Nucleon--nucleon interactions in the double folding model for fusion reactions

Nucleus--nucleus potentials are determined in the framework of double folding model for M3Y--Reid and M3Y--Paris effective nucleon--nucleon (NN) interactions. Both zero-range and finite-range exchange parts of NN interactions are considered in the folding procedure. In this paper the spherical projectile--spherical target system ¹⁶O+²⁰⁸Pb is selected for calculating the barrier energies, fusion cross sections and barrier distributions with the density-independent and density-dependent NN interactions on the basis of M3Y--Reid and M3Y--Paris NN interactions. The barrier energies become lower for Paris NN interactions in comparison with Reid NN interactions, and also for finite-range exchange part in comparison with zero-range exchange part. The density-dependent NN interactions give similar fusion cross sections and barrier distributions, and the density-independent NN interaction causes the barrier distribution moving to a higher position. However, the density-independent Reid NN interaction with zero-range exchange part gives the lowest fusion cross sections. We find that the calculated fusion cross sections and the barrier distributions are in agreement with the experimental data after renormalization of the nuclear potential due to coupled-channel effect.     

活性靶技术熔合截面测量极限研究

天体环境中丰中子核素熔合反应率对研究中子星表面超级暴现象的点火机制有重要意义。由于次级束流强过低,无法使用传统固体靶实验技术测量垒下熔合反应截面。活性靶技术的发展为垒下丰中子核素熔合反应截面的测量提供了可行的途径。基于Geant4模拟详细地分析了多重采样电离室（MUSIC）与时间投影室（TPC）两种活性靶探测器中熔合反应与弹性散射的运动学性质,给出了4种熔合反应鉴别判据,并且计算了由这些判据误判引起的熔合截面系统误差。在E_cm=13.6 MeV时,MUSIC与TPC的弹性散射误判截面分别为0.5 mb和2.9×10-3 mb,都远小于此时熔合截面（877 mb）。在垒下,MSUIC的熔合截面系统误差已经超出实验测量要求,而TPC能够进行实验测量的能量可以降低至E_cm=4.7 MeV。Reaction rates of fusion reactions among neutron-rich nuclei in the astrophysical environment are of great significance to understand the ignition of superbursts on neutron stars. Since beam intensity is rather low for radioactive ion beams, it is extremely difficult to operate a direct measurement for cross sections of such fusion reactions below the Coulomb barrier using thick target technique. In this case, a novel technique, active target technique, has been developed recently. To study the energy limit for measurement below Coulomb barrier, the kinematics of elastic scattering and fusion reaction in MUSIC and TPC are discussed with Geant4 simulation. Four identification methods are used and uncertainties of cross sections resulted from misjudgments are calculated. With E_cm=13.6 MeV, the uncertainties of cross sections for MUSIC and TPC are 0.5 mb and 2.9×10-3 mb, respectively. The uncertainties for MUSIC become far beyond measurement when below coulomb barrier, while TPC remains to be a suitable detector for measuring fusion cross sections until E_cm=4.7 MeV.     

近垒能区6Li+208Pb熔合激发函数测量

测量了6Li+208Pb熔合反应近垒能区全熔合截面,并与考虑非弹道耦合和不考虑耦合的CCFUS程序计算做了比较. 结果表明在垒上能区,破裂使熔合截面减小,在垒下能区,破裂对熔合截面的影响基本上可以忽略.     

Fusion and transfer reactions in beams of light loosely bound nuclei at energies in the vicinity of the Coulomb barrier

Experiments devoted to studying cross sections for fusion and transfer reactions induced by the interaction of beams of halo-like (⁶He), cluster (⁶Li and ⁷Li), and loosely bound (³He) nuclei with nuclei of light and heavy elements are described. The cross sections obtained experimentally for such reactions are analyzed. Special features in the behavior of the cross sections for the formation of evaporation residues and products of transfer reactions at energies in the vicinity of the Coulomb barrier are revealed. In particular, an increase in the cross sections for fusion and transfer reactions involving halo-like nuclei and proceeding at energies in the subbarrier region is observed. The cross sections for neutron-transfer and light-cluster-transfer reactions reachmaximum values at an energy in the vicinity of the Coulomb barrier for the reaction being considered.     

Fusion reactions around the barrier for Be+~(238)U

Fusion-evaporation cross sections of ~(238)U (~9Be,5n)~(242)Cm are measured over a wide energy range around the Coulomb barrier.These measured cross sections are compared with model calculations using two codes,namely HIVAP2 and KEWPIE2.HIVAP2 calculations overestimate the measured fusion-evaporation cross sections by a factor of approximately 3.In KEWPIE2 calculations,two approaches,namely the Wentzel-Kramers-Brillouin(WKB) approximation and the empirical barrier-distribution (EBD) method,are used for the capture probability;both of them properly describe the measured cross sections.Additionally,fusion cross sections of ~(7,9)Be+~(238)U measured in two experiments are applied to constrain model calculations further through three codes,i.e.,HIVAP2,KEWPIE2,and CCFULL.Parameters in these codes are also examined by comparison with measured fusion cross sections.All the comparisons indicate that the KEWPIE2 calculations using the WKB approximation agree well with the measured cross sections of both fusion reactions ~(7,9)Be+~(238)U and the fusion-evaporation reaction ~(238)U (~9Be,5n)~(242)Cm.Calculations using the fusion code CCFULL are also in good agreement with the measured fusion cross sections of ~(7,9)Be+~(238)U.     

Distribution of fusion barriers

Heavy ion fusion cross sections and compound nucleus average spin values obtained from distribution of fusion barriers are discussed. Various shapes of distribution functions are studied using a truncated Gaussian distribution function (TGD). It is shown that fusion cross section and average spin values are less sensitive to different parametrization of TGD function, whereas the second derivative of the product of energy and fusion cross sections (w.r.t. energy), obtained from the corresponding TGD functions are significantly different depending on the shape of the barrier distribution function. It is also shown byχ ² analysis of fusion cross section data that some systems favour a narrow Gaussian distribution function whereas others, for which the vibrational and rotational collective states are less important, favour a flat barrier distribution. A physical interpretation of the dynamical process that gives rise to different barrier distribution is given in the framework of microscopic coupled channel calculations.     

近垒能区32S+90,96Zr势垒分布的研究

精确测量了³²S+^90,96Zr两系统的背角准弹散射激发函数, 总体误差小于1%, 从中分别抽取了它们的势垒分布, 对比观测到³²S+⁹⁶Zr的势垒结构扁平且向低能区展宽, 这种 势垒可导致在垒下能区该体系的熔合截面的大大增强. ³²S+⁹⁶Zr与³²S+⁹⁰Zr相比 存在较强的中子转移反应, 且转移Q值为正. ³²S+⁹⁶Zr势垒的扁平结构可能是中子转移道耦合所致, 这会导致³²S+⁹⁶Zr垒下熔合截面大的增强.     

Barrier distributions derived from quasielastic backscattering of 48Ti, 54Cr, 56Fe, 64Ni, and 70Zn projectiles on a 208Pb target

In order to study the nucleus-nucleus interaction in Pb-based cold fusion, we have measured excitation functions for quasielastic scattering of 48Ti, 54Cr, 56Fe, 64Ni, and 70Zn projectiles on a 208Pb target at backward angles. The barrier distributions were derived from the first derivative of measured quasielastic scattering cross sections relative to the Rutherford scattering cross section. The centroids of the barrier distributions show a deviation from several predicted barrier heights toward the low energy side. The shape of the barrier distributions is well reproduced by the results of a coupled-channel calculation taking account of the coupling effects of two phonon excitations of the quadrupole vibration for the projectiles and of the octupole vibration for the 208Pb target.     

Fusion probability of symmetric heavy,nuclear systems determined from evaporation-residue cross sections

Cross sections were measured for the formation of evaporation residues in ⁴⁸Ca-, ⁸⁶Kr- and ¹²⁴ Sn-induced reactions with Yb, Sb and Zr isotopes. For the nearly symmetric systems, the energy dependence of the fusion probability in central collisions was determined. The fusion probability at the expected fusion barrier as calculated from a one-dimensional heavy-ion potential was found to be reduced by several orders of magnitude. The fusion cross sections increase gradually, and only at energies appreciably above the expected fusion barrier the major part of the cross section of central collisions leads to fusion. The observed hindrance of the fusion process is compared with model predictions.     

Enhanced fusion-evaporation cross sections in neutron-rich 132Sn on 64Ni

Evaporation residue cross sections have been measured with neutron-rich radioactive 132Sn beams on 64Ni in the vicinity of the Coulomb barrier. The average beam intensity was 2 x 10(4) particles per second and the smallest cross section measured was less than 5 mb. Large sub-barrier fusion enhancement was observed. Coupled-channel calculations taking into account inelastic excitation significantly underpredict the measured cross sections below the barrier. The presence of several neutron transfer channels with large positive Q values suggests that multinucleon transfer may play an important role in enhancing the fusion of 132Sn and 64Ni.     

The interaction and fusion of arbitrarily oriented deformed nuclei

The fusion/capture cross sections between various deformed nuclei are calculated. It is shown that quadrupole and hexadecapole deformations of heavy nuclei are important for evaluating the barrier height, capture well depth, and fusion/capture cross sections of heavy nuclei. It is found that calculations of the capture cross section of two heavy deformed nuclei must be performed with averaging over all possible mutual orientations of the colliding nuclei.     

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.     

Angular momentum and cross sections for fusion with weakly bound nuclei: breakup,a coherent effect

Results for the cross section and average angular momentum for complete fusion at energies around the Coulomb barrier are presented for 7Li with 165Ho. Comparison of the cross sections with a one-dimensional barrier penetration model, using a potential consistent with the measured elastic scattering, showed a reduction above the barrier and an enhancement below it. An increase in the measured average angular momentum, , above the barrier and its consistency with that obtained from the fusion excitation function for weakly bound nuclei, is reported. These results together with a reanalysis of existing data conclusively demonstrate that the effect of breakup on fusion is coherent, like coupling to any nonelastic channel.     

Fusion-fission and neutron-evaporation-residue cross-sections in 40Ar- and 50Ti-induced fusion reactions

For the reactions ⁴⁰Ar+ ¹⁶⁵Ho. ¹⁶⁹Tm, ¹⁷⁴Yb. ¹¹⁵Lu, ^176–180Hf, ¹⁸¹Ta, ²⁰⁸Pb and ⁵⁰Ti + ²⁰⁸Pb, ²⁰⁹Bi the cross sections for the fusion-fission process were determined by measuring energy and time-of-flight of the reaction products. In addition, the neutron-evaporation-residue cross sections were measured by using the velocity filter SHIP. A σ versus 1/E analysis of the fusion-fission cross sections is used to determine fusion barriers and fusion radii. The evaporation- residue cross sections are used to extract in an approximate way barriers for compound-nucleus formation. These barriers are found to agree with the fusion barriers determined from the fission cross sections. For all systems investigated the neutron-evaporation-residue cross sections reach their maximum close to the fusion barrier as calculated from the Bass potential.     

用QMD模型研究晕核 11 Be+208Pb的熔合机制

通过用QMD模型研究晕核^11Be ^208Pb的近垒熔合反应,发现晕核引起的熔合反应中,并存着两种相互竞争的机制：一方面当入射晕核^11Be靠近靶核时,由于^11Be是弱束缚体系,与靶核的相互作用可使其很容易破裂或少数核子被靶核俘获形成核子转移反应,从而对于熔合表现出压制;另一方面当^11Be的少数中子进入靶核并与靶核相互作用而使得靶核有些激发,而使局部半径增大,导致熔合势垒降低,熔合截面增强。用QMD模型计算出的熔合截面与实验值基本符合,垒附近表现出增强效应。     

Fusion excitation functions near and below the Coulomb barrier for symmetric and asymmetric medium-mass systems

Fusion excitation functions for the systems ¹²C + ^{46, 48, 50}Ti, ^{28, 30}Si + ³⁰Si and ¹⁸O + ⁴⁴Ca have been determined at energies near and below the Coulomb barrier. Inelastic excitation functions for the targets ^{48, 50}Ti and ⁴⁴Ca have been also measured in the same energy range. The absolute cross sections were obtained by in-beam γ-ray spectroscopy technique using a rotating target. Fusion cross sections ranging in magnitude from ～ 0.3 mb to ～ 1300 mb were determined with an accuracy of 10–20%. The fusion excitation functions are analysed in the frame of a semiclassical barrier-penetration model. From the analysis, the height, the radius and the curvature of the fusion barrier for the different systems are extracted. The fusion cross sections are compared with the calculations performed using different heavy-ion potentials. The enhancement of the cross sections at sub-Coulomb energies can be reproduced with a one-dimensional barrier-penetration model taking into account the zero-point motion of the surface of the reaction partners. The fusion cross section of the system ¹⁸O + ⁴⁴Ca is well reproduced by quantum-mechanical calculations, introducing a new degree of freedom taking into account the formation of a neck during the fusion process.     

Effects of the entrance channel mass asymmetry in fusion reactions

The symmetric and asymmetric fusion reaction systems forming the same compound nuclei 26Al,30Si,38Ar and 170Hf are investigated with the frame of 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,the Coulomb barriers and the fusion cross sections.The calculated fusion cross sections agree quantitatively with the experimental data.The results indicate that compound nucleus formation is favorable for the systems with larger mass asymmetry because of the smaller Coulomb contribution to the fusion barrier.