Adopted values for the reduced electric quadrupole transition probability, B(E2)↑, from the ground state to the first-excited 2+ state of even–even nuclides are given in Table I. Values of τ, the mean life of the 2+ state; E, the energy; and β, the quadrupole deformation parameter, are also listed there. The ratio of β to the value expected from the single-particle model is presented. The intrinsic quadrupole moment, Q0, is deduced from the B(E2)↑ value. The product E×B(E2)↑ is expressed as a percentage of the energy-weighted total and isoscalar E2 sum-rule strengths.

Table II presents the data on which Table I is based, namely the experimental results for B(E2)↑ values with quoted uncertainties. Information is also given on the quantity measured and the method used. The literature has been covered to November 2000.

The adopted B(E2)↑ values are compared in Table III with the values given by systematics and by various theoretical models. Predictions of unmeasured B(E2)↑ values are also given in Table III.

Transition probability from the ground to the first-excited 2^+ state of even-even nuclides

Recent developments in fusion and direct reactions with weakly bound nuclei

Fusion and direct reactions of halo nuclei at energies around the Coulomb barrier

Energy levels of light nuclei A = 12

A large number of precision fusion excitation functions, at energies above the average fusion barriers, have been fitted using the Woods-Saxon form for the nuclear potential in a barrier passing model of fusion. They give values for the empirical diffuseness parameter $a$ ranging between 0.75 and $1.5\phantom{\rule{0.3em}{0ex}}\mathrm{fm}$, compared with values of about $0.65\phantom{\rule{0.3em}{0ex}}\mathrm{fm}$ which generally reproduce elastic scattering data. There is a clear tendency for the deduced $a$ to increase strongly with the reaction charge product ${Z}_{1}{Z}_{2}$, and some evidence for the effect of nuclear structure on the value of $a$, particularly with regard to the degree of neutron richness of the fusing nuclei, and possibly with regard to deformation. The measured fusion-barrier energies are always lower than those of the bare potentials used, which is expected as a result of adiabatic coupling to high energy collective states. This difference increases with increasing ${Z}_{1}{Z}_{2}$ and calculations show that about $1∕3$ of it may be attributed to coupling to the isoscalar giant-quadrupole resonances in the target and projectile. Coupling to all giant resonances may account for a significant part. Fluctuations about the trend line may be due to systematic errors in the data and/or structure effects such as coupling to collective octupole states. Previously suggested reasons for the large values of $a$ have been related to departures from the Woods-Saxon potential and to dissipative effects. This work suggests that the apparently large values of $a$ may be an artifact of trying to describe the dynamical fusion process by use of a static potential. Another partial explaination might reside in fusion inhibition, due for example to deep-inelastic scattering, again a process requiring dynamical calculations.

Systematic Failure of the Woods-Saxon Nuclear Potential to Describe Both Fusion and Elastic Scattering: Possible Need for a New Dynamical Approach to Fusion

Extensive systematizations of theoretical and experimental nuclear densities and of optical potential strengths extracted from heavy-ion elastic scattering data analyses at low and intermediate energies are presented. The energy dependence of the nuclear potential is accounted for within a model based on the nonlocal nature of the interaction. The systematics indicates that the heavy-ion nuclear potential can be described in a simple global way through a double-folding shape, which basically depends only on the density of nucleons of the partners in the collision. The possibility of extracting information about the nucleon-nucleon interaction from the heavy-ion potential is investigated.

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Toward a global description of the nucleus-nucleus interaction

A parameter-free optical potential for the heavy-ion elastic scattering process

Thirty elastic scattering angular distributions for seven heavy-ion systems, in wide energy ranges, have been studied with the aim of systematizing the optical potential, real and imaginary parts, in a global way. The framework is: i) an extensive systematization of nuclear densities, ii) the energy dependence of the bare potential accounted by a model based on the nonlocal nature of the interaction, and iii) the real and imaginary parts of the optical potential assumed to have the same radial shape.

A parameter-free optical potential for the heavy-ion elastic scattering proces

We have developed a model for the nuclear interaction which is based on the effects of the Pauli nonlocality. In earlier works, we have successfully used this interaction to describe the elastic scattering for several systems in a very wide energy range. In the present work, we have checked the validity of the same interaction in the description of about 2500 fusion cross section data for 165 different systems. By introducing only one energy- and system-independent effective parameter, the nonlocal model describes the global behavior of the fusion process with good precision.

Global and consistent analysis of the heavy-ion elastic scattering and fusion processes

Evaporation residue cross sections for the {sup 18}O+{sup 58}Ni and {sup 16}O+{sup 60}Ni fusion reactions have been measured in the energy range from 3 below to 20 MeV above the Coulomb barrier. The low-energy fusion enhancements found in the two systems are very different. A comparative analysis suggests that collective pair transfer modes play an important role in the sub-barrier fusion of {sup 18}O+{sup 58}Ni.

E. S. Rossi

Papers

Toward a global description of the nucleus-nucleus interaction

A parameter-free optical potential for the heavy-ion elastic scattering process

A parameter-free optical potential for the heavy-ion elastic scattering proces

Global and consistent analysis of the heavy-ion elastic scattering and fusion processes

Pair transfer and the sub-barrier fusion of O 18 + 58 Ni