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.     

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.     

Near-barrier quasi-elastic cross sections and barrier distribution of 32S+90,96Zr

Quasi-elastic cross sections have been measured for ³²S+^90,96Zr with high accuracy near the Coulomb barrier at backward angles and the barrier distributions are extracted from them. We find that barrier distribution of ³²S+⁹⁶Zr is flat and extends to low energies. The sub-barrier fusion cross sections are strongly enhanced because of such barrier distribution. Compared with the reaction of ³²S+⁹⁰Zr, ³²S+⁹⁶Zr has stronger neutron transfers up to the six-neutron pickup, which is due to the positive Q values of neutron transfers in the latter. This indicates that the neutron transfer may play a role in the enhancement of sub-barrier fusion for ³²S+⁹⁶Zr.     

Hindrance of fusion in central collisions of heavy,symmetric nuclear systems

The energy dependence of the fusion probabilities for central collisions of the systems¹²⁴Sn +^92,94,96Zr and⁸⁶Kr +¹²³Sb was determined from neutron-evaporation-residue cross sections. Near the barrier as calculated from one-dimensional barrier-penetration models, the fusion probability was found to be reduced by several orders of magnitude.     

Production cross sections for the heaviest nuclei in complete fusion reactions induced by heavy ions

Production of the heaviest nuclei in complete fusion reactions induced by heavy ions has been considered in a systematic way in the framework of the conventional barrier passing model coupled with the statistical model. Available data on excitation functions for fission and production of evaporation residues (ER) in very asymmetric combinations induced by ions lighter than Ne on actinide target nuclei are described rather well in the framework of these models. The data allow one to adjust model parameters and to reveal the quasi-fission effect caused by the interaction with deformed target nuclei, which is manifested in the suppression of the ER production at sub-barrier energies. For reactions induced by Mg and heavier projectiles, quasi-fission is starting to suppress fusion (ER production) at energies above the Coulomb barrier. One has to introduce empirically the quantity of the fusion probability P_fus to reproduce the ER excitation functions in the framework of the conventional approach. The exponential dependence of P_fus on the combined fissility parameter (a similar parameter that was introduced for the extra-push energy scaling) was found in search for scaling for the P_fus values resulting from the data analysis.     

Comparison of sub-coulomb stripping and analog resonance results in Zr

The ⁹²Zr(d, p)⁹³Zr reaction, leading to states in ⁹³Zr which are parents of analog states observed in ⁹²Zr(p, p) elastic scattering, has been studied for incident deuteron energies below the Coulomb barrier. For each of the parent states the reduced normalization has been extracted, and these have been compared with the reduced normalizations calculated for the analog resonances on the basis of various analog resonance theories.     

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.     

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     

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.     

Heavy-ion fusion at low energies

Through precision measurements of fusion cross sections at energies close to the Coulomb barrier and through the application of the method of “experimental barrier distributions” which these permit, many recent advances have been made in our understanding of the dynamical processes occurring during a heavy-ion collision. It is now clear that the target and projectile reach one another in superpositions of states which correspond to different orientations for rotational nuclei or to different induced deformations for vibrational nuclei. The creation of a neck of neutron matter has also long been postulated and by studying the isotopic dependence of the fusion reaction, some recent results in the ¹⁰Ca+^90,96Zr systems appear to confirm this result. For large Z ₁ Z ₂ a type of extra-push effect can arise from the same inelastic entrance-channel effects which enhance the fusion of lighter systems, though this will be absent in cases where the enhancement arises from neutron transfers. The existence of different barriers will of course influence all other reaction channels. Fusion simply allows one to visualise the barriers most easily, since for this process, the total cross section is an incoherent sum of the contributions from all relevant eigenchannels. Some effects in other channels have already been observed. Other possible effects will be discussed. These include; the exploitation of the lowest-energy barrier to produce exotic evaporation residues and strongly deformed high-spin states at low excitation energy.     

Neutron transfers and collective excitations at frontal and grazing low-energy collisions of heavy ions

Semi-classical models have been used to investigate the evolution of the wave functions of external neutrons and rotation of a deformed ¹⁵⁴Sm nucleus upon collision with a spherical ¹⁶O nucleus with energies near the Coulomb barrier. The probabilities of neutron transfers in the ⁴⁰Ca + ⁹⁶Zr reaction are determined.     

Fusion using radioactive ion beams

The capture-fission cross-section is measured for the collision of the massive nucleus ¹³²Sn with ⁹⁶Zr at near-barrier energies and compared with the collision of ¹²⁴Sn with ⁹⁶Zr. This study gives insight into fusion enhancement and hindrance in systems involving neutron-rich nuclei. The dinuclear system model (DNS) calculations describe the excitation function reasonably well and if we use the barrier heights predicted by this model we can conclude that fusion hindrance (represented by extra push energy) is greater for the more neutron-rich systems.     

A new scenario for the application of very intense lasers to nuclear fusion

The ponderomotive motion of a charged particle inside a Terawatt-Petawatt laser pulse is studied. Based on a very simple classical model to account for the Coulomb repulsion, the possibility of nuclear collisions in the keV-MeV range is shown. Also, a simple analytical expression for the minimum internuclear distance is given. Since this range of energies is significant to trigger nuclear fusion reactions, this may result in an alternative approach to controlled fusion based on a non-thermalized plasma. The proposed system works for the deuterontriton fusion reaction, but is more appropriate for other reactions like the proton-⁷Li reaction, and also like the ecologically clean, boron-¹¹B reaction.     

Formation and application of correlated states in nonstationary systems at low energies of interacting particles

We consider prerequisites and investigate some optimal methods for the formation of a correlated coherent state of interacting particles in nonstationary systems. We study the influence of the degree of particle correlation on the probability of their passage through the Coulomb barrier for the realization of nuclear reactions at low energies. For such processes, the tunneling probability and, accordingly, the probability of nuclear reactions can grow by many orders of magnitude (in particular, the barrier transparency increases from D _{r = 0} ≈ 10⁻⁴² for an uncorrelated state to D _{|r| = 0.98} ≈ 0.1 at a correlation coefficient |r| ≈ 0.98). The formation of a correlated particle state is considered in detail for different types of monotonic decrease in the frequency of a harmonic oscillator with the particle located in its parabolic field. For the first time, we have considered the peculiarities and investigated the efficiency of the creation of a correlated state under a periodic action on a harmonic oscillator. This method is shown to lead to rapid formation of a strongly correlated particle state that provides an almost complete clearing of the potential barrier even for a narrow range of oscillator frequency variations.     

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.     

Elastic and inelastic scattering of 58Ni +90,94Zr

Pure elastic and inelastic scattering cross sections have been measured for the systems ⁵⁸Ni +^90,94Zr at energies near the Coulomb barrier where not only quasi-elastic and fusion but also deep-inelastic process come into play. Coupled channels calculations including both projectile and target inelastic excitations can successfully explain the elastic and inelastic scattering angular distributions with an energy-independent semi-empirical bare potential. The calculation reproduces also the sum of the total quasi-elastic, fusion and deep-inelastic cross sections. Received: 14 September 1998 / Revised version: 21 October 1998     

Multi-nucleon transfer reactions and fusion with unstable nuclei

We show that a large number of neutrons are expected to be transferred from the projectile to the target if a neutron rich unstable nucleus with a neutron skin is used as the projectile in heavy-ion collisions at energies about twice the Coulomb barrier. We then show that though the neutron halo enhances the fusion cross section through the size effect, the additional effect due to the molecular bond formation is not significant in the fusion between ¹¹Li and ⁹Li at energies near and below the Coulomb barrier.     

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     

Study of optimum Q-value in 16O induced reactions on even Zr isotopes

Angular behaviour and optimum Q-value of ¹⁶O induced transfer reactions on the even Zr isotopes have been studied near the Coulomb barrier as a function of various parameters. The results are compared to semiclassical estimates including recoil effects and nuclear distortions of the Coulomb trajectories.     

An electrostatic deflector for a fusion reaction

An electrostatic deflector for separating the fusion evaporation residues from the beam-like products in heavy ion reactions was installed.The evaporation residue separation and identification with the electrostatic deflector setup was tested with the reaction 32S+96Zr at several energies.The fusion evaporation residues and the beam-like particles were well separated after the electrical separation and the experimental fusion cross section obtained from the angular distribution is in good agreement with the calculated value well above the Coulomb barrier.This confirms the reliability of the setup.