Calculation of Interaction Potentials between Spherical and Deformed Nuclei

The interaction potential for spherical-deformed reaction partners is calculated. The shape, separation and orientation dependence of the interaction potential and fusion cross section of the system ^32S＋^154Sm are investigated within the double-folding model of the deformed nuclei. The effective nucleon-nucleon interaction is taken to be the M3Y-Reid potential. The density is considered for three terms of the expansion using the truncated multipole expansion method, which is a deformed Fermi shape With quadrupole and hexadecapole for the density distribution of ^154Sm. It is found for the interaction potential that the height and the position of barrier strongly depend on the deformations, the orientation angle of the deformed nucleus, and hence produce great effects on fusion cross section. The integrated fusion cross section is in good agreement with the experimental data.     

How does fusion hindrance show up in medium-light systems? The case of Ca + Ca

The fusion excitation function of ⁴⁸Ca + ⁴⁸Ca has been measured above and well below the Coulomb barrier, thereby largely extending the energy range of a previous experiment down to very low cross sections. This system has a negative Q  -value for compound nucleus formation. The fusion cross section decreases steadily below the barrier with no conspicuous change of slope below ?300 μb$?300\text{μb}$. Coupled-channels calculations using a Woods–Saxon potential indicate that a large diffuseness parameter is needed to reproduce the sub-barrier cross sections. A close analogy with the case of ³⁶S + ⁴⁸Ca, with Q>0$Q>0$, is pointed out. The sign of the Q-value does not influence fusion cross sections down to the 300–600 nb level.     

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.     

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.     

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.     

Origin of Unexpected Isotopic Trends in Synthesis of Superheavy Nuclei

We investigate the dependence of the yield of superheavy nuclei with Z = 110, 112, 114 on the neutron excess of the projectile nucleus with a two-parameter Smoluchowski equation. It is confirmed that in some cases, the cold fusion reactions with less neutron excess are more favourable than those with more neutron excess. In order to probe the origin of these unexpected isotopic trends, we also investigate the probabilities of capture, fusion and survival in the cold fusion reactions in detail It is found that the maximal ER cross sections of the superheavy nuclei exponentially increase as a function of Bf - Sn with Bf being the fission barrier and Sn being the neutron separation energy. Although the probabilities of capture and fusion have some influences, the unexpected isotopic trends mainly due to the dependence of the ER cross sections on the Bf - Sn value. Therefore, the reactions with larger Bf - Sn values should be more favourable for synthesis of superheavy nuclei.     

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.     

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.     

Calculation of the Coulomb potential between spherical-deformed and deformed-deformed nuclei using the Monte Carlo method

The Coulomb potential between spherical-deformed and deformed-deformed nuclei has been calculated using the Monte Carlo simulation. The results obtained for the Coulomb potential in the ¹⁶O$ + $²³⁸U and ²⁷Al$ + $⁷⁰Ge reactions are in good agreement with those obtained using the double-folding method. The simulation technique employed here has the ability of calculating the Coulomb potential taking into account the finite diffuseness parameter, all the possible deformation degrees of freedom, and different orientations of the symmetry axes of the target and the projectile nuclei with respect to each other. The accuracy of this simulation technique is high and the computer time taken to do these calculations is much less than those of the double-folding method.     

Optical Potential Parameters of Weakly Bound Nuclear System 17F+13C

Elastic scattering angular distributions of the 14^N＋16^O system and the angular distributions of transfer reaction 16^O（14^N,13^C）17^F at ELab=76.2 MeV and 57 MeV have been measured and calculated by means of the exact finiterange distorted-wave Born approximation with the PTOLEMY code. The optical potential parameters for the weakly bound nuclear system 17^F＋13^C have been deduced and applied to analyse the elastic scattering angular distributions of the similar systems 17^F＋12^C and 17^F＋14^N which are taken from literature. The result shows that the transfer reaction with stable projectile and target combination can be used as an alternative method to extract the optical potential parameters for the weakly bound nuclear system.     

On the analysis of intermediate–energy Coulomb excitation experiments

In a recent publication [C.A. Bertulani, G. Cardella, M. De Napoli, G. Raciti, E. Rapisarda, Phys. Lett. B 650 (2007) 233] the validity of analysis methods used for intermediate-energy Coulomb excitation experiments was called into question. Applying a refined theory large corrections of results in the literature seemed needed. We show that this is not the case and that the large deviations observed in above mentioned reference are due to the use of the wrong experimental parameters in that publication. We furthermore show that an approximate expression derived in above mentioned reference is in fact equivalent to the theory of Winther and Alder, an analysis method often used 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.     

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.     

Competition between binary reactions and fusion in heavy-ion collisions at the Coulomb barrier

Mass and charge distributions for binary reaction channels have been measured for the reactions⁸⁶Kr with⁷⁶Ge,¹⁰⁴Ru and¹³⁰Te at the Coulomb barrier using chemical separations and-ray spectroscopy. These systems span the region where dynamical hindrance to complete fusion sets in. The binary reactions can be subdivided into two components associated withi) reflection from the outer potential barrier (quasielastic), andii) reseparation after passing the barrier (complex reactions). The sum of complex-reaction channels and evaporation residues from complete fusion can be reproduced by a barrier passing calculation. The fraction of the barrier passing flux leading to reseparation increases from 26±10% for the lightest system to more than 90% for the heaviest system. The data indicate that fusion hindrance is primarily caused by reseparation shortly after passage of the barrier before Swiatecki's conditional saddlepoint is overcome, resulting in partitions close to the entrance channel configuration. In addition, for the heaviest system, a quasifission component representing somewhat less than 20% of the barrier-passing flux was observed. From the missing masses of fragment pairs we can deduce that the reseparating complex-reaction products have kinetic energies well below the fusion barrier and share the excitation energy in a way similar to the sawtooth-like curve known from low-energy fission. The quasielastic, predominantly one- and two-nucleon transfer channels, have strongly varying cross sections for the three systems despite similar effectiveQ-values. A systematics of one-neutron transfer cross sections at the Coulomb barrier is established and shown to differ considerably from the smooth behaviour observed at energies 20–30% above the barrier. The connection to nuclear polarization phenomena and orbit matching is pointed out.Nuclear reactions:⁷⁶Ge,¹⁰⁴Ru,¹³⁰Te(⁸⁶Kr, X).E=3.22 MeV/u, (3.64) 3.84 MeV/u, 3.96 MeV/u; enriched targets; catcher foil technique, chemical separations,-ray spectroscopy; deduced mass and charge distributions for binary reactions; competition with complete fusion     

Angular Distribution of the 12C(6He, 7Li)11B Reaction

Angular distribution of the ¹²C(⁶He,⁷Li)¹¹B transfer reaction is measured with a secondary ⁶He beam of 36.4MeV for the first time. The experimental angular distribution is well reproduced by the distorted-wave Born approximation (DWBA) calculation. The success of the present experiment shows that it is feasible to measure one-nucleon transfer reaction on a light nucleus target with the secondary beam facility of the HI-13 tandem accelerator at China Institute of Atomic Energy (CIAE), Beijing.     

The Li exclusive breakup on Si at 13 MeV

We have undertaken the study of ⁶Li breakup on a ²⁸Si target near the Coulomb barrier through an angular distribution measurement. Alpha particles were recorded in coincidence with deuterons in order to determine exclusively the breakup of lithium. The results are analysed and are discussed, in a continuum discretized coupled channel framework (CDCC).     

Fusion-evaporation cross-sections for 48Ca + 154Sm near the Coulomb barrier

Measurements of fusion-evaporation cross-sections for the system ⁴⁸Ca + ¹⁵⁴Sm have been performed in the sub- and near-barrier energy range. Barrier-passing cross-sections have been obtained by adding recently measured capture-fission cross-sections at the same energies, and the barrier distribution for capture has been extracted. The data have been analyzed within a coupled-channel model, and a large subbarrier cross-section enhancement is observed, due to the ground-state prolate deformation of ¹⁵⁴Sm. The ⁴⁸Ca + ¹⁵⁴Sm capture cross-sections are compared to existing data on ¹⁶O + ¹⁸⁶W fusion, leading to the same CN, where a few higher-energy points have also been measured. The evaporation residue cross-sections for the two systems above the barrier indicate that complete fusion is inhibited for ⁴⁸Ca + ¹⁵⁴Sm by 40% in that energy region, with respect to ¹⁶O + ¹⁸⁶W.     

Isotope Dependence of Superheavy Nucleus Formation Cross Section

The dynamical process in the superheavy nucleus synthesis is studied on the basis of the two-dimensional Smoluchowski equation. Special attention is paid to the isotope dependence of the cross section for the superheavy nucleus formation by means of making a comparison among the reaction systems of ^54Re＋204pb, ^56Re ＋206Pb, and ^58Fe＋^208Pb. It is found by this comparison that the formation cross section is very sensitive to the conditional saddle-point height and the neutron separation energy of the compound nucleus. Reaction systems with lower height of conditional saddle-point and smaller neutron separation energy are more favourable for the synthesis of the superheavy nucleus.