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The vast knowledge of strong influence of quadrupole deformation $\beta_2$ of colliding nuclei on heavy-ion subbarrier fusion reactions inspires a desire to quest the sensitivity of fusion dynamics to higher order deformations, such as $\beta_4$ and $\beta_6$ deformations. However, such studies have rarely been carried out, especially for deformation of projectile nuclei. In this article, we investigated the role of $\beta_4$ of the projectile nucleus in fusion of the $^{28}$Si + $^{92}$Zr system. We demonstrated that the fusion barrier distribution is sensitive to the sign and the value of the $\beta_4$ parameter of the projectile, $^{28}$Si, and confirmed that the $^{28}$Si nucleus has a large positive $\beta_4$. This study opens an indirect way to estimate deformation parameters of radioactive nuclei using fusion reactions, which is otherwise difficult due to experimental constraints.

The nuclear fusion is a reaction to form a compound nucleus. It plays an important role in several circumstances in nuclear physics as well as in nuclear astrophysics, such as synthesis of superheavy elements and nucleosynthesis in stars. Here we discuss two recent theoretical developments in heavy-ion fusion reactions at energies around the Coulomb barrier. The first topic is a generalization of the Wong formula for fusion cross sections in a single-channel problem. By introducing an energy dependence to the barrier parameters, we show that the generalized formula leads to results practically indistinguishable from a full quantal calculation, even for light symmetric systems such as $^{12}$C+$^{12}$C, for which fusion cross sections show an oscillatory behavior. We then discuss a semi-microscopic modeling of heavy-ion fusion reactions, which combine the coupled-channels approach to the state-of-the-art nuclear structure calculations for low-lying collective motions. We apply this method to subbarrier fusion reactions of $^{58}$Ni+$^{58}$Ni and $^{40}$Ca+$^{58}$Ni systems, and discuss the role of anharmonicity of the low-lying vibrational motions., Comment: 10 pages, 6 figures. A talk given at the 5th International Workshop on Compound-Nuclear Reactions and Related Topics (CNR*15), October 9-23, 2015, Tokyo, Japan

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 figures

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, Turkey

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, India

Conventional coupled-channels analyses, that take account of only the collective excitations of the colliding nuclei, have failed to reproduce the different behavior of the experimental quasi-elastic barrier distributions for the $^{20}$Ne + $^{90,92}$Zr systems. To clarify the origins of this difference, we investigate the effect of non-collective excitations of the Zr isotopes. Describing these excitations in a random-matrix model, we explicitly take them into account in our coupled-channels calculations. The non-collective excitations are capable of reproducing the observed smearing of the peak structure in the barrier distribution for $^{20}$Ne + $^{92}$Zr, while not significantly altering the structure observed in the $^{20}$Ne + $^{90}$Zr system. The difference is essentially related to the closed neutron shell in $^{90}$Zr., Comment: 8 pages, 9 figures

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 figures

Despite the supposed simplicity of double-closed shell nuclei, conventional coupled-channels calculations, that include all of the known collective states of the target and projectile, give a poor fit to the fusion cross section for the $^{16}$O + $^{208}$Pb system. The discrepancies are highlighted through the experimental barrier distribution and logarithmic derivative, that are both well defined by the precise experimental fusion data available. In order to broaden our search for possible causes for this anomaly, we revisit this system and include in our calculations a large number of non-collective states of the target, whose spin, parity, excitation energy and deformation paramter are known from high-precision proton inelastic-scattering measurements. Although the new coupled-channels calculations modify the barrier distribution, the disagreemnt with experiment remains both for fusion and for quasi-elastic (QE) scattering. We find that the Q-value distributions for large-angle QE scattering become rapidly more important as the incident energy increases, reflecting the trend of the experimental data. The mass-number dependence of the non-collective excitations is discussed., Comment: 8 pages, 7 figures

An experimental overview of reactions induced by the stable, but weakly-bound nuclei 6Li, 7Li and 9Be, and by the exotic, halo nuclei 6He, 8He, 8B, and 11Be on medium-mass targets, such as 58Ni, 59Co or 64Zn, is presented. Existing data on elastic scattering, total reaction cross sections, fusion processes, breakup and transfer channels are discussed in the framework of a CDCC approach taking into account the breakup degree of freedom., Comment: 7 pages, 2 figures, Proceedings of Sotancp2 Workshop, Brussels, May 2010, to be publihed in Int. Jour. Mod. Phys. E

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 figures

An experimental overview of reactions induced by the stable, but weakly-bound nuclei 6Li, 7Li and 9Be, and by the exotic, halo nuclei 6He, 8B, 11Be and 17F on medium-mass targets, such as 58Ni, 59Co or 64Zn, is presented. Existing data on elastic scattering, total reaction cross sections, fusion processes, breakup and transfer channels are discussed in the framework of a CDCC approach taking into account the breakup degree of freedom., Comment: 7 pages, 6 figures, Invited Talk given by C. Beck to the 10th International Conference on Nucleus-Nucleus Collisions, August 16-21, 2009 Beijing, China; Paper submitted to the NN2009 Proceedings, Nuclear Physics A (to be published)

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, China

For a single potential barrier, the barrier penetrability can be inverted based on the WKB approximation to yield the barrier thickness. We apply this method to heavy-ion fusion reactions at energies well below the Coulomb barrier and directly determine the inter-nucleus potential between the colliding nuclei. To this end, we assume that fusion cross sections at deep subbarrier energies are governed by the lowest barrier in the barrier distribution. The inverted inter-nucleus potentials for the $^{16}$O +$^{144}$Sm and $^{16}$O +$^{208}$Pb reactions show that they are much thicker than phenomenological potentials. We discuss a consequence of such thick potential by fitting the inverted potentials with the Bass function., Comment: 8 pages, 5 figures. Uses aipxfm.sty. A talk given at the FUSION08: New Aspects of Heavy Ion Collisions Near the Coulomb Barrier, September 22-26, 2008, Chicago, USA

With the aid of the Geant4 Monte Carlo simulation package a new detection system has been designed for the focal plane of the recoil separator VASSILISSA situated at the Flerov Laboratory of Nuclear Reactions, JINR, Dubna. GABRIELA (Gamma Alpha Beta Recoil Investigations with the Electromagnetic Analyser VASSILISSA) has been optimised to detect the arrival of reaction products and their subsequent radioactive decays involving the emission of alpha- and beta-particles, fission fragments, gamma- and X-rays, and conversion electrons. The new detector system is described and the results of the first commissioning experiments are presented., Comment: 24 pages, Submitted to NIM A

Symmetric heavy-ion collisions are known to display an `extra-push' effect. That is, the energy at which the s-wave transmission is 0.5 lies significantly higher than the nominal Coulomb barrier. Despite this, however, the capture cross section is still greatly enhanced below the uncoupled barrier. It is shown that this phenomenon can be simply explained in terms of entrance-channel effects which account for long-range Coulomb excitations., Comment: 9 pages, 4 ps figures, uses elsart.cls

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 Physics

The influence on the fusion process of coupling to collective degrees of freedom has been explored. The significant enhancement of he fusion cross setion at sub-barrier energies was understood in terms of the dynamical processes arising from strong couplings to collective inelastic excitations of the target and projectile. However, in the case of reactions where breakup becomes an important process, conflicing model predictions and experimental results have been reported in the literature. Excitation functions for sub- and near-barrier total (complete + incomplete) fusion cross sections have been measured for the $^{6,7}$Li + $^{59}$Co at the Vivitron facility and at the 8UD Pelletron tandem facility using standard $\gamma$-ray techniques. The data extend to medium-mass systems previous works exploring the coupling effects in fusion reactions of both lighter and heavier systems. Results of continuum-discretized coupled channel (CDCC) calculations indicate a small enhancement of total fusion for the more weakly bound $^{6}$Li at sub-barrier energies, with similar cross sections for both reactions at and above the barrier. A systematic study of $^{4,6}$He induced fusion reactions with the CDCC method is in progress. The understanding of the reaction dynamics involving couplings to the breakup channels requires th explicit measurement of precise elastic scattering data as well as yields leading to the breakup itself. Recent coincidence experiments for $^{6,7}$Li + $^{59}$Co are addressing this issue. The particle identification of the breakup products have been achieved by measuring the three-body final-state correlations.

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 figures

We perform exact coupled-channels calculations, taking into account properly the effects of Coulomb coupling and the finite excitation energy of collective excitations in the colliding nuclei, for three Fm formation reactions, $^{37}$Cl + $^{209}$Bi, $^{45}$Sc + $^{197}$Au, and $^{59}$Co + $^{181}$Ta. For the $^{37}$Cl + $^{209}$Bi and $^{45}$Sc + $^{197}$Au reactions, those calculations well reproduce the experimental total fission cross sections, and a part of the extra-push phenomena can be explained in terms of the Coulomb excitations to multi-phonon states. On the other hand, for the heaviest system, the deep-inelastic collisions become much more significant, and the fission cross sections are strongly overestimated. We also discuss the surprisingly large surface diffuseness parameters required to fit recent high-precision fusion data for medium-heavy systems, in connection with the fusion supression observed in massive systems., Comment: 10 pages, 6 ps figures. Uses aipxfm.sty. A talk given at the Tours Symposium on Nuclear Physics V, August 26 - 29, 2003, Tours, France

A recent publication reports that heavy-ion fusion cross sections at extreme subbarrier energies show a continuous change of their logarithmic slope with decreasing energy, resulting in a much steeper excitation function compared with theoretical predictions. We show that the energy dependence of this slope is partly due to the asymmetric shape of the Coulomb barrier, that is its deviation from a harmonic shape. We also point out that the large low-energy slope is consistent with the surprisingly large surface diffusenesses required to fit recent high-precision fusion data., Comment: 9 pages, 3 eps figures

For nuclei with N = Z, the isospin degree of freedom is important and, for deformed systems, rotational bands of different isospin may be expected at low excitation energies. We have investigated, in a simple model space, the influence of the isospin-breaking Coulomb interaction on the degree of chaoticity of these rotational bands. The statistical measures used rely on an analysis of level-spacing distributions, which are extremely difficult to measure experimentally. We show, however, that the overlap intergrals between states of similar frequency reflect well the degree of chaoticity. This quantity is closely related to the experimentally more accessible gamma-decay ``spreading width''., Comment: 13 pages, 9 figures, Elsevier

A FORTRAN77 program is presented that calculates fusion cross sections and mean angular momenta of the compound nucleus under the influence of couplings between the relative motion and several nuclear collective motions. The no-Coriolis approximation is employed to reduce the dimension of coupled-channels equations. The program takes into account the effects of non-linear couplings to all orders, which have been shown to play an important role in heavy-ion fusion reactions at subbarrier energies., Comment: 14 pages, submitted to CPC, the program is available upon request from hagino@phys.washington.edu

$\alpha-$decay through a deformed potential barrier produces significant mixing of angular momenta when mapped from the nuclear interior to the outside. Using experimental branching ratios and either semi-classical or coupled-channels transmission matrices, we have found that there is a set of internal amplitudes which are essentially constant for all even--even actinide nuclei. These same amplitudes also give good results for the known anisotropic $\alpha-$particle emission of the favored decays of odd nuclei in the same mass region. PACS numbers: 23.60.+e, 24.10.Eq, 27.90.+b, Comment: 5 pages, latex (revtex style), 2 embedded postscript figures uuencoded gz-compressed .tar file To appear in Physical Review Letters