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.     

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.     

Reactions involving loosely bound cluster nuclei: Heavy ions and new technologies

Experimental results on excitation functions for complete-fusion and transfer reactions in the interaction of ⁶He and ^6,8,9Li nuclei with various target nuclei are presented. Data on fusion-reaction cross sections in the case of ⁶He differ strongly from the predictions of the statistical model. A strong enhancement of the cross section at barrier energies is observed for this reaction channel. Also, an increase in the cross sections for neutron-transfer reactions (in the case of ⁶He and ^8,9Li beams) and deuteron-transfer reactions (in the case of ⁶Li) is observed in the deep-subbarrier energy region. The results are discussed from the point of view of the effect of the cluster structure of nuclei on the probability of interaction at barrier energies. The results of employing heavy-ion beams in new technologies are presented.     

Proton transfer in quasi-elastic and deep-inelastic reactions in the systems86Kr on88Sr,90Zr and92Mo at energies close to the coulomb barrier

Reaction products corresponding to the transfer of one and several protons have been measured over a large angular range for incident energies of 380 MeV and 400 MeV in reactions of⁸⁶Kr with⁸⁸Sr,⁹⁰Zr and⁹²Mo. For transitions with smallQ-values (total kinetic energy loss TKEL≦10 MeV) the transfer probabilities are deduced. The magnitudes and slopes of these probabilities as function of the distance of closest approach between two nuclei are discussed. The results for single proton transfer are well described by tunneling, whereas the transfer of two and more nucleons into low lying states of the final nuclei seems to be influenced by intermediate transfer steps with larger TKEL. The data give the possibility to discuss the relation between deep-inelastic and quasi-elastic processes. The deep-inelastic data are analyzed successfully by including deformations, charge transfer and statistical fluctuations into the frictional model of Gross and Kalinowski.     

Effect of neutron transfer channels in fusion reactions with weakly bound nuclei at subbarrier energies

The role of neutron transfer in fusion reactions of weakly-bound nuclei at subbarrier energies is studied within the empirical model of channel coupling. The results from calculating the fusion cross sections for the ⁷Li + ²⁰⁹Bi, ^{9, 11}Li + ^{208, 206}Pb, ^{6, 7, 9, 11}Li + ¹⁵²Sm reactions are presented. Good agreement with the available experimental data is shown. Several combinations of colliding nuclei for which the strong enhancement of subbarrier fusion due to the effect of neutron transfer processes are predicted.     

Heavy-ion fusion below the Coulomb barrier: The systems 28,30Si + 58,62,64Ni and 32,34,36S + 58,64Ni

Fusion cross-sections for the 12 systems ^28,30Si + ^58,62,64Ni and ^32,34,36S + ^58,64Ni were measured at many energies from well below up to about 1.5 times the Coluomb barriers. The data show large sub-barrier fusion probabilities with strong isotopic dependences. The results of coupled-channel calculations involving the lowest 2⁺ and 3⁻ levels of both colliding nuclei and the 2-neutron transfer channel are compared with the measured excitation functions. Indications for the importance of the transfer channels are found. Signatures of system-dependent effects of the positive Q-value transfer channels are evidenced, also from a systematic intercomparison of the data.     

Probing the structure of exotic nuclei by transfer reactions

Low energy single nucleon transfer reactions are proposed as a tool to investigate the structure of nuclei far off stability. Experimental concepts and conditions are discussed, in particular high resolution γ-ray spectroscopy after single nucleon pickup reactions. Nuclear structure is described by Skyrme Hartree-Fock calculations including pairing. As representative examples, binding energies, radii and wave functions for Mg and Sn isotopes are calculated. In the neutron deficient Mg isotopes a proton skin is found. At the neutron driplines the Mg and Sn isotopes develop extended neutron skins. The nuclear structure results are used in DWBA and EFR-DWBA transfer calculations. Single nucleon transfer reactions of ^32,36Mg and exotic Sn beams on targets ranging from ²H to ²⁴Mg in inverse kinematics are explored. The one-nucleon transfer cross sections decrease strongly for high-Z targets. An impact parameter analysis shows that the transfer process is selective on the tails of the wave functions. The largest cross sections are obtained for ²H and ⁹Be targets at incident energies of E _lab = 2-5 MeV/u. The energy-momentum dependence is closely related to the special properties of wave functions of weakly bound states. Two-neutron (p,t) stripping reactions are studied for a ⁶He projectile. A strong competition of sequential and direct processes is found at low energies. Received: 1 October 1997 / Revised version: 25 November 1997     

Properties of the low-lying positive-parity states in Be and C

Excitation energies and electromagnetic form factors of the low-lying positive-parity states have been calculated in⁹Be and ¹³C on the basis of a particle-core coupling model. The results are compared with recent electron scattering experiments and photon data. The first excited levels in the two nuclei show a large contribution from the spin term of the electromagnetic interaction at low-momentum transfer q² < 0.6 fm⁻².     

Evolution from deep inelastic transfer to quasi-fission

Recoil techniques have been used to study the evolution of the features of four-charge transfer reactions in ¹⁴⁸Sm targets when the mass and energy of the projectile are varied. Beams of ⁶³Cu and ⁵⁶Fe were used, and their energies were chosen in order to be equal to 1.2B and 1.5B for both projectiles, B being the interaction barrier. The residual nuclei ^149gTb, ¹⁵⁰Dy and ¹⁵¹Dy were identified by their radioactive properties. This study has shown a continuous evolution of the characteristics of the c.m. angular distributions, especially the position of the maxima, from typical deep inelastic transfer to quasi-fission features, when the value of $\text{E}\text{B}$ decreases. For equal values of this ratio, no difference was observed between Fe and Cu induced reactions. The c.m, energies corresponding to the maximum cross section increases when the incident energy is increased, for a given projectile. At low incident energies (igE = 1.2B), the relative motion appears to be completely damped, and the distance of the two nuclei after separation is equal to about 5 fm. At higher incident energies, the c.m. energy is significantly higher. This may mean that the relative motion is not completely damped. Part of the effect may be explained by the differences in the angular momenta involved in the reaction.     

Effect of nuclear-reaction mechanisms on the population of excited nuclear states and isomeric ratios

Experimental data on the cross sections for channels of fusion and transfer reactions induced by beams of radioactive halo nuclei and clustered and stable loosely bound nuclei were analyzed, and the results of this analysis were summarized. The interplay of the excitation of single-particle states in reaction-product nuclei and direct reaction channels was established for transfer reactions. Respective experiments were performed in stable (⁶Li) and radioactive (⁶Не) beams of the DRIBs accelerator complex at the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, and in deuteron and ³Не beams of the U-120M cyclotron at the Nuclear Physics Institute, Academy Sciences of Czech Republic (?e? and Prague, Czech Republic). Data on subbarrier and near-barrier fusion reactions involving clustered and loosely bound light nuclei (⁶Li and ³He) can be described quite reliably within simple evaporation models with allowance for different reaction Q-values and couple channels. In reactions involving halo nuclei, their structure manifests itself most strongly in the region of energies below the Coulomb barrier. Neutron transfer occurs with a high probability in the interactions of all loosely bound nuclei with light and heavy stable nuclei at positive Q-values. The cross sections for such reactions and the respective isomeric ratios differ drastically for nucleon stripping and nucleon pickup mechanisms. This is due to the difference in the population probabilities for excited single-particle states.     

Damping of high-lying single-particle modes in heavy nuclei

The recent experimental and theoretical results on the damping of high-lying single-particle modes in heavy nuclei are reviewed. In one-nucleon transfer reactions these states manifest themselves as broad “resonance”-like structures superimposed on a large continuum. The advantages and the limitations of the transfer reaction approach will be presented using the results from neutron and proton pick-up and stripping reactions. The problem raised by the subtraction of the underlying background, the assumptions made to describe the reaction process and the method used to extract the strength distributions are presented. The existing empirical systematics is summarized for nuclei ranging from ⁹⁰Zr to ²⁰⁸Pb.The theoretical approaches used to explain the damping of the high-lying single-particle modes are based on the coupling between collective and single-particle degrees of freedom. In a first step the bare single-particle mode is spread over several doorway collective states due to the interaction with surface vibrations. In a second step the doorway states spread their strengths over many other degrees of freedom. These two steps of the damping mechanism are discussed in detail within the framework of the quasiparticle-phonon nuclear model. A large-scale comparison between the measured and calculated average energies, spreading widths and spectroscopic strengths of the high-lying single-particle (hole) states in heavy nuclei is presented. The systematic features of the damping (energy, angular momentum and isotopic dependence) are discussed. Recent advances of the experimental approaches, such as the γ-decay of the high-lying states or the use of heavy-ion transfer reactions at intermediate energies, are outlined.The detailed study of the damping mechanism of high-lying single-particle modes reveals new features and leads us to a new field in nuclear structure: “the spectroscopy of inner and outer subshells”.     

Single-nucleon transfer reactions induced by16O on14C

Angular distributions of the proton and neutron transfer reactions¹⁴C(¹⁶O,¹⁵N)¹⁵N and¹⁴C(¹⁶O,¹⁷O)¹³C leading to the ground states of the final nuclei were measured atE _lab=20, 25 and 30 MeV. A DWBA analysis was performed using the no-recoil approximation of Buttle and Goldfarb. All angular distributions, including the pronounced structures of the proton transfer arising from the fact that the final nuclei are identical, are well reproduced. The spectroscopic factor for the neutron transfer is in agreement with shell model calculations whereas the proton transfer into aj _<-state yields a value which is too high. Exact finite-range calculations do not show this discrepancy, indicating that recoil effects are important even for light targets and lower energies. Contributions of the nonnormall-transfer, however, are small.     

Periodic multi-proton transfer strength in collisions between heavy nuclei

A periodic variation of the multi-proton transfer probability as a function of the nuclear charges of the residual nuclei has been observed in collisions of ²³⁸U with ¹¹⁰Pd and ¹²⁴Sn at bombarding energies close to the Coulomb barrier. After the N = 82 closed neutron shell of the light reaction partner is filled through multi-neutron transfer and an energy dissipation of about 100 MeV, transfer of pairs of protons is observed with modulated transfer strength. The proton multi-pair transfer dissipates no further energy.     

Momentum transfer in light-ion-induced fission reactions

Angular correlations and angular distributions of the fission fragments produced in the bombardment of a ²³²Th target with protons, deuterons and α-particles in the energy range between 35 and 1000 MeV/nucleon have been measured. From these measurements, the distributions of linear momentum imparted to fissioning nuclei have been deduced in the various energy regimes; dominating reaction mechanisms are classified according to the fraction of the available incident momentum transferred to the target. The experimental results are compared to the predictions of intra-nuclear cascade calculations. An optimum excitation energy supported by the fissioning nuclei could be the dominant limitation to momentum transfer at high incident energies. The angular distributions of the fission fragments were used to extract fission cross sections and upper limits of the angular momentum imparted to the fissioning nuclei.     

Time-dependent quantum description of few-nucleon transfers upon nuclear reactions 40Ca + 96Zr, 40Ca + 208Pb, and 90Zr + 208Pb

The time-dependent Schrödinger equation is solved numerically using the difference approach for outer nucleons of the spherical nuclei ⁴⁰Ca, ⁹⁰Zr, and ²⁰⁸Pb upon their grazing collisions. The neutron and proton transfer probabilities are determined for energies near the Coulomb barrier as functions of the minimum internuclear distance and quantum numbers of initial nucleon states.     

Calculation of single-particle energies in the <Stack><Subscript>38</Subscript><Superscript>96</Superscript></Stack>Sr nucleus within the mean field model with the dispersive optical potential

Evaluated and experimental neutron single-particle energies of the ^{88, 94, 96}Sr and ^{90, 96, 98}Zr nuclei near the Fermi energy are compared. A possibility of formation of a considerable particle-hole gap in the ^{94, 96}Sr typical of traditional magic nuclei is investigated. Agreement is obtained between the single-particle energies calculated within the mean field model with the dispersive optical potential and the evaluated energies for the ^{94, 96}Sr nuclei.     

In-beam γ -ray study of the neutron-rich nuclei 240U, 246Pu, and 250Cm produced by the (18O, 16O) reaction

We have measured deexcitation γ rays in the neutron-rich nuclei of ²⁴⁰U, ²⁴⁶Pu, and ²⁵⁰Cm produced by the (¹⁸O, ¹⁶O) two-neutron transfer reactions, in coincidence with the ¹⁶O particles using Si ΔE−E detectors. The γ rays in these nuclei were identified by selecting the kinetic energies of ¹⁶O particles, which correspond to the excitation energies in the residual nuclei below the neutron separation energies. The ground-state bands of ²⁴⁰U, ²⁴⁶Pu, and ²⁵⁰Cm were established up to 12⁺ states and the K ^π = 0⁻ octupole band of ²⁴⁰U was established up to 9⁻ states. The systematics of the moments of inertia of the ground-state bands for actinide nuclei shows that the deformed subshell closure at N = 152 is sustained for ₉₆Cm isotopes and that it disappears for ₉₄Pu isotopes. The text was submitted by the authors in English.     

Investigation of clustering in light nuclei by means of relativistic-multifragmentation processes

New results concerning the topology of the fragmentation of relativistic nuclei ⁷Li and ¹⁰B are presented. A program is proposed for studying the cluster structure of stable and radioactive nuclei. The use of emulsions in the investigation of nuclear clustering in the fragmentation of light nuclei at energies are in excess of 1 GeV per nucleon is discussed.