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 has been used to produce super strong electric fields and to test non perturbative quantum electrodynamics theory. Indeed, if the life time of such giant system is of the order of few 10^-21 s, its electric field should induce spontaneous electron-positron pair emissions from vacuum. In our calculations, highest collision times are reached in the 238U+238U reaction for center of mass energies between 1000 and 1300 MeV.
Two systematic sources of error in most current microscopic evaluations of fission-barrier heights are studied. They are concerned with an approximate treatment of the Coulomb exchange terms (known as the Slater approximation) in the self-consistent mean fields and the projection on good parity states (e.g., of positive parity for the spontaneous fission of an even-even nucleus) of left-right reflection asymmetric intrinsic solutions (e.g., around the second barrier). Approximate or unprojected solutions are shown to lead each to an underestimation of the barrier heights by a few hundred keV.
We evaluate the performance of modern nuclear energy density functionals for predicting inner and outer fission barrier heights and energies of fission isomers of even-even actinides. For isomer energies and outer barrier heights, we find that the self-consistent theory at the HFB level is capable of providing quantitative agreement with empirical data.
The concept of fission barrier - a parameter which enters in quantitative estimates of various observables related to nuclear fission - is presented from the point of view of theory based on the picture of nuclear deformation and energy dependent on it. We describe the macroscopic-microscopic method of calculating energy landscapes which is simpler than the selfconsistent mean field approach, and, due to its two-component nature, seems to be easier to adjust to experimental data. We present some models and methods used to find the fission saddles. For the purpose of illustration, we present re…
In this work, we introduce a new method to reduce the microscopic mean-field theory to a classical macroscopic dynamics during the initial stage of fusion reactions. We show that TDHF (Time-dependent Hartree-Fock) could be a useful tool to gain information on fusion barriers as well as on one-body dissipation effects. We apply the mean-field theory to the case of head-on reaction between $^{16}$O and $^{16,22,24,28}$O in order to quantify the effect of neutron skin on fusion. We show that the determination of fusion barrier requires, in addition to a precise knowledge of the relative distance …
We perform a study of $^{16}$O+$^{16}$O fusion at above and below the interaction barrier energies using three-dimensional time-dependent Hartree-Fock (TDHF) calculations at above barrier energies and density-constrained TDHF calculations for the entire energy range. We discuss the variations of the experimental data at above the barrier energies. Calculations reasonably reproduce the observed energy-dependent broad oscillations in the fusion excitation functions. These oscillations result from overcoming $L$-dependent fusion barriers. The role of the coupling to low-lying octupole states is a…
With a help of the selfconsistent Hartree-Fock-Bogoliubov (HFB) approach with the D1S effective Gogny interaction and the Generator Coordinate Method (GCM) we incorporate the transverse collective vibrations to the one-dimensional model of the fission-barrier penetrability based on the traditional WKB method. The average fission barrier corresponding to the least-energy path in the two-dimensional potential energy landscape as function of quadrupole and octupole degrees of freedom is modified by the influence of the transverse collective vibrations along the nuclear path to fission. The set of…
We provide a theoretical analysis of recently measured fusion cross sections which show a surprising enhancement at low $E_\mathrm{c.m.}$ energies for the system $^{132}$Sn+$^{40}$Ca as compared to the more neutron-rich system $^{132}$Sn+$^{48}$Ca. Dynamic microscopic calculations are carried out on a three-dimensional lattice with a time-dependent density-constrained density functional theory. There are no adjustable parameters, the only input is the Skyrme effective NN interaction. Heavy-ion potentials $V(R)$, coordinate-dependent mass parameters $M(R)$, and total fusion cross sections $σ(E_…
We investigate the fusion barriers for reactions involving Ca isotopes $\mathrm{^{40}Ca}+\mathrm{^{40}Ca}$, $\mathrm{^{40}Ca}+\mathrm{^{48}Ca}$, and $\mathrm{^{48}Ca}+\mathrm{^{48}Ca}$ using the microscopic time-dependent Hartree-Fock theory coupled with a density constraint. In this formalism the fusion barriers are directly obtained from TDHF dynamics. We also study the excitation of the pre-equilibrium GDR for the $\mathrm{^{40}Ca}+\mathrm{^{48}Ca}$ system and the associated $γ$-ray emission spectrum. Fusion cross-sections are calculated using the incoming-wave boundary condition approach. …
Recently measured fusion cross-sections for the neutron-rich system 20O+12C are compared to dynamic, microscopic calculations using time-dependent density functional theory. The calculations are carried out on a three-dimensional lattice and performed both with and without a constraint on the density. The method has no adjustable parameters, and its only input is the Skyrme effective NN interaction. While the microscopic DC-TDHF calculations lie closer to the experimental data than standard fusion systematics they underpredict the experimental data significantly.
Important efforts have been dedicated in the past few years to describe near-barrier heavy-ion collisions with microscopic quantum theories like the time-dependent Hartree-Fock approach and some of its extensions. However, this field is still facing important challenges such as the description of cluster dynamics, the prediction of fragment characteristics in damped collisions, and sub-barrier fusion by quantum tunnelling. These challenges are discussed and possible approaches to solve them are presented.
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.
We introduce a microscopic approach for calculating the excitation energies of systems formed during heavy-ion collisions. The method is based on time-dependent Hartree-Fock (TDHF) theory and allows the study of the excitation energy as a function of time or ion-ion separation distance. We discuss how this excitation energy is related to the estimate of the excitation energy using the reaction $Q$-value, as well as its implications for dinuclear pre-compound systems formed during heavy-ion collisions.
We provide a microscopic description of the fusion reactions between $^{40,48}$Ca and $^{78}$Ni. The internuclear potentials are obtained using the density-constrained (DC) time-dependent Hartree-Fock (TDHF) approach and fusion cross sections are calculated via the incoming wave boundary condition method. By performing DC-TDHF calculations at several selected incident energies, the internuclear potentials for both systems are obtained and the energy-dependence of fusion barrier are revealed. The influence of tensor force on internuclear potentials of $^{48}\mathrm{Ca}+{}^{78}\mathrm{Ni}$ is mo…
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+…
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…
The nucleus-nucleus potential is calculated in the frame work of the double folding model (DFM) to obtain the Coulomb barrier parameters (barrier position and height), starting from M3Y-Reid nucleon-nucleon interaction and realistic nuclear matter distribution. The systematic behavior of the barrier parameters with mass numbers, charges, and radii of interacting nuclei is studied. The relation between the barrier height and radius is also discussed. The systematic behavior of the barrier parameters is presented in the form of simple analytical formulae, which can be used to calculate the barri…
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 agr…
Dissipation and fluctuations of one-body observables in heavy-ion reactions around the Coulomb barrier are investigated with a microscopic stochastic mean-field approach. By projecting the stochastic mean-field dynamics on a suitable collective path, transport coefficients associated with the relative distance between colliding nuclei and a fragment mass are extracted. Although microscopic mean-field approach is know to underestimate the variance of fragment mass distribution, the description of the variance is much improved by the stochastic mean-field method. While fluctuations are consisten…
The fission processes of thermal excited nuclei are conventionally studied by statistical models which rely on inputs of phenomenological level densities and potential barriers. Therefore the microscopic descriptions of spontaneous fission and induced fission are very desirable for a unified understanding of various fission processes. We propose to study the fission rates, at both low and high temperatures, with microscopically calculated temperature-dependent fission barriers and collective mass parameters. The fission barriers are calculated by the finite-temperature Skyrme-Hartree-Fock+BCS …
We investigate the effect of Pauli non-locality in the heavy-ion optical potential on sub-barrier fusion reactions. The São Paulo potential, which takes into account the Pauli non-locality and has been widely used in analyzing elastic scattering, has also recently been applied to heavy-ion fusion. However, the approximation employed in deriving the São Paulo potential, based on the Perey-Buck semi-classical treatment of neutron induced reactions, must be assessed for charged particles tunneling through a barrier. It is the purpose of this note to look into this question. We consider the widely…
The understanding of the fusion probability is of particular importance to reveal the mechanism of producing superheavy elements. We present a microscopic study of the compound nucleus formation by combining time-dependent density functional theory, coupled-channels approach, and dynamical diffusion models. The fusion probability and compound nucleus formation cross sections for cold-fusion reactions $^{48}$Ca+$^{208}$Pb, $^{50}$Ti+$^{208}$Pb, and $^{54}$Cr+$^{208}$Pb are investigated and it is found that the deduced capture barriers, capture cross sections for these reactions are consistent w…
We discuss the effects of coupling of the relative motion to nuclear collective excitations which have a finite lifetime on heavy-ion fusion reactions at energies near and below the Coulomb barrier. Both spreading and escape widths are explicitly taken into account in the exit doorway model. The coupled-channels equations are numerically solved to show that the finite resonance width always hinders fusion cross sections at subbarrier energies irrespective of the relative importance between the spreading and the escape widths. We also show that the structure of fusion barrier distribution is sm…
An isospin and spin dependent form of the equation of state for nuclear matter is presented. This form is used for the description of nucleon interaction in a new dynamic model. Preliminary calculations show that the new approach makes possible predicting the alpha structures appearing in the case of the ground state even-even nuclei.
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…
Realistic fusion barriers are calculated in a macroscopic-microscopic model for several soft-fusion heavy-ion reactions leading to heavy and superheavy elements. The results obtained in such a realistic picture are very different from those obtained in a purely macroscopic model. For reactions on 208:Pb targets, shell effects in the entrance channel result in fusion-barrier energies at the touching point that are only a few MeV higher than the ground state for compound systems near Z = 110. The entrance-channel fragment-shell effects remain far inside the touching point, almost to configuratio…
We study reactions between neutron-rich $^{132}$Sn nucleus and $^{96}$Zr within a dynamic microscopic theory at energies in the vicinity of the ion-ion potential barrier peak, and we compare the properties to those of the stable system $^{124}$Sn+$^{96}$Zr. The calculations are carried out on a three-dimensional lattice using the density-constrained Time-Dependent Hartree-Fock method. In particular, we calculate the dynamic excitation energy $E^*(t)$ and the quadrupole moment of the dinuclear system, $Q_{20}(t)$, during the initial stages of the heavy-ion collision. Capture cross sections for …
Nucleon drift and diffusion mechanisms in central collisions of asymmetric heavy-ions at near-barrier energies are investigated in the framework of a stochastic mean-field approach. Expressions for diffusion and drift coefficients for nucleon transfer deduced from the stochastic mean-field approach in the semiclassical approximation have similar forms familiar from the phenomenological nucleon exchange model. The variance of fragment mass distribution agrees with the empirical formula $σ^2_{AA}(t)= N_{\rm exc}(t)$. The comparison with the time-dependent Hartree-Fock calculations shows that, be…
The density-constrained time-dependent Hartree-Fock (DC-TDHF) theory is a fully microscopic approach for calculating heavy-ion interaction potentials and fusion cross sections below and above the fusion barrier. We discuss recent applications of DC-TDHF method to fusion of light and heavy neutron-rich systems.
An approach is proposed to calculate the direct reaction (DR) and fusion probabilities for heavy ion collisions at near-Coulomb-barrier energies as functions of the distance of closest approach D within the framework of the optical model that introduces two types of imaginary potentials, DR and fusion. The probabilities are calculated by using partial DR and fusion cross sections, together with the classical relations associated with the Coulomb trajectory. Such an approach makes it possible to analyze the data for angular distributions of the inclusive DR cross section, facilitating the deter…
Measurement of the energy dependence of the fusion cross-sec on at sub-barrier energies provides an important test for theoretical models of fusion. To extend the measurement of fusion cross-sections in the sub-barrier domain for the 18O+12C system. Use the new experimental data to confront microscopic calculations of fusion. Evaporation residues produced in fusion of 18O ions with 12C target nuclei were detected with good geometric efficiency and identified by measuring their energy and time-of-flight. Theoretical calculations with a density constrained time dependent Hartree-Fock (DC-TDHF) t…
We investigate the effect of single-particle excitations on heavy-ion reactions at energies near the Coulomb barrier. To this end, we describe single-particle degrees of freedom with the random matrix theory and solve the coupled-channels equations for one-dimensional systems. We find that the single-particle excitations hinder the penetrability at energies above the barrier, leading to a smeared barrier distribution. This indicates that the single-particle excitations provide a promising way to explain the difference in a quasi-elastic barrier distribution recently observed in $^{20}$Ne + $^{…
Direct photon emission in heavy-ion collisions is calculated within a relativistic micro+macro hybrid model and compared to the microscopic transport model UrQMD. In the hybrid approach, the high-density part of the collision is calculated by an ideal 3+1-dimensional hydrodynamic calculation, while the early (pre-equilibrium-) and late (rescattering-) phase are calculated with the transport model. Different scenarios of the transition from the macroscopic description to the transport model description and their effects are studied. The calculations are compared to measurements by the WA98-coll…
Systematic calculations of the Coulomb barrier parameters for collisions of spherical nuclei are performed within the framework of the double folding approach. The value of the parameter $B_Z=Z_PZ_T/(A^{1/3}_P+(A^{1/3}_P)$ (which estimates the Coulomb barrier height) varies in these calculations from 10 MeV up to 150 MeV. The nuclear densities came from the Hartree-Fock calculations which reproduce the experimental charge densities with good accuracy. For the nucleon-nucleon effective interaction two analytical approximations known in the literature are used: the M3Y and Migdal forces. The cal…
The nucleus-nucleus interaction potentials in heavy-ion fusion reactions are extracted from the microscopic time-dependent Hartree-Fock theory for mass symmetric reactions $^{16}$O${}+^{16}$O, $^{40}$Ca${}+^{40}$Ca, $^{48}$Ca${}+^{48}$Ca and mass asymmetric reactions $^{16}$O$ +^{40,48}$Ca, $^{40}$Ca${}+^{48}$Ca, $^{16}$O+$^{208}$Pb, $^{40}$Ca+$^{90}$Zr. When the center-of-mass energy is much higher than the Coulomb barrier energy, potentials deduced with the microscopic theory identify with the frozen density approximation. As the center-of-mass energy decreases and approaches the Coulomb bar…
We study heavy-ion fusion reactions at energies near the Coulomb barrier, in particular with neutron-rich radioactive ion beams. Dynamic microscopic calculations are carried out on a three-dimensional lattice using the Density-Constrained Time-Dependent Hartree-Fock (DC-TDHF) method. New results are presented for the $^{132}$Sn+$^{40}$Ca system which are compared to $^{132}$Sn+$^{48}$Ca studied earlier. Our theoretical fusion cross-sections agree surprisingly well with recent data measured at HRIBF. We also study the near- and sub-barrier fusion of $^{24,16}$O on $^{12}$C which is important to…
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…
This is a short review of methods and results of calculations of fission barriers and fission half-lives of even-even superheavy nuclei. An approvable agreement of the following approaches is shown and discussed: The macroscopic-microscopic approach based on the stratagem of the shell correction to the liquid drop model and a vantage point of microscopic energy density functionals of Skyrme and Gogny type selfconsistently calculated within Hartree-Fock-Bogoliubov method. Mass parameters are calculated in the Hartree-Fock-Bogoliubov cranking approximation. A short part of the paper is devoted t…
The (semi-)microscopic double-folding nucleus-nucleus optical potentials are suggested for consideration of inelastic scattering with excitation of collective nuclear states by using the adiabatic approach and the elastic scattering amplitude in the high-energy approximation. The analytical expression for inelastic scattering amplitude is obtained keeping the first order terms in the deformation parameter of a potential. Calculations of inelastic cross sections for the $^{17}$O heavy ions scattered on different nuclei at about hundred Mev/nucleon are made, and the acceptable qualitative agreem…
The vast knowledge of strong influence of quadrupole deformation $β_2$ of colliding nuclei on heavy-ion subbarrier fusion reactions inspires a desire to quest the sensitivity of fusion dynamics to higher order deformations, such as $β_4$ and $β_6$ deformations. However, such studies have rarely been carried out, especially for deformation of projectile nuclei. In this article, we investigated the role of $β_4$ of the projectile nucleus in fusion of the $^{28}$Si + $^{92}$Zr system. We demonstrated that the fusion barrier distribution is sensitive to the sign and the value of the $β_4$ paramete…
In order to describe heavy-ion fusion reactions around the Coulomb barrier with an actinide target nucleus, we propose a model which combines the coupled-channels approach and a fluctuation-dissipation model for dynamical calculations. This model takes into account couplings to the collective states of the interacting nuclei in the penetration of the Coulomb barrier and the subsequent dynamical evolution of a nuclear shape from the contact configuration. In the fluctuation-dissipation model with a Langevin equation, the effect of nuclear orientation at the initial impact on the prolately defor…
In the density distribution of a deformed target-nucleus, the spherical $λ= 0$ and the deformed $λ= 2$ parts were considered. On this basis, the corresponding potential parts $U_0$ and $U^{(2)}_{int}$ of a double -folding microscopic nucleus-nucleus optical potential are obtained. Then, for these potentials and by using the coupled-channel technique (ECIS), the elastic and inelastic amplitudes are calculated for $^{17}O$ heavy ion scattering on $2^{+}$ collective excited state of various target nuclei. Besides, the same cross-sections are calculated in the frame of an adiabatic approach of the…
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…
With the recent availability of state-of-the-art heavy-ion stable and radioactive beams, there has been a renew interest in the investigation of nuclear reactions with heavy ions. I first present the role of inelastic and transfer channel couplings in fusion reactions induced by stable heavy ions. Analysis of experimental fusion cross sections by using standard coupled-channel calculations is discussed. The role of multi-neutron transfer is investigated in the fusion process below the Coulomb barrier by analyzing $^{32}$S+$^{90,96}$Zr as benchmark reactions. The enhancement of fusion cross sec…
The role of higher order coupling of surface vibrations to the relative motion in heavy-ion fusion reactions at near-barrier energies is investigated. The coupled channels equations are solved to all orders, and also in the linear and the quadratic coupling approximations. Taking $^{64}$Ni + $^{92,96}$Zr reactions as examples, it is shown that all order couplings lead to considerably improved agreement with the experimentally measured fusion cross sections and average angular momenta of the compound nucleus for such heavy nearly symmetric systems. The importance of higher order coupling is als…
The best fit to the published APEX U+Th data describes a sharp line of 123 pairs of width 23 keV at 793$\pm$7 keV; also, the data impose a positive 99.0%CL lower bound of 23 sharp pairs. It is therefore untenable to argue from the APEX data against the existence of sharp pairs. Data-only ratios APEX/EPOS pair counts show empirically that the two experiments' pair data are mutually consistent and of comparable statistical potency: conflicts, if any, can be resolved only by other independent evidence. A perspective is offered on the current status of the Sharp Lepton Problem, and alternative non…
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…
Relativistic mean field theory allowing for triaxial deformations is applied for a systematic study of fission barriers in the actinide region. Different pairing schemes are studied in details and it is shown that covariant density functional theory is able to describe fission barriers on a level of accuracy comparable with non-relativistic calculations, even with the best phenomenological macroscopic+microscopic approaches. Triaxiality in the region of the first saddle plays a crucial role in achieving that.
A microscopic mean-field description of heavy ions fusion is performed in the framework of the Time-Dependent Hartree-Fock (TDHF) theory using a Skyrme interaction with the SLy4d parametrization. A good agreement with experiments is obtained on the position of the fusion barriers for various total masses, mass asymmetries and deformations. The excitation function of the 16O+208Pb is overestimated by about 16% above the barrier. The restriction to an independent particles state in the mean-field dynamics prevents the description of sub-barrier fusion. Effect of transfer on fusion is discussed.
The effect of pairing correlation on transfer reaction below the Coulomb barrier is investigated qualitatively and quantitatively using a simplified version of the Time-Dependent Hartree-Fock + BCS approach. The effect of particle number symmetry breaking on the description of reaction and dedicated methods to extract one and two-nucleon transfer probabilities (P_{1n} and P_{2n}) in a particle number symmetry breaking approach are discussed. Influence of pairing is systematically investigated in the ^{40}Ca+ ^{40,42,44,46,48,50}Ca reactions. A strong enhancement of the two-particle transfer pr…
The density-constrained time-dependent Hartree-Fock (DC-TDHF) theory is a fully microscopic approach for calculating heavy-ion interaction potentials and fusion cross sections below and above the fusion barrier. We discuss recent applications of DC-TDHF method to fusion of light and heavy systems.
We have constructed an empirical formulae for the fusion and interaction barriers using experimental values available till date. The fusion barriers so obtained have been compared with different model predictions based on the proximity, Woods-Saxon and double folding potentials along with several empirical formulas, time dependent Hartree-Fock theories, and the experimental results. The comparison allows us to find the best model, which is nothing but the present empirical formula only. Most remarkably, the fusion barrier and radius show excellent consonance with the experimental findings for …
We present a new model for the creation of \J mesons in ultrarelativistic heavy ion collisions, which allows to follow the individual heavy quarks from their creation until the detector through the Quark Gluon Plasma (QGP), which is formed in these collisions and described by the EPOS2 event generator. The \cc quarks interact via a potential, based on results of lattice gauge calculations. The annihilation and creation of \J is described by a density matrix approach whose time evolution is studied in the expanding system. The comparison with PbPb data at $\sqrt{s}$=5.02 TeV shows that this mod…
We study fusion reactions of $^{16}$O with $^{154}$Sm, $^{186}$W and $^{238}$U at sub-barrier energies by a coupled-channels framework. We focus especially on the effects of $β_{6}$ deformation and low-lying vibrational excitations of the target nucleus. It is shown that the inclusion of $β_{6}$ deformation leads to a considerable improvement of the fit to the experimental data for all of these reactions. For the $^{154}$Sm and $^{238}$U targets, the octupole vibration significantly affects the fusion barrier distribution. The effect of $β$ band is negligible in all the three reactions, while …
A complete set of existing data on hot fusion reactions leading to synthesis of superheavy nuclei of Z =114-118, obtained in a series of experiments in Dubna and later in GSI Darmstadt and LBNL Berkeley, was analyzed in terms of a new angular-momentum dependent version of the Fusion by Diffusion (FBD) model with fission barriers and ground-state masses taken from the Warsaw macroscopic-microscopic model (involving non-axial shapes) of Kowal et al. The only empirically adjustable parameter of the model, the injection-point distance (sinj), has been determined individually for all the reactions …
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…
