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Fusion data for $^{40}$Ca+$^{96}$Zr are analyzed by coupled-channels calculations that are based on a standard Woods-Saxon potential and include couplings to multiphonon excitations and transfer channels. The couplings to multiphonon excitations are the same as used in a previous work. The transfer couplings are calibrated to reproduce the measured neutron transfer data. This type of calculation gives a poor fit to the fusion data. However, by multiplying the transfer couplings with a $\sqrt{2}$ one obtains an excellent fit. The scaling of the transfer strengths is supposed to simulate the combined effect of neutron and proton transfer, and the calculated one- and two-nucleon transfer cross sections are indeed in reasonable agreement with the measured cross sections., Comment: 20 pages, 7 figures

The study of exotic nuclear structures, such as halo nuclei, is usually performed through nuclear reactions. An accurate reaction model coupled to a realistic description of the projectile is needed to correctly interpret experimental data. In this contribution, we briefly summarise the assumptions made within the modelling of reactions involving halo nuclei. We describe briefly the Continuum-Discretised Coupled Channel method (CDCC) and the Dynamical Eikonal Approximation (DEA) in particular and present a comparison between them for the breakup of 15C on Pb at 68AMeV. We show the problem faced by the models based on the eikonal approximation at low energy and detail a correction that enables their extension down to lower beam energies. A new reaction observable is also presented. It consists of the ratio between angular distributions for two different processes, such as elastic scattering and breakup. This ratio is completely independent of the reaction mechanism and hence is more sensitive to the projectile structure than usual reaction observables, which makes it a very powerful tool to study exotic structures far from stability., Comment: Contribution to the proceedings of the XXI International School on Nuclear Physics and Applications & the International Symposium on Exotic Nuclei, dedicated to the 60th Anniversary of the JINR (Dubna) (Varna, Bulgaria, 6-12 September 2015), 7 pages, 4 figures

Fusion cross sections of 28Si + 28Si have been measured in a range above the barrier with a very small energy step (DeltaElab = 0.5 MeV). Regular oscillations have been observed, best evidenced in the first derivative of the energy-weighted excitation function. For the first time, quite different behaviors (the appearance of oscillations and the trend of sub-barrier cross sections) have been reproduced within the same theoretical frame, i.e., the coupled-channel model using the shallow M3Y+repulsion potential. The calculations suggest that channel couplings play an important role in the appearance of the oscillations, and that the simple relation between a peak in the derivative of the energy-weighted cross section and the height of a centrifugal barrier is lost, and so is the interpretation of the second derivative of the excitation function as a barrier distribution for this system, at energies above the Coulomb barrier., Comment: submitted to Physics Letters B

Fusion data for $^{48}$Ca+$^{90,96}$Zr are analyzed by coupled-channels calculations that are based on the M3Y+repulsion, double-folding potential. By applying a previously determined nuclear density of $^{48}$Ca, the neutron densities of the zirconium isotopes are adjusted to optimize the fit to the fusion data, whereas the proton densities are determined by electron scattering experiments. It is shown that the fusion data can be explained fairly well by including couplings to one- and two-phonon excitations of the reacting nuclei and to one- and two-nucleon transfer reactions but there is also some sensitivity to multiphonon excitations. The neutron skin thicknesses extracted for the two zirconium isotopes are consistent with anti-proton measurements. The densities of the zirconium isotopes are used together with the previously determined nuclear density of $^{40}$Ca to calculate the M3Y+repulsion potentials and predict the fusion cross sections of $^{40}$Ca+$^{90,96}$Zr. The predicted cross sections for $^{40}$Ca+$^{90}$Zr are in reasonable agreement with the data when the influence of multiphonon excitations and a modest transfer is considered. The prediction of the $^{40}$Ca+$^{96}$Zr fusion cross section, on the other hand, is poor and under-predicts the data by 30 to 40%. Although couplings to transfer channels with positive $Q$ values were expected to play an important role, they are not able to explain the data, primarily because the predicted Coulomb barrier is about 1.5 MeV too high. Possible reasons for this failure are discussed., Comment: 36 pager, 13 figures

Halo nuclei are exotic nuclei which exhibit a strongly clusterised structure: they can be seen as one or two valence nucleons loosely bound to a core. Being observed at the ridge of the valley of stability, halo nuclei are studied mostly through reactions. In this contribution the reaction models most commonly used to analyse experimental data are reviewed and compared to one another. A reaction observable built on the ratio of two angular distributions is then presented. This ratio enables removing most of the sensitivity to the reaction mechanism, which emphasises the effects of nuclear structure on the reaction., Comment: Invited talk given by Pierre Capel at the "10th International Conference on Clustering Aspects of Nuclear Structure and Dynamics" (Cluster12), Debrecen, Hungary, 24-28 September 2012. To appear in the Cluster12 Proceedings in the Open Access Journal of Physics: Conference Series (JPCS). (5 pages, 3 figures)

Structures observed in heavy-ion fusion cross sections at energies above the Coulomb barrier are interpreted as caused by the penetration of centrifugal barriers that are well-separated in energy. The structures are most pronounced in the fusion of lighter, symmetric systems, where the separation in energy between successive angular momentum barriers is relatively large. It is shown that the structures or peaks can be revealed by plotting the first derivative of the energy weighted cross section. It is also shown how an orbital angular momentum can be assign to the observed peaks by comparing to coupled-channels calculations. This is illustrated by analyzing high-energy fusion data for $^{12}$C+$^{16}$O and $^{16}$O+$^{16}$O, and the possibility of observing similar structures in the fusion of heavier systems is discussed., Comment: 22 pager, 12 figures

Breakup reactions of loosely-bound nuclei are often used to extract structure and/or astrophysical information. Here we compare three non-perturbative reaction theories often used when analyzing breakup experiments, namely the continuum discretized coupled channel model, the time-dependent approach relying on a semiclassical approximation, and the dynamical eikonal approximation. Our test case consists of the breakup of 15C on Pb at 68 MeV/nucleon and 20 MeV/nucleon., Comment: 8 pages, 6 figures, accepted for publication in Phys. Rev. C

Fusion data for $^{13}$C+$^{13}$C, $^{12}$C+$^{13}$C and $^{12}$C+$^{12}$C are analyzed by coupled-channels calculations that are based on the M3Y+repulsion, double-folding potential. The fusion is determined by ingoing-wave-boundary conditions (IWBC) that are imposed at the minimum of the pocket in the entrance channel potential. Quadrupole and octupole transitions to low-lying states in projectile and target are included in the calculations, as well as mutual excitations of these states. The effect of one-neutron transfer is also considered but the effect is small in the measured energy regime. It is shown that mutual excitations to high-lying states play a very important role in developing a comprehensive and consistent description of the measurements. Thus the shapes of the calculated cross sections for $^{12}$C+$^{13}$C and $^{13}$C+$^{13}$C are in good agreement with the data. The fusion cross sections for $^{12}$C+$^{12}$C determined by the IWBC are generally larger than the measured cross sections but they are consistent with the maxima of some of the observed peak cross sections. They are therefore expected to provide an upper limit for the extrapolation into the low-energy regime of interest to astrophysics., Comment: 34 pages, 17 figures

Rare isotopes are most often studied through nuclear reactions. Nuclear reactions can be used to obtain detailed structure information but also in connection to astrophysics to determine specific capture rates. In order to extract the desired information it is crucial to have a reliable framework that describes the reaction process accurately. A few recent developments for transfer and breakup reactions will be presented. These include recent studies on the reliability of existing theories as well as effort to reduce the ambiguities in the predicted observables., Comment: 12 pages, 6 figures, conference proceedings for CGS14, Guelph, September 2011

Carbon burning is a crucial process for a number of important astrophysical scenarios. The lowest measured energy is around E$_{\rm c.m.}$=2.1 MeV, only partially overlapping with the energy range of astrophysical interest. The currently adopted reaction rates are based on an extrapolation which is highly uncertain because of potential resonances existing in the unmeasured energy range and the complication of the effective nuclear potential. By comparing the cross sections of the three carbon isotope fusion reactions, ${}^{12}$C+${}^{12}$C, ${}^{12}$C+${}^{13}$C and ${}^{13}$C+${}^{13}$C, we have established an upper limit on the molecular resonance strengths in ${}^{12}$C+${}^{12}$C fusion reaction. The preliminary results are presented and the impact on nuclear astrophysics is discussed., Comment: 4 pages, 3 figures, FUSION11 conference proceeding

The structure of 15C, with an s1/2 neutron weakly bound to a closed-neutron shell nucleus 14C, makes it a prime candidate for a one-neutron halo nucleus. We have for the first time studied the cross section for the fusion-fission reaction 15C + 232Th at energies in the vicinity of the Coulomb barrier and compared it to the yield of the neighboring 14C + 232Th system measured in the same experiment. At sub-barrier energies, an enhancement of the fusion yield by factors of 2-5 was observed for 15C, while the cross sections for 14C match the trends measured for 12,13C., Comment: 4 pages, 2 figures, Phys. Rev. Lett. (accepted)

The coupled-channels technique is applied to analyze recent fusion data for $^{48}$Ca+$^{48}$Ca. The calculations include the excitations of the low-lying $2^+$, $3^-$ and $5^-$ states in projectile and target, and the influence of mutual excitations as well as the two-phonon quadrupole excitations is also investigated. The ion-ion potential is obtained by double-folding the nuclear densities of the reacting nuclei with the M3Y+repulsion effective interaction but a standard Woods-Saxon potential is also applied. The data exhibit a strong hindrance at low energy compared to calculations that are based on a standard Woods-Saxon potential but they can be reproduced quite well by applying the M3Y+repulsion potential with an adjusted radius of the nuclear density. The influence of the polarization of high-lying states on the extracted radius is discussed., Comment: 8 pages, 7 figures

The semiclassical, dynamical description of diffraction dissociation of weakly bound nuclei is applied to analyze the decay-energy spectra of $^{15}$C that have been measured at 68 MeV/nucleon on a Pb target. The optical potentials that are used to describe the nuclear interaction of $^{15}$C with the target nucleus are realistic because the fits to the two measured spectra, one with a small and one with a very large acceptance angle, are consistent and of similar quality. The cross section for the radiative neutron capture on $^{14}$C to the 1/2$^+$ ground state of $^{15}$C is deduced from the analysis. When combined with an estimated contribution from the capture to the 5/2$^+$ excited state of $^{15}$C, an excellent agreement with a recent direct capture measurement is achieved.

Fusion data for $^{48}$Ca+$^{96}$Zr are analyzed by coupled-channels calculations. Puzzling features of a previous analysis are eliminated by applying a potential that has a shallow pocket in the entrance channel. Thus the observed $S$ factor for fusion, which develops a maximum at low energy, can be reproduced fairly well. The high-energy data can also be accounted for but that requires the use of a weak, short-ranged imaginary potential that absorbs the incoming flux near the location of the minimum of the potential pocket. Predictions of the fusion hindrance in other Ca+Zr systems are made and are compared with the systematics that has been developed previously., Comment: 1 text file, 7 figures

Straight line trajectories are commonly used in semi-classical calculations of the first-order Coulomb excitation cross section at intermediate energies, and simple corrections are often made for the distortion of the trajectories that is caused by the Coulomb field. These approximations are tested by comparing to numerical calculations that use exact Coulomb trajectories. In this paper a model is devised for including relativistic effects in the calculations. It converges at high energies towards the relativistic straight-line trajectory approximation and approaches the non-relativistic Coulomb trajectory calculation at low energies. The model is tested against a number of measurements and analyses that have been performed at beam energies between 30 and 70 MeV/nucleon, primarily of quadrupole excitations. Remarkably good agreement is achieved with the previous analyses, and good agreement is also achieved in the few cases, where the B(E$\lambda$) value is known from other methods. The magnitudes of the relativistic and Coulomb distortion effects are discussed.

Fusion data for $^{16}$O+$^{16}$O are analyzed by coupled-channels calculations. It is shown that the calculated cross sections are sensitive to the couplings to the $2^+$ and $3^-$ excitation channels even at low energies, where these channels are closed. The sensitivity to the ion-ion potential is investigated by applying a conventional Woods-Saxon potential and the M3Y+repulsion potential, consisting of the M3Y double-folding potential and a repulsive term that simulates the effect of the nuclear incompressibility. The best overall fit to the data is obtained with a M3Y+repulsion potential which produces a shallow potential in the entrance channel. The stepwise increase in measured fusion cross sections at high energies is also consistent with such a shallow potential. The steps are correlated with overcoming the barriers for the angular momenta $L$ = 12, 14, 16, and 18. To improve the fit to the low-energy data requires a shallower potential and this causes a even stronger hindrance of fusion at low energies. It is therefore difficult, based on the existing fusion data, to make an accurate extrapolation to energies that are of interest to astrophysics., Comment: 18 pages, 7 figures

We investigate the consistency of the measured charge radius and dipole response of $^{11}$Li within a three-body model. We show how these observables are related to the mean square distance between the $^9$Li core and the center of mass of the two valence neutrons. In this representation we find by considering the effect of smaller corrections that the discrepancy between the results of the two measurements is of the order of 1.5$\sigma$. We also investigate the sensitivity to the three-body structure of $^{11}$Li and find that the charge radius measurement favors a model with a 50% s-wave component in the ground state of the two-neutron halo, whereas the dipole response is consistent with a smaller s-wave component of about 25% value., Comment: 6 pages, 3 figures

We extend a recent study that explained the steep falloff in the fusion cross section at energies far below the Coulomb barrier for the symmetric dinuclear system 64Ni+64Ni to another symmetric system, 58Ni+58Ni, and the asymmetric system 64Ni+100Mo. In this scheme the very sensitive dependence of the internal part of the nuclear potential on the nuclear equation of state determines a reduction of the classically allowed region for overlapping configurations and consequently a decrease in the fusion cross sections at bombarding energies far below the barrier. Within the coupled-channels method, including couplings to the low-lying 2+ and 3- states in both target and projectile as well as mutual and two-phonon excitations of these states, we calculate and compare with the experimental fusion cross sections, S-factors, and logarithmic derivatives for the above mentioned systems and find good agreement with the data even at the lowest energies. We predict, in particular, a distinct double peaking in the S-factor for the far subbarrier fusion of 58Ni+58Ni which should be tested experimentally., Comment: 34 pages, 10 figures, to appear in Phys. Rev. C

We propose a new mechanism to explain the unexpected steep falloff of fusion cross sections at energies far below the Coulomb barrier. The saturation properties of nuclear matter are causing a hindrance to large overlap of the reacting nuclei and consequently a sensitive change of the nuclear potential inside the barrier. We report in this letter a good agreement with the data of coupled-channels calculation for the {64}Ni+{64}Ni combination using the double-folding potential with M3Y-Reid effective N-N forces supplemented with a repulsive core that reproduces the nuclear incompressibility for total overlap., Comment: 4 pages, 3 figures

Measured cross sections for the fusion of {64}Ni with {64}Ni, {74}Ge, and {100}Mo targets are analyzed in a coupled-channels approach. The data for the {64}Ni target above 0.1 mb are reproduced by including couplings to the low-lying 2^+ and 3^- states and the mutual and two-phonon excitations of these states. The calculations become more challenging as the fusing nuclei become softer and heavier, and excitations to multi-phonon states start to play an increasingly important role. Thus it is necessary to include up to four-phonon excitations in order to reproduce the data for the {64}Ni+{74}Ge system. Similar calculations for {64}Ni+{100}Mo, and also for the symmetric {74}Ge+{74}Ge system, show large discrepancies with the data. Possible ways to improve the calculations are discussed., Comment: 24 pages, 7 figures, 4 tables

The recent discovery of hindrance in heavy-ion induced fusion reactions at extreme sub-barrier energies represents a challenge for theoretical models. Previously, it has been shown that in medium-heavy systems, the onset of fusion hindrance depends strongly on the "stiffness" of the nuclei in the entrance channel. In this work, we explore its dependence on the total mass and the $Q$-value of the fusing systems and find that the fusion hindrance depends in a systematic way on the entrance channel properties over a wide range of systems., Comment: Submitted to Phys. Rev. Lett., 5 pages, 3 figures

The excitation function for the fusion-evaporation reaction 64Ni+100Mo has been measured down to a cross-section of ~5 nb. Extensive coupled-channels calculations have been performed, which cannot reproduce the steep fall-off of the excitation function at extreme sub-barrier energies. Thus, this system exhibits a hindrance for fusion, a phenomenon that has been discovered only recently. In the S-factor representation introduced to quantify the hindrance, a maximum is observed at E_s=120.6 MeV, which corresponds to 90% of the reference energy E_s^ref, a value expected from systematics of closed-shell systems. A systematic analysis of Ni-induced fusion reactions leading to compound nuclei with mass A=100-200 is presented in order to explore a possible dependence of the fusion hindrance on nuclear structure., Comment: 10 pages, 9 figures, Submitted to Phys. Rev. C

Fusion-evaporation cross sections for $^{64}$Ni+$^{64}$Ni have been measured down to the 10 nb level. For fusion between two open-shell nuclei, this is the first observation of a maximum in the $S$-factor, which signals a strong sub-barrier hindrance. A comparison with the $^{58}$Ni+$^{58}$Ni, $^{58}$Ni+$^{60}$Ni, and $^{58}$Ni+$^{64}$Ni systems indicates a strong dependence of the energy where the hindrance occurs on the stiffness of the interacting nuclei., Comment: Submitted to Phys. Rev. Lett. 4 pages, 3 figures

Angular distributions of oxygen produced in the breakup of $^{17}$F incident on a $^{208}$Pb target have been measured around the grazing angle at beam energies of 98 and 120 MeV. The data are dominated by the proton stripping mechanism and are well reproduced by dynamical calculations. The measured breakup cross section is approximately a factor of 3 less than that of fusion at 98 MeV. The influence of breakup on fusion is discussed., Comment: 7 pages, 8 figures

We derive a general expression for the multipole expansion of the electro-magnetic interaction in relativistic heavy-ion collisions, which can be employed in higher-order dynamical calculations of Coulomb excitation. The interaction has diagonal as well as off-diagonal multipole components, associated with the intrinsic and relative coordinates of projectile and target. A simple truncation in the off-diagonal components gives excellent results in first-order perturbation theory for distant collisions and for beam energies up to 200 MeV/nucleon., Comment: 3 figures, Accepted for publication in Phys. Rev. C

Angular distributions of fluorine and oxygen produced from 170 MeV 17^F incident on 208^Pb were measured. The elastic scattering data are in good agreement with optical model calculations using a double-folding potential and parameters similar to those obtained from 16^O+208^Pb. A large yield of oxygen was observed near \theta_lab=36 deg. It is reproduced fairly well by a calculation of the (17^F,16^O) breakup, which is dominated by one-proton stripping reactions. The discrepancy between our previous coincidence measurement and theoretical predictions was resolved by including core absorption in the present calculation., Comment: 9 pages, 5 figures

In an effort to better determine the 7Be(p,gamma)8B reaction rate, we have performed inclusive and exclusive measurements of the Coulomb dissociation of 8B. The former was a study of longitudinal momentum distributions of 7Be fragments emitted in the Coulomb breakup of intermediate energy 8B beams on Pb and Ag targets. Analysis of these data yielded the E2 contribution to the breakup cross section. In the exclusive measurement, we determined the cross section for the Coulomb breakup of 8B on Pb at low relative energies in order to infer the astrophysical S factor for the 7Be(p,gamma)8B reaction. Interpreting the measurements with 1st-order perturbation theory, we obtained SE2/SE1 = 4.7 (+ 2.0,- 1.3) times 10^-4 at Erel = 0.6 MeV, and S17(0) = 17.8 (+ 1.4,- 1.2) eV b. Semiclassical 1st-order perturbation theory and fully quantum mechanical continuum-discretized coupled channels analyses yield nearly identical results for the E1 strength relevant to solar neutrino flux calculations, suggesting that theoretical reaction mechanism uncertainties need not limit the precision of Coulomb breakup determinations of the 7Be(p,gamma)8B S factor. A recommended value of S17(0) based on a weighted average of this and other measurements is presented.

A kinematically complete measurement was made of the Coulomb dissociation of 8B nuclei on a Pb target at 83 MeV/nucleon. The cross section was measured at low relative energies in order to infer the astrophysical S factor for the 7Be(p,gamma)8B reaction. A first-order perturbation theory analysis of the reaction dynamics including E1, E2, and M1 transitions was employed to extract the E1 strength relevant to neutrino-producing reactions in the solar interior. By fitting the measured cross section from Erel = 130 keV to 400 keV, we find S17(0) = 17.8 (+1.4, -1.2) eV b.

The inner crust of a neutron star is a superfluid and inhomogeneous system, consisting of a lattice of nuclei immersed in a sea of neutrons. We perform a quantum calculation of the associated pairing gap and compare it to the results one obtains in the Local Density Approximation (LDA). It is found that the LDA overestimates the spatial dependence of the gap, and leads to a specific heat of the system which is too large at low temperatures, as compared with the quantal result. This is caused by the neglect of proximity effects and the delocalized character of the single-particle wavefunctions close to the Fermi energy. It is possible to introduce an alternative, simple semiclassical approximation of the pairing gap which leads to a specific heat that is in good agreement with the quantum calculation., Comment: RevteX, 8 Postscript Figures

In an effort to understand the implications of Coulomb dissociation experiments for the determination of the 7Be(p,gamma)8B reaction rate, longitudinal momentum distributions of 7Be fragments produced in the Coulomb dissociation of 44 and 81 MeV/nucleon 8B beams on a Pb target were measured. These distributions are characterized by asymmetries interpreted as the result of interference between E1 and E2 transition amplitudes in the Coulomb breakup. At the lower beam energy, both the asymmetries and the measured cross sections are well reproduced by perturbation theory calculations, allowing a determination of the E2 strength., Comment: 8 pages, 3 figures

We study the eikonal model for the nuclear-induced breakup of Borromean nuclei, using Li11 and He6 as examples. The full eikonal model is difficult to realize because of six-dimensional integrals, but a number of simplifying approximations are found to be accurate. The integrated diffractive and one-nucleon stripping cross sections are rather insensitive to the neutron-neutron correlation, but the two-nucleon stripping does show some dependence on the correlation. The distribution of excitation energy in the neutron-core final state in one-neutron stripping reactions is quite sensitive to the shell structure of the halo wave function. Experimental data favor models with comparable amounts of s- and p-wave in the Li11 halo., Comment: 34 pages REVTeX, 14 postscript figures. Small changes in comparison with experiment