Investigation of the fusion of heavy nearly symmetric systems

Excitation functions in the vicinity of the Coulomb barrier have been measured for the formation of evaporation residues in¹⁰⁰Mo-induced fusion reactions with^{90, 92, 96}Zr,^{92, 96, 98, 100}Mo,¹⁰⁴Ru and¹¹⁰Pd as well as for the system⁹⁶Zr+⁹⁶Zr. From these data the fusion probability in central collisions was extracted covering a range of 4 orders of magnitude. At the fusion barriers expected from systematics we find that the fusion probability is suppressed by one to three orders of magnitude. It is rising very gradually at higher energies and reaches for the heaviest systems saturation only at energies as high as 30 MeV above the barrier. The observed hindrance of the fusion process increases roughly with the growing Coulomb repulsion between the collision partners, but there is also a distinct influence of their individual nuclear structure. The data are compared to the extra-push model, the surface-friction model and the diabatic fusion model. A parameterisation of the extra-push energy and its fluctuation in terms of a macroscopic quantity like the Coulomb repulsion combined with a microscopic quantity characterizing the nuclear structure is proposed. As a byproduct of this work a new alpha emitter,¹⁹¹Po, could be identified. Its half-life is (15.5 _–2.5 ⁺⁶ ) ms, the alpha energy is (7314±20) keV.     

Dynamic Model Study of Fusion Reactions for 40,48Ca+90,96Zr

Based on the Improved Quantum Molecular Dynamics Model the fusion reactions of ^40,48Ca+^90,96Zr are studied by making a more rigorous treatment of the initial condition. The study shows that:(1) the calculated fusion cross sections for all four reactions of ^40,48Ca+^90,96Zr are in good agreement with experiment data; (2) the sub-barrier fusion for the neutron-rich reaction ⁴⁰Ca+⁹⁶Zr is ubstantially enhanced as compared with the other three reactions. In order to understand the reason why the sub-barrier fusion of the neutron-rich reaction ⁴⁰Ca+⁹⁶Zr is enhanced as compared with the non-neutron-rich reaction ⁴⁰Ca+⁹⁶Zr and that of the neutron-rich reaction ⁴⁸Ca+⁹⁶Zr is not enhanced, the further investigations are carried out, those are: the dynamic fusion barriers for four reactions, the relation between dynamic fusion barrier and nucleon transfer and the relation between nucleon transfer and corresponding reaction Q value. It has been found that positive Q value leads to the strong nucleon transfer which reduces the dynamic fusion barrier and enhances the sub-barrier fusion cross section.     

40,48Ca+90,96Zr融合反应的动力学模型研究

应用改进的量子分子动力学模型,在严格挑选初始核考虑弹靶结构效应的基础上,研究了近垒和垒上融合反应^40,48Ca+^90,96Zr. 研究表明: 4个反应的理论计算截面与实验值很好符合; 丰中子反应⁴⁰Ca+⁹⁶Zr的垒下融合截面比其他3个反应有明显增强的现象.为了理解丰中子反应⁴⁰Ca+⁹⁶Zr与⁴⁰Ca+⁹⁰Zr相比垒下融合截面增强,而Ca+⁹⁶Zr垒下融合截面没有明显增强的原因, 进一步分析了484个反应的融合位垒,中子转移与融合位垒的关系、中子转移与Q值的关系,结果表明: 正反应Q值会引起核子(特别是中子)转移的增强,从而导致动力学融合位垒的下降和垒下融合截面增强.     

The influence of Isospin Dependence of In-Medium NN Cross Sections on the Ratio of Emitted Neutrons to Protons in HICs

The influence of isospin dependence of in-medium nucleon-nucleon cross sections on the nip ratios for emitted nucleons in reactions 96Zr-j-96Zr and 96Ru-j-96RH at Eb z 400 AMeV is investigated by means of an improved quantum molecular dynamics model. Our results show that the high energy part of the spectra of the n//p ratios for emitted nucleons is sensitive to the isospin dependence of in-medium nucleon-nucleon cross sections for neutron-rich reaction systems. Therefore, we propose that the nip ratio of emitted high energy nucleons in a very neutron-rich reaction system at several hundreds of AMeV can be taken as sensitive observables to constrain the isospindependence of in-medium nucleon-nucleon cross sections.     

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.     

Dynamics of low-energy heavy-ion fusion

Preliminary data on the fusion of ³⁶S+⁹⁶Zr are reported; the excitation function near the barrier is intermediate between those of ⁴⁰Ca+^90,96Zr. The peculiar role of the strong 3⁻ octupole vibration of ⁹⁶Zr is pointed out, in addition to the couplings to neutron transfer channels with positive Q-values. Recent data on ⁴⁰Ca+¹²⁴Sn are also shown; for that system the fusion barrier distribution is wide without separated peaks, similar to the case of ⁴⁰Ca+⁹⁶Zr. Simplified coupled-channel calculations have been performed, including surface vibrations and sequential neutron pick-up channels, with form factors that fit the single- and multi-nucleon transfer data for ⁴⁰Ca+¹²⁴Sn. A good agreement with the data is found.     

Microscopic calculation of 58,64Ni + 124,132Sn sub-barrier fusion

The fusion cross-sections of ^58,64Ni + ^124,132Sn are investigated through a coupled-channel approach using a density- and energy-dependent effective Brueckner G-matrix interaction. Microscopic Skyrme-Hartree-Fock proton and neutron density distributions are used in the calculations. A good agreement with the experimental data of the fusion cross-sections of these neutron-rich systems has been obtained, which favors the present microscopic approach for calculating the interaction potentials and fusion cross-sections.     

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.     

Theoretical study of fusion reactions 32S + 94,96Zr and 40Ca + 94,96Zr and quadrupole deformation of 94Zr

The dynamic coupling effects on fusion cross sections for reactions~(32)S + ~(94,96)Zr and ~(40)Ca + ~(94,96)Zr are studied with the universal fusion function formalism and an empirical coupled channel(ECC) model. An examination of the reduced fusion functions shows that the total effect of couplings to inelastic excitations and neutron transfer channels on fusion in ~(32)S +~(94)Zr(~(40)Ca +~(94)Zr) is almost the same as that in ~(32)S +~(96)Zr(~(40)Ca +~(96)Zr). The enhancements of the fusion cross section at sub-barrier energies due to inelastic channel coupling and neutron transfer channel coupling are evaluated separately by using the ECC model. The results show that effect of couplings to inelastic excitations channels in the reactions with94 Zr as target should be similar as that in the reactions with ~(96) Zr as target. This implies that the quadrupole deformation parameters β_2of ~(94)Zr and~(96) Zr should be similar to each other.However, β_2 's predicted from the finite-range droplet model, which are used in the ECC model, are quite different. Experiments on~(48) Ca +~(94)Zr or~(36) S +~(94)Zr are suggested to solve the puzzling issue concerning β_2for~(94)Zr.     

Light ion fusion in deformation model

Experiments with heavy ions at moderate energies show the importance of deformation in heavy ion collisions. A deformation model which takes deformation dynamically into account is developed. Having described fusion and deep inelastic collision for a very heavy system (Xe + Bi) and a medium heavy system (Ar + Th) at various energies successfully, we turn to some comparatively lighter heavy ions where fusion is the most dominant feature. Fusion cross-sections for six pairs of lighter systems (³⁵Cl +¹¹⁶Sn,⁵⁸Ni+⁶²Ni,³⁵Cl+⁶²Ni,³²S+²⁴Mg,²⁴Mg+²⁴Mg and¹²C+²⁷Al) have been obtained using our deformation model which agree well with experiment. The two-slope-behaviour of fusion excitation function which is an important feature of light ion fusion systematics is also obtained, in our model calculations for all the systems studied.     

A theoretical description of energy spectra and two-neutron separation energies for neutron-rich zirconium isotopes

Very recently the atomic masses of neutron-rich Zr isotopes, from ⁹⁶Zr to ¹⁰⁴Zr, have been measured with high precision. Using a schematic Interacting Boson Model (IBM) Hamiltonian, the evolution from spherical to deformed shapes along the chain of Zr isotopes, describing at the same time the excitation energies as well as the two-neutron separation energies, can be rather well reproduced. The interplay between phase transitions and configuration mixing of intruder excitations in this mass region is succinctly addressed.     

Traces of Landau-Zener transitions in the fusion cross section of heavy nuclei?

Nucleus-nucleus collisions with center-of-mass energies E_c.m. close to the Coulomb barrier are investigated within the framework of time-dependent two-center shell-model states. The influence of Landau-Zener transitions on the nucleus-nucleus potential is studied in detail as a function of E_c.m. Dynamical barrier shifts and barrier fluctuations are evaluated for central collisions of ⁹⁰Zr + ⁹⁰Zr, ⁹²Zr + ⁹²Zr, ⁹⁶Zr + ⁹⁶Zr and their effect on the fusion probability is discussed explicitly. While for ⁹⁰Zr + ⁹⁰Zr no modification of the barrier penetration is found a relative enhancement (reduction) of the fusion probability up to a factor of 4 is obtained for ⁹²Zr + ⁹²Zr and⁹⁶Zr + ⁹⁶Zr.     

Theory of fusion for superheavy elements

A new model is proposed for fusion mechanisms of massive nuclear systems, where so-called fusion hindrance exists. The model describes the whole process in two steps: two-body collision processes in an approaching phase and shape evolutions of an amalgamated system into the compound nucleus formation. It is applied to ⁴⁸Ca-induced reactions and is found to reproduce the experimental fusion cross sections extremely well, without any free parameter. A schematic case is solved in an analytic way, the results of which shed light on fusion mechanisms. Combined with statistical decay theory, residue cross sections for superheavy elements can be readily calculated. Examples are given.     

The barrier for compound-nucleus formation in the nearly symmetric systems86Kr+123Sb→209Fr and124Sn +94Zr→218Th

Evaporation residues from the fusion of the nearly symmetric systems⁸⁶Kr+¹²³Sb and¹²⁴Sn+⁹⁴Zr have been detected. The compound nucleus²¹⁸Th could be produced with an excitation energy as low as 21 MeV. The barriers for the formation of a compound nucleus were deduced from the evaporation residue cross sections. There is no evidence for an additional amount of energy needed to fuse these systems, if compared with the extrapolation of fusion barrier systematics or with results of fusion model calculations not including friction phenomena. One of the systems reaches a value ofZ ₁·Z ₂=2,000, about the highest value where evaporation residues have ever been observed.     

Isospin effects on squeeze-out flow in heavy-ion collisions

The squeeze-out flow in reactions of ¹²⁴Sn + ¹²⁴Sn and ¹²⁴Ba + ¹²⁴Ba at different incident energies for different impact parameters is investigated by means of an isospin-dependent quantum molecular dynamics model. For the first time, it is found that the more neutron-rich system (¹²⁴Sn + ¹²⁴Sn) exhibits weaker squeeze-out flow. This isospin dependence of the squeeze-out flow is shown to mainly result from the isospin dependence of nucleon-nucleon cross-section and the symmetry energy. Received: 14 March 2000 / Accepted: 29 September 2000     

Transfer reactions and sub-barrier fusion in 40Ca + 90, 96Zr

The two systems ⁴⁰Ca + ^90,96Zr have been studied by measuring nucleon transfer reactions at two energies near the Coulomb barrier, thus complementing the available sub-barrier fusion cross-sections. Angular distributions for various transfer channels have been determined. Significantly larger neutron transfer cross-sections are found for the target ⁹⁶Zr that exhibits the larger enhancement in the sub-barrier fusion cross-sections. All data have been analyzed with a new model for heavy-ion collisions that calculates simultaneously transfer cross-sections, fusion excitation functions and barrier distributions. The model gives a good account of both transfer and fusion data. Received: 2 May 2002 / Accepted: 4 June 2002 / Published online: 26 November 2002 RID="a" ID="a"e-mail: montagnoli@pd.infn.it, Fax +39049 8277102, Tel. +39049 8277117. RID="b" ID="b"On leave from the China Institute for Atomic Energy, 102413 Beijing, China. Communicated by C. Signorini     

Measurements of proton radiative capture cross sections relevant to the astrophysical rp- and γ-processes

Measurements have been made of the ⁹⁶Zr(p,γ)⁹⁷Nb, ¹¹²Sn(p,γ)¹¹³Sb, and ¹¹⁹Sn(p,γ)¹²⁰Sb cross section excitation functions. Incident proton energies ranged from 2.8 MeV to 8.5 MeV. These reactions are relevant to several processes of stellar nucleosynthesis. The resulting astrophysical S-factors are compared to those from theoretical statistical model calculations using the SMOKER, and the more recent NON-SMOKER, codes to judge their applicability to these reactions.     

Gas-cell-based setup for the production and study of neutron rich heavy nuclei

The present limits of the upper part of the nuclear map are very close to stability while the unexplored area of heavy neutron-rich nuclides along the neutron closed shell N = 126 is extremely important for nuclear astrophysics investigations and, in particular, for the understanding of the r-process of astrophysical nucleosynthesis. This area of the nuclear map can be reached neither in fusion–fission reactions nor in fragmentation processes widely used nowadays for the production of exotic nuclei. A new way was recently proposed for the production of these nuclei via low-energy multi-nucleon transfer reactions. The estimated yields of neutron-rich nuclei are found to be significantly high in such reactions and several tens of new nuclides can be produced, for example, in the near-barrier collision of ¹³⁶Xe with ²⁰⁸Pb. A new setup is proposed to produce and study heavy neutron-rich nuclei located along the neutron closed shell N = 126.     

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 ...     

同位旋效应对中能重离子反应中轻粒子产物的影响

利用同位旋相关的量子分子动力学模型,研究了¹¹²Sn+¹¹²Sn和¹²⁴Sn+¹²⁴Sn两反应系统在不同入射能量、不同碰撞参数、不同势场和不同核子-核子碰撞截面下的粒子发射特征.阐述了发射体系的同位旋对轻粒子产额比的影响.发现轻粒子产额比是同位旋的敏感观测量.另外,还发现中快度区发射的粒子有更高的丰中子程度.同时,轻粒子的比不敏感于核子核子碰撞截面,而敏感于核态方程,这使得从轻粒子比提取同位旋相关的核态方程变成一种可能. 关键词： 同位旋相关的量子分子动力学 同位旋效应 轻粒子产额比