Fusion Barrier Research Articles

Quantum effect in the diffusion along a potential barrier: Comments on the synthesis of superheavy elements

We discuss a quantum effect in the diffusion process by developing a theory, which takes the finite curvature of the potential field into account. The transport coefficients of our theory satisfy the well-known fluctuation-dissipation theorem in the limit of Markovian approximation in the cases of diffusion in a flat potential and in a potential well. For the diffusion along a potential barrier, the diffusion coefficient can be related to the friction coefficient by an analytic continuation of the fluctuation-dissipation theorem for the case of diffusion along a potential well in the asymptotic time, but contains strong non-Markovian effects at short times. By applying our theory to the case of realistic values of the temperature, the barrier curvature, and the friction coefficient, we show that the quantum effects will play significant roles in describing the synthesis of superheavy elements, i.e., the evolution from the fusion barrier to the conditional saddle, in terms of a diffusion process. We especially point out the importance of the memory effect, which increases at lower temperatures. It makes the net quantum effects enhance the probability of crossing the conditional saddle.

Heavy-Ion Fusion Cross Sections in Microscopic Barrier Penetration Model

Heavy ion fusion barrier parameters are calculated by making use of configuration of classical nucleon positions of the colliding nuclei. Calculated fusion cross sections and barrier distributions of 154Sm + 16O, 12C + 232Th, and 86Kr + 208Pb reactions agree well with the experiments.

Systematics of precise nuclear fusion cross sections: the need for a new dynamical treatment of fusion?

A large number of precision fusion excitation functions, at energies above the average fusion barriers, have been fitted using the Woods–Saxon form for the nuclear potential. Values of the empirical diffuseness parameter greatly exceed those which generally reproduce elastic scattering data and tend to increase strongly with the reaction charge product Z1Z2. Possible reasons for this may lie in the Woods–Saxon form being inappropriate, or in the reduction of fusion cross sections by processes such as deep-inelastic collisions. These results point to a need for renewed efforts in dynamical calculations of fusion.

Double folding nucleus-nucleus potential applied to heavy-ion fusion reactions

Double folding model calculations to obtain the bare nucleus-nucleus potential have been carried out with the Reid and Paris M3Y effective nucleon-nucleon (NN) interactions. The exchange part of the interaction was taken to be of finite range and the density dependence of the NN interaction was accounted for. The calculated fusion barrier energies are generally lower than those expected taking into account potential renormalization due to coupling to collective states at high excitation energies. Fitting the potentials at the barrier radii with a Woods-Saxon form results in effective potential diffuseness of $\ensuremath{\sim}0.65--0.70\phantom{\rule{0.3em}{0ex}}\text{fm}$, smaller than the values of $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\text{fm}$ generally found from fitting fusion cross sections at above-barrier energies. These discrepancies raise questions about both the determination of the bare nucleus-nucleus potential with the folding model, and the boundary of the effect of friction on the fusion process.

Uncoated endocytic vesicles require the unconventional myosin, Myo6, for rapid transport through actin barriers.

After clathrin-mediated endocytosis, clathrin removal yields an uncoated vesicle population primed for fusion with the early endosome. Here we present the first characterization of uncoated vesicles and show that myo6, an unconventional myosin, functions to move these vesicles out of actin-rich regions found in epithelial cells. Time-lapse microscopy revealed that myo6-associated uncoated vesicles were motile and exhibited fusion and stretching events before endosome delivery, processes that were dependent on myo6 motor activity. In the absence of myo6 motor activity, uncoated vesicles remained trapped in the actin mesh, where they exhibited Brownian-like motion. Exit from the actin mesh occurred by a slow diffusion-based mechanism, delaying transferrin trafficking to the early endosome. Expression of a myo6 mutant that bound tightly to F-actin produced immobilized vesicles and blocked trafficking. Depolymerization of the actin cytoskeleton rescued this block and specifically accelerated transferrin delivery to the early endosome without affecting earlier steps in endocytosis. Therefore actin is a physical barrier impeding uncoated vesicle trafficking, and myo6 is recruited to move the vesicles through this barrier for fusion with the early endosome.

HOW MANY FUSION BARRIERS?

Fusion barrier distributions for the 20 Ne + 112,116,118 Sn systems have been extracted from quasi-elastic scattering cross sections measured at the Warsaw HIL Cyclotron. Results are compared to coupled-channels calculations performed with the CCFULL code. The overall widths of the distributions are reproduced on taking account of the low-lying collective states of the target and projectile but some puzzling discrepancies in their shapes remain to be explained.

IMPORTANCE OF DEFORMATION AND ORIENTATION OF NUCLEAR SHAPES FOR THE SYNTHESIS OF SUPER-HEAVY ELEMENTS

We are studying the potential energy describing the entrance channel of a heavy-ion collisions for the axially symmetric deformed and arbitrarily oriented nuclear shapes. The paper presents an analysis of the influence of different orientations of the deformed ions on the height and shape of the fusion barrier. The net effect of the deformation degree of freedom on the transmission at sub-barrier energies is to enhance the fusion cross section. This problem is very important especially in the perspective of the synthesis of super-heavy elements.

SELFCONSISTENT FUSION BARRIERS AT NEAR BARRIER ENERGIES

Fusion potentials are calculated for a number of reactions within the static Hartree-Fock method with the Skyrme force SkM*. Fusion barriers agree with the data considerably better than reaction Q values. This suggests some error cancellation, possibly with the relative kinetic energy term. Our results are consistent with the idea of fusion hindrance in tip collisions. Some comparison to results of the frozen density method is made.

Fusion Reactions as a Probe of the Nucleus-Nucleus Potential at Short Distances

The semi-classical model GRAZING is used to analyze fusion excitation functions and barrier distributions for several projectile and target combinations. It is shown that the main contribution to the fusion enhancements is coming from the excitation of collective surface modes. The behavior of the fusion excitation function at very low energies is shown to be sensitive to the actual shape of the ion-ion potential at distances shorter than the position of the Coulomb barrier.

The Nuclear Potential in Heavy-Ion Fusion

Fits to high precision fusion cross-sections even for Z P Z T < 1000 appear to need a value of the diffuseness parameter a of the Woods-Saxon potential of ≃1 fm, which is much larger than the commonly accepted value of ≃ 0.65 fm. However, use of large values of a necessarily makes the potential pocket very shallow for realistic values of the nuclear potential depth. For larger values of angular momenta the pocket disappears, and a fusion barrier energy or radius can no longer be defined. In the absence of a potential pocket, fusion does not occur in the commonly used realistic coupled channels code CCFULL where fusion is calculated by applying an incoming wave boundary condition at the position of the minimum of the attractive pocket. For this reason, realistic coupled channels calculations with large values of a have needed unrealistically deep nuclear potentials. Once the potential depth is constrained to reasonable values, the data cannot be explained by simply changing the diffuseness of the nuclear potential. This indicates the necessity to go beyond the potential model, and incorporate dynamical effects as the two nuclei move towards fusion, even for light systems with Z P Z T < 1000.

EFFECT OF THE ADIABATIC VIBRATIONAL COUPLING ON THE FUSION OF THE 16O-238U INTERACTION

The effect of both rotation and vibration of a deformed target nucleus on the fusion cross-section and barrier distributions was studied. This was done in the framework of the microscopically derived heavy-ion (HI) potential. Moreover, the effect of target deformation up to β6 and the density dependence of the NN force on the fusion process was studied in the presence of vibrational excitations of the target. The results obtained were compared with experimental data.

Adiabatic heavy-ion fusion potentials for fusion at deep sub-barrier energies

The fusion cross sections from well above barrier to extreme sub-barrier energies have been analysed using the energy (E) and angular momentum (L) dependent barrier penetration model ({\small{ELDBPM}}). From this analysis, the adiabatic limits of fusion barriers have been determined for a wide range of heavy ion systems. The empirical prescription of Wilzynska and Wilzynski has been used with modified radius parameter and surface tension coefficient values consistent with the parameterization of the nuclear masses. The adiabatic fusion barriers calculated from this prescription are in good agreement with the adiabatic barriers deduced from {\small{ELDBPM}} fits to fusion data. The nuclear potential diffuseness is larger at adiabatic limit, resulting in a lower $\hbar\omega$ leading to increase of logarithmic slope observed at energies well below the barrier. The effective fusion barrier radius and curvature values are anomalously smaller than the predictions of known empirical prescriptions. A detailed comparison of the systematics of fusion barrier with and without L-dependence has been presented.

Deformed Potential Energy of 263Db in a GeneralizedLiquid Drop Model

The macroscopic deformed potential energy for super-heavy nuclei263Db, which governs the entrance and alpha decay channels,is determined within a generalized liquid drop model (GLDM). Aquasi-molecular shape is assumed in the GLDM, which includesvolume-, surface-, and Coulomb-energies, proximity effects,mass asymmetry, and an accurate nuclear radius. The microscopicsingle particle energies are derived from a shell model in anaxially deformed Woods–Saxon potential with a quasi-molecularshape. The shell correction is calculated by the Strutinskymethod. The total deformed potential energy of a nucleus can becalculated by the macro-microscopic method as the summation of theliquid-drop energy and the Strutinsky shell correction. The theoryis applied to predict the deformed potential energy of theexperiment 22Ne + 241Am →263Db*→ 259Db + 4n, which wasperformed on the Heavy Ion Accelerator in Lanzhou. It is foundthat the neck in the quasi-molecular shape is responsible for thedeep valley of the fusion barrier due to the shell corrections. Inthe cold fusion path, the double-hump fusion barrier is predictedby the shell correction and complete fusion events may occur.

Mean-field description of fusion barriers with Skyrme's interaction

Fusion barriers are determined in the framework of the Skyrme energy-density functional together with the semi-classical approach known as the Extended Thomas–Fermi method. The barriers obtained in this way with the Skyrme interaction SkM ∗ turn out to be close to those generated by phenomenological models like those using the proximity potentials. It is also shown that the location and the structure of the fusion barrier in the vicinity of its maximum and beyond can be accurately described by a simple analytical form depending only on the masses and the relative isospin of target and projectile nucleus.

Effects of Charge Fluctuation on Two-Membrane Instability and Fusion

Membrane fusion is fundamental to diverse biological processes ranging from intercellular and intracellular transport to egg fertilization. We study the effects of coupling between membrane undulation and charge fluctuation on its fusion. We find that, at concentrations of millimolar range, multivalent cations such as calcium in solution induce a strong correlated-charge fluctuation on each membrane, leading to inversion and overcondensation of surface charges. When the charge fluctuation is cooperatively coupled to undulation, two apposing membranes undergo a dynamic instability to spontaneous growth of in-phase undulation with submicron wavelengths, thereby greatly reducing fusion barrier.

Shape isomerism of rotating44Tiand48Cr

Fusion barriers have been determined for light nucleus reactions leading to the synthesis of ${}^{44}\mathrm{Ti}$ and ${}^{48}\mathrm{Cr}.$ Different deformation paths from target and projectile initial ellipsoidal shapes to the final synthesized nucleus are taken into account. The microscopic effects are obtained with a deformed two-center shell model and the Strutinsky method. The macroscopic energy is calculated within a generalized liquid drop model. The results show the possibility of isomeric state formation within energy minima corresponding to a certain stage of partially overlapping target and projectile nuclei, in an angular momentum and excitation energy range depending on the asymmetry of the reaction and the shell structure of the nucleus partners.

Breakup and transfer processes in the9Be+208Pbreaction

$\ensuremath{\alpha}$-Particle singles and doubles yields for the reaction of ${}^{9}\mathrm{Be}{+}^{208}\mathrm{Pb}$ have been measured from below to well above the fusion barrier energy. These yields have been reproduced by calculations including both neutron transfer and inelastic excitation. The calculations predict breakup cross sections to persist to very low energies, where the latter process dominates.

Quasi-elastic barrier distribution of the 16,18O+ 92Mo

Precise quasi-elastic scattering excitation functions have been measured for the systems 16,18O+ 92Mo at energies near the Coulomb barrier. In order to obtain a representation of the fusion barrier distributions, the quasi-elastic excitation functions have been differentiated with respect to energy by using the point difference approximation with small steps in energy. The experimental representations of the barrier distributions were compared with coupled-channel calculations. In the 16O+ 92Mo system a good fit was obtained by coupling the quadrupole and octupole vibrations of the target. However, in the more complex barrier distribution of the system 18O+ 92Mo inelastic excitations of the target and projectile were unable to explain the data.

Insights into the influence of breakup on fusion through reactions with weakly bound stable nuclei

Complete fusion of 6Li, 7Li, and 9Be with targets of 208Pb and 209Bi are found to be suppressed by about 30% at energies above the fusion barrier. Sub-barrier break-up measurements for the 9Be + nat Pb reaction show that prompt breakup of 9Be occurs close to the nuclear surface, and with sufficient probability to explain the suppression of complete fusion. The suppression is predicted to be proportional to the charge of the target nucleus. A simple classical trajectory model which makes the distinction between complete and incomplete fusion shows that following breakup of the projectile close to the target, there is a significant probability of capture of all fragments by the target. This implies that fusion of exotic nuclei far from the line of stability may not be seriously suppressed by breakup.

Spin distributions at the Coulomb barrier in the 58Ni+ 60Ni fusion reaction from gamma-ray multiplicity measurements

Heavy-ion fusion barrier distributions are now routinely obtained directly from experimental data. Measurements of the total γ-ray multiplicity for the fusion channels of the 58Ni + 60Ni system, which has striking yet well understood barrier structures, confirm the theoretical predictions that very high spins can be populated at energies close to (and even below) the nominal Coulomb barrier. The mapping from multiplicities to spin populations shows that structures in the barrier distribution are still evident in the γ-ray results.