series of effective interactions in which the surface energy is systematically varied, using $^{40}$Ca + $^{48}$C…
The time-dependent density functional theory (TDDFT) provides a unified description of the structure and reaction. The linear approximation leads to the random-phase approximation (RPA) which is capable of describing a variety of collective motion in a harmonic regime. Beyond the linear regime, we present applications of the TDDFT to nuclear fusion and fission reaction. In particular, the extraction of the internuclear potential and the inertial mass parameter is performed using two different methods. A fusion hindrance mechanism for heavy systems is investigated from the microscopic point of …
We investigate the applicability of a random-matrix model to the description of non-collective excitations in heavy-ion reactions around the Coulomb barrier. To this end, we study fusion in the reaction $^{16}$O + $^{208}$Pb, taking account of the known non-collective excitations in the $^{208}$Pb nucleus. We show that the random-matrix model for the corresponding couplings reproduces reasonably well the exact calculations, obtained using empirical deformation parameters. This implies that the model may provide a powerful method for systems in which the non-collective couplings are not so well…
The dynamics present in the fusion of neutron-rich nuclei is explored through the comparison of experimental cross-sections at above-barrier energies with measurements of the interaction cross-section at relativistic energies. The increase of fusion dynamics with increasing neutron excess is clearly demonstrated. Experimental cross-sections are compared with the predictions of a Sao Paulo model using relativistic mean field density distributions and the impact of different interactions is explored.
An effective Fourier nuclear shape parametrization which describes well the most relevant degrees of freedom on the way to fission is used to construct a 3D collective model. The potential energy surface is evaluated within the macroscopic-microscopic approach based on the Lublin-Strasbourg Drop (LSD) macroscopic energy and Yukawa-folded single particle potential. A phenomenological inertia parameter is used to describe the kinetic properties of the fissioning system. The fission fragment mass yields are obtained by using an approximate solution of the underlying Hamiltonian. The predicted mas…
We investigate the role of the pairing field dynamics in low-energy heavy ion reactions within the nuclear time-dependent density functional theory extended to superfluid systems. Recently, we have reported on unexpectedly large effects associated with the relative phase of the pairing field of colliding nuclei on the reaction outcomes, such as the total kinetic energy and the fusion cross section [P. Magierski, K. Sekizawa, and G. Wlazłowski, arXiv:1611.10261 [nucl-th]]. We have elucidated that the effects are due to creation of a "domain wall" or a "solitonic structure" of the pairing field …
The coupled-channels method has been a standard tool in analyzing heavy-ion fusion reactions at energies around the Coulomb barrier. We investigate three simplifications usually adopted in the coupled-channels calculations. These are i) the exclusion of non-collective excitations, ii) the assumption of coordinate independent coupling strengths, and iii) the harmonic oscillator approximation for multi-phonon excitations. In connection to the last point, we propose a novel microscopic method based on the beyond-mean-field approach in order to take into account the anharmonic effects of collectiv…
We describe low-lying collective excitations of atomic nuclei with the multi-reference covariant density functional theory, and combine them with coupled-channels calculations for heavy-ion fusion reactions at energies around the Coulomb barrier. To this end, we use the calculated transition strengths among several collective states as inputs to the coupled-channels calculations. This approach provides a natural way to describe anharmonic multi-phonon excitations as well as a deviation of rotational excitations from a simple rigid rotor. We apply this method to subbarrier fusion reactions of $…
The nucleus-nucleus potential and energy dissipation in fusion reactions are obtained from microscopic mean-field dynamics. The deduced potentials nicely reproduce the one extracted from experimental data. Energy dissipation shows a universal behaviour between different reactions. Also, the dispersion of mass distribution in transfer reaction is investigated in a stochastic mean-field dynamics. By including initial fluctuations in collective space, the description of the dispersion is much improved compared to that of mean field only. The result is consistent with the macroscopic phenomenologi…
Effects of nuclear molecular configurations on the astrophysical S-factor for $^{16}$O + $^{16}$O
在基于Woods-Saxon势的双中心壳层模型下，研究了核分子构型对$^{16}$ O + $^{16}$ O的天体物理S因子的影响.这些分子效应指的是相互作用的核之间的颈部和径向依赖的集体质量参数的形成。它表明，前者是至关重要的解释目前的实验数据具有高精度，没有任何自由参数，而另外，后者预测一个明显的最大值的S-因子。与Jiang等人最近的结果相反，当能量降低时，S因子不会向极低值下降。
We investigate the reaction path followed by Heavy Ion Collisions with exotic nuclear beams at low energies. We will focus on the interplay between reaction mechanisms, fusion vs. break-up (fast-fission, deep-inelastic), that in exotic systems is expected to be influenced by the symmetry energy term at densities around the normal value. The evolution of the system is described by a Stochastic Mean Field transport equation (SMF), where two parametrizations for the density dependence of symmetry energy (Asysoft and Asystiff) are implemented, allowing one to explore the sensitivity of the results…
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…
We discuss the implementation and results of a recently developed microscopic method for calculating ion-ion interaction potentials and fusion cross-sections. The method uses the TDHF evolution to obtain the instantaneous many-body collective state using a density constraint. The ion-ion potential as well as the coordinate dependent mass are calculated from these states. The method fully accounts for the dynamical processes present in the TDHF time-evolution and provides a parameter-free way of calculating fusion cross-sections.
Despite recent advances and focus on rigorous uncertainty quantification for microscopic models of quantum many-body systems, the uncertainty on the dynamics of those systems has been under-explored. To address this, we have used time-dependent Hartree-Fock to examine the model uncertainty for a collection of low-energy, heavy-ion fusion reactions. Fusion reactions at near-barrier energies represent a rich test-bed for the dynamics of quantum many-body systems owing to the complex interplay of collective excitation, transfer, and static effects that determine the fusion probability of a given …
A summary of recent researches on nuclear dynamics with realistic microscopic quantum approaches is presented. The Balian-Vénéroni variational principle is used to derive the time-dependent Hartree-Fock (TDHF) equation describing the dynamics at the mean-field level, as well as an extension including small-amplitude quantum fluctuations which is equivalent to the time-dependent random-phase approximation (TDRPA). Such formalisms as well as their practical implementation in the nuclear physics framework with modern three-dimensional codes are discussed. Recent applications to nuclear dynamics, …
We investigate heavy-ion multinucleon transfer reactions using the coupled-channels formalism. We first use the semi-classical approximation and show that a direct coupling between the entrance and the pair transfer channels improves a fit to the experimental one- and two-neutron transfer cross sections for the 40Ca+96Zr and 60Ni+116Sn systems. We then discuss the validity of the perturbative approach and highlight the effect of high order terms. The effect of absorption is also investigated for energies around the Coulomb barrier. Finally, we use a quantal coupled-channels approach to achieve…
