Nuclear Potential and Fusion Cross Sections for Synthesizing Super-Heavy Elements in Di-nuclear Systems

A double foMing method with simplified Skyrme-type nucleon nucleon interaction is used to calculate the nuclear interaction potential between two nuclei. The calculation is performed in tip-to-tip orientation of the two nuclei if they are deformed. Based on this method, the potential energy surfaces~ the fusion probabilities and the evaporation residue cross sections for some cold fusion reactions leading to super-heavy elements within di-nuclear system model are evaluated. It is indicated that after the improvement, the exponential decreasing systematics of the fusion probability with increasing charge number of projectile on the Pb based target become better and the evaporation residue cross sections are in better agreement with the experimental data.     

Isoscaling in Statistical Sequential Decay Model

A sequential decay model is used to study isoscaling, i.e. the factorization of the isotope ratios from sources of different isospins and sizes over a broad range of excitation energies, into fugacity terms of proton and neutron number, R21（N, Z） = Y2（ N, Z）/Y1（ N, Z） = Cexp（αN -βZ）. It is found that the isoscaling parameters α and β have a strong dependence on the isospin difference of equilibrated source and excitation energy, no significant influence of the source size on α andβ has been observed. It is found that α and β decrease with the excitation energy and are linear functions of 1/T and △（Z/A）2 or△（N/A）2 of the sources. Symmetry energy coefticient Gsym is constrained from the relationship of a and source △（Z/A）2, /3 and source △（N/A）2.     

Probing Balance Energy Using Momentum- and Isospin-Dependent Potential

Using the momentum- and isospin-dependent Boltmann-Uehling-Uhlenbeck （BUU） model, we investigate the transverse flow and balance energy in two isotopic colliding systems ^48Ca＋^58Fe and ^48Cr＋^58Ni by adopting different symmetry potentials. By comparing the results between the two colliding systems, we find that the difference between the balance energies of two isotopic systems can be considered as a sensitive probe to the density dependence of symmetry energy.     

Entrance channel mass asymmetry dependence of compound nucleus formation

The fusion reactions ⁴⁸Ca + ¹⁵⁴Sm and ¹⁶O + ¹⁸⁶W leading to the same compound nucleus ²⁰²Pb are studied within the framework of an improved isospin dependent quantum molecular dynamics model. The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies, Coulomb barriers and fusion cross sections. The calculated fusion cross sections agree quantitatively with the experimental data. We conclude that the compound nucleus formation is favorable for the system with larger mass asymmetry.     

The Average Lifetime of Giant Composite Systems Formed in Strongly Damped Collisions

The dynamic, adiabatic and diabat ic entrance potentials in strongly damped reactions of ^238 U＋^238 U, ^232 Th ＋ ^250Cf are calculated and compared. The feature of the dynamical potential implies that it is possible for the composite systems to stick together for a period of time. By means of the improved quantum molecular dynamics model the time evolution of the density and charge distributions of giant composite systems and their fragments for reactions ^238U＋^238U, ^232Th＋^250Cf are investigated, from which the lifetimes of giant composite systems at different energies are obtained. The longest average lifetime of ^238U＋^238U is found when the incident energy is about Ec.m =1080 MeW, which is about 1200 fm/c.     

Isospin Effects of Threshold Energy of Radial Flow in Heavy Ion Collisions

The threshold energies of radial flow in reactions of ^40 Ca-^40Ca and ^48Ca＋ ^48Ca in central collisions are investigated within an isospin dependent quantum molecular dynamics model by using three different forms of symmetry energy. It is found that the neutron-rich system has smaller threshold energy of radial flow and this quantity depends on the form of symmetry potential. It is indicated that the threshold energy of radial flow can provide a new method to determine the symmetry energy of asymmetric nuclear matter.     

Possible Mechanisms of Ternary Fission in the 197Au+197Au System at 15 A MeV

Ternary fission in ^197Au＋^197Au collisions at 15 A MeV is investigated by using the improved quantum molecular dynamical （ImQMD） model. The experimental mass distributions for each of the three fragments are reproduced for the first time without any freely adjusting parameters. The mechanisms of ternary fission in central and semicentral collisions are dynamically studied. In direct prolate ternary fission, two necks are found to be formed almost simultaneously and rupture sequentially in a very short time interval. Direct oblate ternary fission is a very rare fission event, in which three necks are formed and rupture simultaneously, forming three equally sized fragments along space-symmetric directions in the reaction plane. In sequential ternary fission a binary division is followed by another binary fission event after hundreds of fm/c.     

Impact Parameter Dependence of the Double Neutron/Proton Ratio of Nucleon Emissions in Isotopic Reaction Systems

Within the transport model IBUU04, we investigate the double neutron/proton ratio of free nucleons taken from two reaction systems using two Sn isotopes at a beam energy of 50 MeV/nucleon and with impact parameters 2fm, 4fm and 8fm, respectively. It is found that the double neutron/proton ratio from peripheral collisions is more sensitive to the density dependence of the symmetry energy than those from mid-central and central collisions.     

Neutron and Proton Diffusion in Fusion Reactions for the Synthesis of Superheavy Nuclei

The restriction of the one dimensional （1D） master equation （ME） with the mass number of the projectile-like fragment as a variable is studied, and a two-dimensional （2D） master equation with the neutron and proton numbers as independent variables is set up, and solved numerically. Our study showed that the 2D ME can describe the fusion process well in all projectile target combinations. Therefore the possible channels to synthesize super-heavy nuclei can be studied correctly in wider possibilities. The available condition for employing 1D ME is pointed out.     

Density and Symmetric Potential Dependences of Isoscaling Behaviour in the Lattice Gas Model

Isoscaling behaviour of the statistical emission fragments from the equilibrated sources with Z=30 and N=30, 33, 36 and 39 is investigated in the framework of the isospin-dependent lattice gas model. The dependences of isoscaling parameters α on source isospin asymmetry, temperature andfreeze-out density are studied, and the `symmetry energy' is deduced from isoscaling parameters. The results show that symmetry energy C_sym is insensitive to the change of temperature but follows the power-law dependence on the freeze-out density ρ. The effect of strength of asymmetry of nucleon--nucleon interaction potential on the density dependence of the symmetry energy is discussed.     

Double neutron/proton ratio of nucleon emissions in isotopic reaction systems as a robust probe of nuclear symmetry energy

The double neutron/proton ratio of nucleon emissions taken from two reaction systems using four isotopes of the same element, namely, the neutron/proton ratio in the neutron-rich system over that in the more symmetric system, has the advantage of reducing systematically the influence of the Coulomb force and the normally poor efficiencies of detecting low energy neutrons. The double ratio thus suffers less systematic errors. Within the IBUU04 transport model the double neutron/proton ratio is shown to have about the same sensitivity to the density dependence of nuclear symmetry energy as the single neutron/proton ratio in the neutron-rich system involved. The double neutron/proton ratio is therefore more useful for further constraining the symmetry energy of neutron-rich matter.     

Shell Correction and Pairing Energies in the Dinuclear System Model

We investigate the dependences of the potential energy surfaces （PES） and the fusion probabilities for some cold fusion reactions leading to super-heavy elements on the nuclear shell effect and pairing energy. It is found that the shell effect plays an important role in the fusion of the super-heavy element while pairing energy＇s contribution is insignificant. The fusion probabilities and evaporation residue cross sections as functions of the Ge-isotope projectile bombarding ^208Pb are also investigated. It is found that evaporation residue cross sections do not always increase with the increasing neutron number of Ge-isotope.     

Fragmentation Cross Sections of 12C on Different Targets at Beam Energies from 50 to 100MeV/Nucleon

The fragmentation cross sections of reactions ^12C＋^2H, ^12C, ^14N, ^16O at beam energies from 50 to 100 MeV/nucleon are investigated using the isospin-dependent Boltzmann-Langevin equation model. It is found that fragment species increase approximately with the increasing target mass. The fragment species and some fragments production cross sections in reactions of ^12C＋^12C, ^14N, ^16O show an obvious variation at the beam energies from 50 to 80 MeV/nucleon. However the calculated fragment production cross sections do not change much when the incident energy increases from 80 to 100 MeV/nucleon.     

Nuclear Hexadecapole Deformation Effects on the Production of Super-Heavy Elements

We investigate the effects of the nuclear hexadecapole deformations on the interaction potentials between nuclei, the driving potentials and the fusion probabilities for some cold fusion reactions leading to super-heavy elements. It is found that nuclear hexadecapole deformations change significantly the structure of the driving potentials and the fusion probabilities for some reaction channels.     

Entrance-Channel Dependence of Isospin Effects on Double n/p Ratio in HIC

Within the hadronic transport model IBUU04, we investigate the effect of density-dependent symmetry energy on double neutron/proton (n/p) ratio of free nucleons in heavy ion collisions by taking four isotopic Sn+Sn reaction systems. Especially the entrance-channel asymmetry and impact-parameter dependence of the effect of symmetry energy are discussed. It is found that in both central and semi-central collisions the sensitivity of the double n/p ratio to the density-dependent symmetry energy is more pronounced in neutron-richer systems. Our results also indicate clearly that the effect of symmetry energy is stronger in central collisions than that in semi-central collisions.     

Optical Potential Parameters for Halo Nucleus System ^6He＋^12C from Transfer Reaction ^11B（^7Li, ^6He）^12C

The optical potential parameters for the halo nucleus system ^6He＋^12C are extracted from fits to the measured angular distributions of ^11B（^7Li, ^6He）12C reaction at energies of 18.3 and 28.3MeV with distorted-wave Born approximation analysis. The characters of the obtained optical potentiM parameters are basically consistent with the results extracted from the fits to the elastic-scattering angular distributions in the literature.     

Fusion near the Coulomb barrier for the synthesis of heavy and superheavy elements: A theoretical approach

The compound nucleus formation is considered as a two-step process of touching and subsequent tunneling of the projectile into the target. The deep minima in the potential energy curve are due to shell effects in the experimental binding energies and give possible target-projectile combinations for the synthesis of heavy and superheavy elements. The asymmetric channels thus obtained are in remarkable agreement with the known experimental channels. In our model, the colliding partners are first shown to be captured in the pocket behind the outer (touching) barrier and the composite system so formed finally tunnels through the inner (fusion) barrier to form the resulting compound nucleus. These calculations reveal the importance of the fusion barrier, which occur only for the asymmetric target-projectile combinations. The calculated fusion cross-sections show a reasonable comparison with the observed one-neutron evaporation residue cross-sections. An estimate of the excitation energy carried by the compound nucleus is also obtained from our model calculations.     

Challenges in nuclear dynamics and thermodynamics

The purpose and contents of this topical issue, Dynamics and Thermodynamics with Nuclear Degrees of Freedom, which grew out of a series of workshops in the years 2004 and 2005, are introduced. The central topics are the nuclear density functional, nuclear multi-fragmentation, and nuclear phase transitions.     

Possible Way to Synthesize Superheavy Element Z=117

Within the framework of the dinuclear system model, the production of superheavy element Z = 117 in possible projectile-target combinations is analysed systematically. The calculated results show that the production cross sections are strongly dependent on the reaction systems. Optimal combinations, corresponding excitation energies and evaporation channels are proposed, such as the isotopes^248.249 Bk in ^48 Ca induced reactions in 3n evaporation channels and the reactions ^45Sc＋246.248Cm in 3n and 4n channels, and the system ^51 V＋ 244pu in 3n channel.