Influence of entrance channel properties on heavy-ion reaction dynamics

In the fusion of heavy nuclei, there is a distribution of fusion barrier energies resulting from coupling between intrinsic motion and internal degrees of freedom. Precise experimental measurements of excitation functions have allowed the extraction of the distributions by taking the second derivative using a point-difference method. In the case of statically deformed nuclei, experimental data shows that the different fusion barrier energies correspond to different physical configurations of the colliding nuclei, the latter affecting the subsequent dynamical trajectories over the potential energy surface, influencing the ultimate reaction products, as for example in quasi-fission. The fusion barrier distribution is also valuable in understanding the fusion of weakly bound nuclei, enabling a reliable prediction of the expected fusion cross-sections, and thus the determination of fusion suppression factors at above-barrier energies. Received: 1 May 2001 / Accepted: 4 December 2001     

QMD模型的改进及其在低能重离子反应中的应用

丰中子核以及重核熔合机制的研究以及中能重离子碰撞中多重碎裂的研究都迫切需要一个统一的、自洽的微观动力学模型.经过对量子分子动力学模型进行根本的改进,发展了一个新的、适用于低能以及中能重离子反应的统一描述的微观动力学模型.改进的量子分子动力学(ImQMD)模型能够将整个熔合反应过程中的动力学效应、同位旋效应以及弹靶质量不对称效应等比较全面地、自洽地考虑进来,从而给熔合反应的研究提供了一个新的途径.ImQMD模型能够很好地再现一系列核的基态性质以及10多个熔合反应的激发函数(包括丰中子核熔合体系以及实验最新测量的132Sn+64Ni熔合体系).此外还运用该模型初步探索了重核熔合过程中复合体系的寿命与体系的入射能量、体系大小以及体系的中子质子比的依赖关系. We have developed a new microscopic dynamical model called improved quantum molecular dynamical model (ImQMD). This model can describe the fusion process at energies near the Coulomb barrier as well as the multifragmentation process at intermediate energies in heavy-ion collision (HIC) uniformly. By using this model, fusion cross sections (including some of neutron-rich nuclei reactions and that of newly measured~(132)Sn+~(64)Ni fusion reaction) of tens reactions can be reproduced remarkably well. In fusi...     

Heavy ion reactions around the Coulomb barrier

The angular distributions of fission fragments for the 32S+184W reaction near Coulomb barrier energies are measured. The ex perimental fission excitation function is obtained. The measured fission cross sections are decomposed into fusion-fission, quasi-fission and fast fission contributions by the dinuclear system (DNS) model. The hindrance to completing fusion both at small and large collision energies is explained. The fusion excitation functions of 32S+90,96Zr in an energy range from above to below the ...     

On the focussing effect and the large energy loss in the quasi-fission reaction

A classical dynamical model is applied to the deep inelastic reactions between heavy ions. Assuming that the range of the nuclear interaction depends on the intrinsic excitation energies, the sharp angular distribution and the large energy loss in the quasi-fission reaction are explained systematically.     

Sub-barrier fusion excitation function data and energy dependent Woods–Saxon potential

This paper analyzed the role of intrinsic degrees of freedom of colliding nuclei in the enhancement of sub-barrier fusion cross-section data of various heavy ion fusion reactions. The influences of inelastic surface vibrations of colliding pairs are found to be dominant and their couplings result in the significantly larger fusion enhancement over the predictions of the one dimensional barrier penetration model at sub-barrier energies. The theoretical calculations are performed by using energy dependent Woods–Saxon potential model (EDWSP model) in conjunction with the one dimensional Wong formula. The effects of dominant intrinsic channels are entertained within framework of the coupled channel calculations obtained by using the code CCFULL. It is quite interesting to note that the energy dependence in Woods–Saxon potential simulates the effects of inelastic surface vibrational states of reactants wherein significantly larger value of diffuseness parameter ranging from a = 0.85fm to a = 0.95fm is required to address the observed fusion excitation function data of the various heavy ion fusion reactions.     

Special features of nuclear reactions induced by loosely bound <Superscript>6</Superscript>He and <Superscript>6,7</Superscript>Li nuclei in the vicinity of the Coulomb barrier height

Excitation functions are measured for complete-fusion and transfer reactions induced by the interaction of ⁶He and ⁶Li with ²⁰⁶Pb, ²⁰⁹Bi, and Pt. Data obtained for fusion reactions induced by ⁶He ions deviate from the predictions of the statistical model of compound-nucleus decay at projectile energies in the vicinity of the Coulomb barrier height. A strong enhancement of cross sections for fusion reactions induced by the interaction of ⁶He with target nuclei is observed. The cross sections for reactions of cluster transfer, neutron transfer from ⁶He, and deuteron transfer from ⁶Li at deep-subbarrier energies are also found to be enhanced. These results are discussed from the point of view of the effect of the cluster structure of nuclei on the interaction probability at energies in the vicinity of the Coulomb barrier height.     

Synthesis of superheavy elements and the process of complete fusion of massive nuclei

The development of various approaches to describing the complete fusion of nuclei and their connections with experimental studies is discussed. A brief account of the dinuclear-system concept (DNSC), the approach proposed at Dubna, is given. The DNSC revealed two important features of the complete fusion of massive nuclei: the existence of the inner fusion barrier B _fus ^* and the competition between complete fusion and quasifission channels in a dinuclear system formed at the capture stage. The DNSC was applied to the analysis of reactions used to synthesize superheavy elements (SHE). The DNSC provided a basis for the models of competition between complete-fusion and quasifission channels. Using these models, one can describe the cross section for SHE production in cold-and warm-fusion reactions.     

The energy dependence of fusion in the 9Be+28Si system

The angular distributions of the energy spectra of the light charged particles (p, d and α) from the ⁹Be + ²⁸Si reaction have been measured in the energy range 12 ≦ E_lab ≦ 30 MeV. The particle evaporation spectra and the angular distributions were analyzed with a spin dependent statistical model. Angular distributions of ⁹Be ions elastically scattered on ²⁸Si have been measured at the energies 12 MeV, 17 MeV, 23 MeV and 30 MeV and were analysed, together with previously measured cross sections, with the optical model. The fusion cut-off angular momentum l_fus(E), the fusion cross section σ_fus(E) and the ratio σ_fus/σ_R^OM(E) were deduced. The excitation function for fusion was analyzed with the Glas and Mosel model. The parameters obtained from the fusion excitation function were compared with the corresponding ones from the ⁹Be + ²⁸Si optical-model interaction potential.     

The sub-barrier fusion of40Ar with144,148,154Sm

The cross sections for production of evaporation residues (σ _er) and for fusion-fission (σ _ff) have been measured for⁴⁰Ar+^{144, 148, 154}Sm at sub-barrier energies by observation of x-ray emission from radioactive products and by direct,ΔE?E identification of fission fragments, respectively. These isotopes span the transition region from spherical (¹⁴⁴Sm) to strongly deformed (¹⁵⁴Sm) equilibrium shapes. The cross section for fusion,σ _fus=σ _er+σ _ff, is found to vary markedly at low energies with the isotope number and, hence, with the quadrupole collectivity of the target. The thresholds for fusion of¹⁴⁸Sm and¹⁴⁴Sm are, respectively, ～3.5 MeV and ～7 MeV (c.m.) higher than for fusion with¹⁵⁴Sm. These differences and the energy dependence of the fusion cross sections are discussed in terms of the effect of nuclear deformation on heavy-ion fusion. A comparative analysis of results for¹⁶O+Sm and⁴⁰Ar+Sm in terms of static deformation indicates thatσ _fus for the Ar+Sm system at very low energies is enhanced relative to the prediction for a one-dimensional barrier based on a fit toσ _fus for¹⁶O+Sm. This may be an indication that additional degrees of freedom (such as formation of a neck or fragment elongation) may be important for fusion with the larger projectile. At energies above the fusion barrier, values ofσ _fus for^{144, 148}Sm are nearly equal, but are significantly smaller than for¹⁵⁴Sm. This is in contrast to the results of previous experiments with¹⁶O projectiles in whichσ _fus (¹⁶O+¹⁴⁸Sm) andσ _fus (¹⁶O+¹⁵⁴Sm) were nearly equal above the barrier. These differences, observed for^{144, 148}Sm and¹⁵⁴Sm at energies above the barrier may reflect a new mechanism which is not encompassed by a static theory.     

Synthesis of heavy and superheavy elements by reactions of massive nuclei

By comparing theoretical and experimental excitation functions of evaporation residues resulting from the same compound nucleus or heavy and superheavy nuclei, it is possible to understand the effect of the entrance channel and the shell structure of reacting nuclei on the fusion mechanism. The competition of complete fusion with the quasifission process is strongly related to the intrinsic fusion barrier B _fus ^* and the quasifission barrier B _qf as well as the size of the well in the nucleus-nucleus potential. In our calculations of the excitation functions for capture, fusion, and evaporation residues, we use the relevant variables such as mass asymmetry of nuclei in the entrance channel, potential energy surface, driving potential, spin distribution, and surviving probability of compound nucleus that are responsible for the mechanism of the fusion-fission process. As a result, we obtain a beam energy window for the capture of the nuclei before the system fuses and the Γ_n/Γ_f ratio at each step along the deexcitation cascade of the compound nucleus. Calculations performed in the framework of the model taking into account the nuclear shell effect and shape of colliding nuclei allow us to reach useful conclusions about the mechanism of the fusion-fission process and the production of the evaporation residues. We analyze the ⁴⁰Ar + ¹⁷⁶Hf, ⁸⁶Kr + ¹³⁰Xe, and ¹²⁴Sn + ⁹²Zr reactions leading to ²¹⁶Th*; the ³²S + ¹⁸²W and ⁶⁰Ni + ¹⁵⁴Sm reactions leading to ²¹⁴Th*; the ⁴⁸Ca + ²⁴⁸Cm reaction leading to the ²⁹⁶116 compound nucleus; and the ⁴⁸Ca + ²⁴⁹Cf reaction leading to the ²⁹⁷118 compound nucleus.     

A study of γ-decay modes from high angular momentum nuclear states by high order multiplicity measurements

Reactions between ¹⁸O and ¹⁶O ions, with energies well above the Coulomb barrier, and ^{148, 150}Nd target nuclei were used to study the cascades of γ-rays in the residual nuclei ^{161, 162}Er. A multi-counter setup was used in which the γ-rays were detected by a Ge(Li) counter coupled in coincidence with up to 9 NaI(Tl) counters. The γ-multiplicity has been studied for γ-rays cascading through states above and along the yrast line. Higher moments of the multiplicity distributions (shape parameters) were deduced from the data. These moments allow the construction of the spin distribution for the entry states. The difference between these spin distributions from reactions induced by ¹⁶O and ¹⁸O ions was studied. Also the fusion cross section was measured for the two systems as a function of bombarding energy and compared to the multiplicity results at two different excitation energies (E_x = 49.5 and 56.2 MeV). A subtraction technique has been applied in the data analysis with the intention to study the decay of a selected part of the high-spin region, and the results show besides the 4n channel an unexpected large contribution of the 5n channel from this region. The sidefeeding patterns of the multiplicity distributions are extracted and show a significant difference for the ¹⁶O and ¹⁸O induced reactions, especially at the lowest bombarding energies. The results are compared with statistical model calculations.     

Fusion, resonances and scattering in12C+12C reaction

The variation of fusion cross-section (σJ_fus) with energy in the¹²C+¹²C collision is linked to the underlying resonance phenomenon through the behavior of reaction cross-section (σ) of which σ_fus is taken as a part. The calculation of σ_fus is done through an energy-dependent imaginary potential in the optical model potential (OMP). Through dispersion relation, such an imaginary potential gives rise to energy-dependent real potential which is incorporated in the OMP. In our calculation, a form of potential for the nuclear part which has a soft repulsive in-built core is introduced based on similar works done earlier. The calculated results of σ_fus are used to explain the oscillatory structure, astrophysical S-factor and the decreasing trend at higher energies of the experimental σ_fus data in the case of¹²C+¹²C system with remarkable success. The potential used for fusion calculation is tested for fitting elastic scattering data at some energies and is found good in forward angles. Further improvement of the fitting of these data is obtained by incorporating a coupling potential in the surface region. About twenty resonances are observed in our calculation in the specific partial waves and some of them are found close to the experimentally identified resonances in¹²C+¹²C reaction. Thus, we provide an integrated and comprehensive analysis of fusion, resonance and scattering data in the best studied case of¹²C+¹²C reaction within the framework of optical potential model.     

Analytical calculation of fusion cross-sections

We analyse the fusion cross-sections, calculated by using two different analytical parameterisations and compare them with the experimental data. Both the parameterisations are based on ion-ion potentials calculated within the framework of Skyrme energy density formalism. In the first case, the ion-ion potential (including the spin-density term) was parameterised and then, by adding the Coulomb potential, one could compute the fusion barrier analytically. In the second case, the calculated fusion barrier heights and positions were parameterised directly. Both of these (previously) reported parameterisations are used here to calculate the fusion barriers and fusion excitation functions for more than 50 reactions belonging to the s-d and f-shell nuclei. A detailed comparison of these parametrisations with the experimental and several other theoretical results shows that both of these parameterisations are able to reproduce the experimental data equally well. As the (second) direct parameterisation depends only on the charges and masses of colliding nuclei, it is very useful for predicting/ understanding the fusion process in low energy heavy-ion reactions. Received: 24 February 1999 / Accepted: 16 March 2000     

Decay time characteristics of the U-like excited nuclei

The unified energy dependence of the induced fission times obtained by the crystal blocking technique for heavy nuclei with Z=91–94 in the range of initial excitation energy from 5 to 250 MeV was analyzed. It was demonstrated that, for excitation energies of the investigated heavy fissionable nuclei up to 60–70 MeV, the fission times can be described in the framework of the statistical theory of nuclear reactions taking into account the double-humped structure of the fission barrier and the lifetimes of both classes of excited nuclear states realized in the first and second potential wells. However, for excitation energies above 70 MeV, there is a need to consider the dynamical effects in the fission channel.     

Fusability and fissionability in 86Kr-induced reactions near and below the fusion barrier

Evaporation-residue excitation functions for the reactions ⁸⁶Kr + ^70,76Ge, ^92,100 Mo, ^99,102,104 Ru have been measured using activation methods and the velocity filter SHIP. The data span the region from well below the fusion barrier up to, and beyond, the energy where limitation by fission competition takes place. The data are shown to be compatible with the concept of complete fusion followed by the statistical decay of the equilibrated compound nucleus. Information on both the fusion probability at and below the fusion threshold and the fissionability of the compound nuclei formed, is extracted. The model dependence of the extracted fission barriers is discussed in detail. In analogy to studies involving lighter projectiles, strong correlations between the low-energy nuclear-structure properties of the nuclei and the subbarrier fusion probability are found. A relative shift of the fusion barrier to higher energies, that increases with the number of valence neutrons in the target nuclei, is observed.     

Heavy ion reactions around the Coulomb barrier

The angular distributions of fission fragments for the ³²S+¹⁸⁴W reaction near Coulomb barrier energies are measured. The experimental fission excitation function is obtained. The measured fission cross sections are decomposed into fusion-fission, quasi-fission and fast fission contributions by the dinuclear system (DNS) model. The hindrance to completing fusion both at small and large collision energies is explained. The fusion excitation functions of ³²S+^90,96Zr in an energy range from above to below the Coulomb barrier are measured and analyzed within a semi-classical model. The obvious effect of positive Q-value multi-neutron transfers on the sub-barrier fusion enhancement is observed in the ³²S+⁹⁶Zr system. In addition, the excitation functions of quasi-elastic scattering at a backward angle have been measured with high precision for the systems of ¹⁶O + ²⁰⁸Pb, ¹⁹⁶Pt, ¹⁸⁴W, and ^154,152Sm at energies well below the Coulomb barrier. Considering the deformed coupling effects, the extracted diffuseness parameters are close to the values extracted from the systematic analysis of elastic and inelastic scattering data. The elastic scattering angular distribution of ¹⁷F+¹²C at 60 MeV is measured and calculated by using the continuum-discretized coupled-channels (CDCC) approach. It is found that the diffuseness parameter of the real part of core-target potential has to be increased by 20% to reproduce the experimental result, which corresponds to an increment of potential depth at the surface region. The breakup cross section and the coupling between breakup and elastic scattering are small.     

Dynamical decay process of <Superscript>219, 220</Superscript>Ra<Superscript>*</Superscript> formed in <Superscript>10, 11</Superscript>B + <Superscript>209</Superscript>Bi reactions

The excitation functions for both the evaporation residue and fission have been calculated for ¹⁰B + ²⁰⁹Bi and ¹¹B + ²⁰⁹Bi reactions forming compound systems ^{219, 220}Ra^* , using the dynamical cluster-decay model (DCM) with effects of deformations and orientations of the nuclei included in it. In addition to this, the excitation functions for complete fusion (CF) are obtained by summing the fission cross-sections, neutron evaporation and charged particle evaporation residue cross-sections produced through the axn\ensuremath \alpha xn and pxn\ensuremath pxn (x = 2, 3, 4) emission channels for the ²¹⁹Ra system at various incident centre-of-mass energies. Experimentally the CF cross-sections are suppressed and the observed suppression is attributed to the low binding energy of ^{10, 11}B which breaks up into charged fragments. The reported complete fusion (CF) and incomplete fusion (ICF) excitation functions for the ²¹⁹Ra system are found to be nicely fitted by the calculations performed in the framework of DCM, without invoking a significant contribution from quasi-fission. Although DCM has been applied for a number of compound nucleus decay studies in the recent past, the same is being used here in reference to ICF and subsequent decay processes along with the CF process. Interestingly the main contribution to complete fusion cross-section comes from the fission cross-section at higher incident energies, which in DCM is found to consist of an asymmetric fission window, shown to arise due to the deformation and orientation effects of formation and decay fragments.     

A systematic study of the fission and evaporation residue excitation functions in complete fusion reactions with weakly bound stable nuclei

We carry out a systematic study on the fusion-fission and evaporation residue excitation functions for the reactions of ^6,7Li, ⁹Be, ^10,11B + ²⁰⁹Bi and ^6,9Li, ⁹Be + ²⁰⁸Pb, in which the projectiles are loosely bound and have low threshold energies against breakup. The fusion cross sections are calculated by the coupled-channel model. The compound nuclei decay are analyzed with the standard statistical model. The fission and evaporation residue excitation functions are well reproduced by our calculations, proving the validity of the standard statistical model in describing the compound nuclei decay in these characteristic reactions. For the compound nuclei with A=215-220 and Z=86-88, the liquid drop fission barriers need to be scaled by 0.80-1.02 to reproduce the experimental data. And a decreasing trend of the scaling factor with increasing fissionability parameter Z²/(50A) is found.