Recent developments in fusion and direct reactions with weakly bound nuclei

A summary of recent researches on nuclear dynamics with realistic microscopic quantum approaches is presented. The Balian-Veneroni variational principle is used to derive the time-dependent Hartree-Fock (TDHF) equation describing the dynamics at the mean-field level, as well as an extension including small-amplitude quantum fluctuations which is equivalent to the time-dependent random-phase approximation (TDRPA). Such formalisms as well as their practical implementation in the nuclear physics framework with modern three-dimensional codes are discussed. Recent applications to nuclear dynamics, from collective vibrations to heavy-ion collisions are presented. Particular attention is devoted to the interplay between collective motions and internal degrees of freedom. For instance, the harmonic nature of collective vibrations is questioned. Nuclei are also known to exhibit superfluidity due to pairing residual interaction. Extensions of the theoretical approach to study such pairing vibrations are now available. Large amplitude collective motions are investigated in the framework of heavy-ion collisions leading, for instance, to the formation of a compound system. How fusion is affected by the internal structure of the collision partners, such as their deformation, is discussed. Other mechanisms in competition with fusion, and responsible for the formation of fragments which differ from the entrance channel (transfer reactions, deep-inelastic collisions, and quasi-fission) are investigated. Finally, studies of actinide collisions forming, during very short times of few zeptoseconds, the heaviest nuclear systems available on Earth, are presented.

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Nuclear quantum many-body dynamics: from collective vibrations to heavy-ion collisions

The nucleus-nucleus interaction potentials in heavy-ion fusion reactions are extracted from the microscopic time-dependent Hartree-Fock theory for the mass symmetric reactions ${}^{16}\mathrm{O} + {}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca} + {}^{40}\mathrm{Ca}$, and ${}^{48}\mathrm{Ca} + {}^{48}\mathrm{Ca}$ and the mass asymmetric reactions ${}^{16}\mathrm{O} + {}^{40, 48}\mathrm{Ca}$, ${}^{40}\mathrm{Ca} + {}^{48}\mathrm{Ca}$, ${}^{16}\mathrm{O} + {}^{208}\mathrm{Pb}$, and ${}^{40}\mathrm{Ca} + {}^{90}\mathrm{Zr}$. When the c.m. energy is much higher than the Coulomb barrier energy, potentials deduced with the microscopic theory identify with the frozen density approximation. As the c.m. energy decreases and approaches the Coulomb barrier, potentials become energy dependent. This dependence indicates dynamical reorganization of internal degrees of freedom and leads to a reduction of the ``apparent'' barrier felt by the two nuclei during fusion of the order of 2--3% compared to the frozen density case. Several examples illustrate that the potential landscape changes rapidly when the c.m. energy is in the vicinity of the Coulomb barrier energy. The energy dependence is expected to have a significant role on fusion around the Coulomb barrier.

Energy dependence of the nucleus-nucleus potential close to the Coulomb barrier

The present status of fusion reactions involving light (A < 20) radioactive projectiles at energies around the Coulomb barrier (E < 10 MeV per nucleon) is reviewed, emphasizing measurements made within the last decade. Data on elastic scattering (providing total reaction cross section information) and breakup channels for the involved systems, demonstrating the relationship between these and the fusion channel, are also reviewed. Similarities and differences in the behavior of fusion and total reaction cross section data concerning halo nuclei, weakly-bound but less exotic projectiles, and strongly-bound systems are discussed. One difference in the behavior of fusion excitation functions near the Coulomb barrier seems to emerge between neutron-halo and proton-halo systems. The role of charge has been investigated by comparing the fusion excitation functions, properly scaled, for different neutron- and proton-rich systems. Possible physical explanations for the observed differences are also reviewed.

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Elastic scattering, fusion, and breakup of light exotic nuclei

New neutron-rich isotope production in $^{154}$Sm+$^{160}$Gd

New measurements of fusion cross sections at deep sub-barrier energies for the reactions 16O+204,208Pb show a steep but almost saturated logarithmic slope, unlike 64Ni-induced reactions. Coupled channels calculations cannot simultaneously reproduce these new data and above-barrier cross-sections with the same Woods-Saxon nuclear potential. It is argued that this highlights an inadequacy of the coherent coupled channels approach. It is proposed that a new approach explicitly including gradual decoherence is needed to allow a consistent description of nuclear fusion.

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Beyond the coherent coupled channels description of nuclear fusion.

Complete fusion cross sections for {sup 9}Be incident on {sup 208}Pb and {sup 209}Bi have been measured at energies greater than the fusion barrier to investigate the large differences in their reported complete fusion cross sections. Relative xn and fission cross sections are in good agreement. Thus, it is concluded that the differences arise from errors in absolute normalization in the previous measurements. The present measurements show that the above-barrier complete fusion cross sections for the reactions of {sup 9}Be with {sup 209}Bi and {sup 208}Pb are very similar, which resolves the previously observed anomaly. Complete fusion for the reaction of {sup 9}Be with {sup 209}Bi is found to be suppressed by {approx}32% compared to the expectations of a single-barrier penetration model, which is in close agreement with the value previously determined for the reaction with {sup 208}Pb.

Suppression of fusion by breakup: Resolving the discrepancy between the reactions of 9 Be with 208 Pb and 20 9Bi

The fission fragment mass ratio distributions of fusion-fission events have been measured for the reactions of $^{19}\mathrm{F}+^{232}\mathrm{Th},^{16}\mathrm{O}+^{235}\mathrm{U}$, and $^{16}\mathrm{O}+^{238}\mathrm{U}$ at energies near and below the fusion barrier. It is found that the mass ratio widths follow a decreasing trend with decreasing energy, contrary to recent claims of anomalous mass widths attributed to a quasifission mechanism.

Fission mass widths in 19 F+ 232 Th, 16 O+ 235,238 U reactions at near-barrier energies

This work presents the essential features of a highly efficient detector system developed to make precise measurements of evaporation residues produced following heavy ion fusion reactions. The details of the measurements of fusion excitation function performed with this device for the system 58Ni + 60Ni are presented, and the results are compared with an existing set of data.

Bertrand Bouriquet

Papers

Beyond the coherent coupled channels description of nuclear fusion.

Suppression of fusion by breakup: Resolving the discrepancy between the reactions of 9 Be with 208 Pb and 20 9Bi

Fission mass widths in 19 F+ 232 Th, 16 O+ 235,238 U reactions at near-barrier energies

Measurement of Fusion Excitation Functions Using a Novel Superconducting Solenoid