Mapping from quasi-elastic scattering to fusion reactions

The fusion barrier distribution has provided a nice representation for the channel coupling effects on heavy-ion fusion reactions at energies around the Coulomb barrier. Here we discuss how one can extract the same representation using the so called sum-of-differences (SOD) method with quasi-elastic scattering cross sections. In contrast to the conventional quasi-elastic barrier distribution, the SOD barrier distribution has an advantage in that it can be applied both to non-symmetric and symmetric systems. It is also the case that the correspondence to the fusion barrier distribution is much better than the quasi-elastic barrier distribution. We demonstrate its usefulness by studying $^{16}$O+$^{144}$Sm, $^{58}$Ni+$^{58}$Ni, and $^{12}$C+$^{12}$C systems.Comment: 6 pages, 9 figures. A talk given at VI International Conference FUSION14, Feb. 24-28, 2014, New Delhi, Indi

Quasi-elastic barrier distribution as a tool for investigating unstable nuclei

The method of fusion barrier distribution has been widely used to interpret the effect of nuclear structure on heavy-ion fusion reactions around the Coulomb barrier. We discuss a similar, but less well known, barrier distribution extracted from large-angle quasi-elastic scattering. We argue that this method has several advantages over the fusion barrier distribution, and offers an interesting tool for investigating unstable nuclei.Comment: 4 pages, 4 eps figures. A talk given at the XXVII Reuniao de Trabalho em Fisica Nuclear no Brazil, September 7 - 11, 2004, Santos, Brazil. To be published in the Brazilian Journal of Physic

On the Wong cross section and fusion oscillations

We re-examine the well-known Wong formula for heavy-ion fusion cross sections. Although this celebrated formula yields almost exact results for single-channel calculations for relatively heavy systems such as $^{16}$O+$^{144}$Sm, it tends to overestimate the cross section for light systems such as $^{12}$C+$^{12}$C. We generalise the formula to take account of the energy dependence of the barrier parameters and show that the energy-dependent version gives results practically indistinguishable from a full quantal calculation. We then examine the deviations arising from the discrete nature of the intervening angular momenta, whose effect can lead to an oscillatory contribution to the excitation function. We recall some compact, analytic expressions for these oscillations, and highlight the important physical parameters that give rise to them. Oscillations in symmetric systems are discussed, as are systems where the target and projectile identities can be exchanged via a strong transfer channel.Comment: 14 pages, 14 figure

Subbarrier fusion of carbon isotopes: from resonance structure to fusion oscillations

At energies below the Coulomb barrier, the fusion excitation function for the $^{12}$C+$^{12}$C system shows prominent fine structures, whereas that for the $^{12}$C+$^{13}$C system behaves more smoothly as a function of energy. We demonstrate that these different behaviors can be simultaneously reproduced using an optical potential in which the strength of the imaginary part is proportional to the level density of each compound nucleus. We also discuss the oscillatory behavior of fusion excitation function for these systems observed at energies above the Coulomb barrier from a view point of quantum mechanical systems with identical particles.Comment: 6 pages, 6 eps figures. A talk given at NUBA conference series-1: Nuclear Physics and Astrophysics, September 15-21, Antalya, Turke

Role of non-collective excitations in low-energy heavy-ion reactions

We investigate the effect of single-particle excitations on heavy-ion reactions at energies near the Coulomb barrier. To this end, we describe single-particle degrees of freedom with the random matrix theory and solve the coupled-channels equations for one-dimensional systems. We find that the single-particle excitations hinder the penetrability at energies above the barrier, leading to a smeared barrier distribution. This indicates that the single-particle excitations provide a promising way to explain the difference in a quasi-elastic barrier distribution recently observed in $^{20}$Ne + $^{90,92}$Zr systems.Comment: 8 pages, 7 figure

Subbarrier fusion reactions with dissipative couplings

Using the random matrix model, we discuss the effect of couplings to non-collective states on the penetrability of a one dimensional potential barrier. We show that these non-collective excitations hinder the penetrability and thus smear the barrier distribution at energies above the barrier, while they do not affect significantly the penetrability at deep subbarrier energies. The energy dependence of the Q-value distribution obtained with this model is also discussed.Comment: 4 pages, 2 figures. A talk given at the 10th international conference on nucleus-nucleus collisions (NN2009), Aug. 16-21, 2009, Beijing, Chin

Non-collective excitations in low-energy heavy-ion reactions: applicability of the random-matrix model

We investigate the applicability of a random-matrix model to the description of non-collective excitations in heavy-ion reactions around the Coulomb barrier. To this end, we study fusion in the reaction $^{16}$O + $^{208}$Pb, taking account of the known non-collective excitations in the $^{208}$Pb nucleus. We show that the random-matrix model for the corresponding couplings reproduces reasonably well the exact calculations, obtained using empirical deformation parameters. This implies that the model may provide a powerful method for systems in which the non-collective couplings are not so well known.Comment: 6 pages, 4 figure

Large-angle scattering and quasi-elastic barrier distributions

We study in detail the barrier distributions extracted from large-angle quasi-elastic scattering of heavy ions at energies near the Coulomb barrier. Using a closed-form expression for scattering from a single barrier, we compare the quasi-elastic barrier distribution with the corresponding test function for fusion. We examine the isocentrifugal approximation in coupled-channels calculations of quasi-elastic scattering and find that for backward angles, it works well, justifying the concept of a barrier distribution for scattering processes. This method offers an interesting tool for investigating unstable nuclei. We illustrate this for the $^{32}$Mg + $^{208}$Pb reaction, where the quadrupole collectivity of the neutron-rich $^{32}$Mg remains to be clarified experimentally.Comment: 26 pages, 10 eps figure