Search

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

Background: Recent measurements of fusion cross sections for the 28 Si + 28 Si system revealed a rather unsystematic behavior; i.e., they drop faster near the barrier than at lower energies. This was tentatively attributed to the large oblate deformation of 28 Si because coupled-channels (CC) calculations largely underestimate the 28 Si + 28 Si cross sections at low energies, unless a weak imaginary potential is applied, probably simulating the deformation. 30 Si has no permanent deformation and its low-energy excitations are of a vibrational nature. Previous measurements of this system reached only 4 mb, which is not sufficient to obtain information on effects that should show up at lower energies. Purpose: The aim of the present experiment was twofold: (i) to clarify the underlying fusion dynamics by measuring the symmetric case 30 Si + 30 Si in an energy range from around the Coulomb barrier to deep sub-barrier energies, and (ii) to compare the results with the behavior of 28 Si + 28 Si involving two deformed nuclei. Methods: 30 Si beams from the XTU tandem accelerator of the Laboratori Nazionali di Legnaro of the Istituto Nazionale di Fisica Nucleare were used, bombarding thin metallic 30 Si targets (50 µ g / cm 2 ) enriched to 99 . 64% in mass 30. An electrostatic beam deflector allowed the detection of fusion evaporation residues (ERs) at very forward angles, and angular distributions of ERs were measured. Results: The excitation function of 30 Si + 30 Si was measured down to the level of a few microbarns. It has a regular shape, at variance with the unusual trend of 28 Si + 28 Si. The extracted logarithmic derivative does not reach the L CS limit at low energies, so that no maximum of the S factor shows up. CC calculations were performed including the low-lying 2 + and 3 - excitations. Conclusions: Using a Woods-Saxon potential the experimental cross sections at low energies are overpredicted, and this is a clear sign of hindrance, while the calculations performed with a M3Y + repulsion potential nicely fit the data at low energies, without the need of an imaginary potential. The comparison with the results for 28 Si + 28 Si strengthens the explanation of the oblate shape of 28 Si being the reason for the irregular behavior of that system.

In this review the main advances in heavy-ion fusion research that have taken place over the last decade are addressed. During this period, experimental studies have been extended to deep subbarrier energies to reveal the unexpected phenomenon of fusion hindrance. The coupled-channels descriptions have been refined to include the effects of nucleon transfer and to account for the fusion hindrance in terms of the ion-ion potential in the strongly overlapping region. Substantial progress has been made in time-dependent Hartree-Fock theory to the point that this approach now can make parameter-free predictions of heavy-ion fusion excitation functions. As several heavy-ion fusion reactions are of crucial importance in late-stage giant-star evolution, these reactions continue to be studied with better experimental and theoretical tools in order to provide improved input to astrophysical models. The effects of loosely bound valence nucleons on the fusion cross sections are the focus of a number of experimental studies involving radioactive beams, which have only recently become available. And finally, as the active field of synthesizing superheavy elements relies on heavy-ion fusion to reach the nuclei of interest, it is important to understand the fusion dynamics that plays a crucial role in both the “cold-fusion” and “hot-fusion” approaches to the superheavy island of stability. Also this area has seen significant progress in several different approaches to the problem of predicting the cross sections for formation and survival of these rare nuclei.

A study of fusion-barrier distributions through an analysis of their moments is presented. The moments can be obtained from least-squares fits of the energy-weighted fusion cross sections without the need of calculating second derivatives. The zeroth and first moments determine the fusion radius $R$ and the Coulomb barrier ${V}_{C}$. These two quantities are the same as the parameters $R$ and ${V}_{C}$ that are used in the well-known expression, $E\ensuremath{\sigma}=\ensuremath{\pi}{R}^{2}(E\ensuremath{-}{V}_{C})$, for the fusion cross section at high energies. The second and third moments, ${M}_{2}$ and ${M}_{3}$, determine the width and skewness of the barrier distribution, respectively. From these global parameters new correlations for the study of heavy-ion-induced fusion reactions can be obtained. Systems exhibiting a large coupling to transfer reactions show a small fusion radius as well as a large second moment. A negative third moment is correlated with a prolate deformation of the target nucleus.

Fusion data for 40Ca + 96Zr 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 those 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 √2 one obtains an excellent fit. Finally, 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.

Angular distributions of the Coulomb breakup of radioactive 17F were measured by impinging a 10 MeV/nucleon beam on 208Pb and on 58Ni to study the dynamic polarization effects. The breakup products, oxygen and a proton, were detected in coincidence. First-order perturbation theory significantly overpredicts the breakup cross section for the 208Pb target. Dynamical calculations with a dynamic polarization as the leading order correction were performed. The calculations reproduce the data for 17F on 58Ni but overpredict the breakup of 17F on 208Pb by a factor of two at forward angles.

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

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, I briefly summarise the assumptions made within the modelling of reactions involving halo nuclei. I 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. I show the problem faced by the eikonal approximation at low energy and detail a correction that enables its 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., SCOPUS: cp.j, info:eu-repo/semantics/published

A detection technique for high-efficiency measurements of fusion reactions with low-intensity radioactive beams was developed. The technique is based on a Multi-Sampling Ionization Chamber (MUSIC) operating as an active target and detection system, where the ionization gas acts as both target and counting gas. In this way, we can sample an excitation function in an energy range determined by the gas pressure, without changing the beam energy. The detector provides internal normalization to the incident beam and drastically reduces the measuring time. In a first experiment we tested the performance of the technique by measuring the 10,13,15C+12C fusion reactions at energies around the Coulomb barrier. Fil: Carnelli, Patricio Francisco Florencio. Argonne National Laboratory; Estados Unidos. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia Física (Centro Atómico Constituyentes). Proyecto Tandar; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Almaraz Calderón, S.. Argonne National Laboratory; Estados Unidos Fil: Rehm, K. E.. Argonne National Laboratory; Estados Unidos Fil: Albers, M.. Argonne National Laboratory; Estados Unidos Fil: Alcorta, M.. Argonne National Laboratory; Estados Unidos Fil: Bertone, P. F.. Argonne National Laboratory; Estados Unidos Fil: Digiovine, B.. Argonne National Laboratory; Estados Unidos Fil: Esbensen, H.. Argonne National Laboratory; Estados Unidos Fil: Fernandez Niello, Jorge Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia Física (Centro Atómico Constituyentes). Proyecto Tandar; Argentina Fil: Henderson, D.. Argonne National Laboratory; Estados Unidos Fil: Jiang, C. L.. Argonne National Laboratory; Estados Unidos Fil: Lai, J.. Argonne National Laboratory; Estados Unidos Fil: Marley, S. T.. Argonne National Laboratory; Estados Unidos Fil: Nusair, O.. Argonne National Laboratory; Estados Unidos Fil: Palchan Hazan, T.. Argonne National Laboratory; Estados Unidos Fil: Pardo, R.. Argonne National Laboratory; Estados Unidos Fil: Paul, M.. The Hebrew University of Jerusalem; Israel Fil: Ugalde, C.. Argonne National Laboratory; Estados Unidos

Measurements of fusion excitation functions of Ni58+Sn124 and Ni64+Sn124 are extended towards lower energy to cross sections of 1 μb and are compared to detailed coupled-channels calculations. The calculations clearly show the importance of including transfer reactions in a coupled-channels treatment for such heavy systems. This result is different from the conclusion made in a previous article which claimed that the influence of transfer on fusion is not important for fusion reactions of Ni+Sn. In the energy region studied in this experiment no indication of fusion hindrance has been observed, which is consistent with a systematic study of this behavior.

Measurements of fusion excitation functions of Ni-58 + Sn-124 and Ni-64 + Sn-124 are extended towards lower energy to cross sections of 1 mu b and are compared to detailed coupled-channels calculations. The calculations clearly show the importance of including transfer reactions in a coupled-channels treatment for such heavy systems. This result is different from the conclusion made in a previous article which claimed that the influence of transfer on fusion is not important for fusion reactions of Ni + Sn. In the energy region studied in this experiment no indication of fusion hindrance has been observed, which is consistent with a systematic study of this behavior.

The excitation function for the fusion–evaporation reaction Si 28 + Ni 64 has been measured down to a cross section of 25 nb. This is the first observation of fusion hindrance at extreme sub-barrier energies for a system with a small, negative Q-value ( − 1.78 MeV ). This result is further proof that heavy-ion fusion hindrance, reported earlier only for systems with large, negative Q-values, is a general phenomenon. The measured behavior can be reproduced by coupled-channels calculations with a modified ion–ion potential incorporating the effects of nuclear incompressibility.

A new measurement of fusion reactions down to 10 nb has been performed for the system 64 Ni + 64 Ni. Coupled-channels analyses have been carried out for the systems 60 Ni + 89 Ya nd 64 Ni + 64 Ni. They demonstrate that coupled-channels calculations are unable to reproduce the unexpected steep falloff of the cross sections at extreme sub-barrier energies. Heavy-ion fusion excitation functions are also analyzed in terms of the S factor, as this offers a pragmatic way to study fusion behavior in the energy regime of interest. It is shown that the steep falloff in cross section observed in several heavy-ion systems translates into a maximum of the S factor. The energies where the maximum occurs can be parameterized with a simple empirical formula. The parameterization, which is derived here for rather stiff heavy-ion systems, provides also an upper limit for reactions involving softer nuclei. The asymptotic behavior of reaction cross sections at very low energies is a critical issue for calculating reaction rates of astrophysical interest. Recently, it was pointed out that fusion cross sections for several heavy-ion systems show an unexpected behavior at very low energies, 1) with a much steeper falloff than predicted by coupled-channels calculations, 2) or from Wong’s formula. 3) In the present work, we first present a new result for the excitation function in an open-shell system, 64 Ni + 64 Ni down to the 10 nb level, we then analyse in a coupled-channels description the fusion of 60 Ni + 89 Ya nd 64 Ni + 64 Ni, i.e. the systems which have been measured to extreme sub-barrier energies. Fusion reactions at extreme sub-barrier energies are then studied in a representation in terms of the S factor. This parametrization, which in the past has been successfully applied to fusion reactions with lighter ions at low energies, proves to be an alternative and pragmatic way of characterizing and exploring the behavior of heavy-ion fusion cross sections in the energy domain of interest. To our surprise, a maximum appears systematically in the evolution of S with decreasing energy for all systems that exhibit the steep falloff in cross section described above. This maximum occurs at rather high excitation energies in the compound nucleus.

The approximations that are commonly made in coupled-channels calculations of heavy-ion fusion reactions are reviewed in order to show where uncertainties exist and improvements can be made. In particular, the failure in modeling the fusion at extreme subbarrier energies is discussed.

In this paper we discuss the excitation of a quantum harmonic system, such as a particle bound in a harmonic oscillator potential, by means of dipole and quadrupole electric fields, focusing on effects of their interference. We obtain an exact solution to this problem with methods that date back to the ideas of Wigner. We discuss the rich class of dynamic polarization effects that are involved in such excitation processes and which are relevant to stopping theory, and electromagnetic excitation of atomic and nuclear systems.

Total fusion cross section of carbon isotopes were obtained using the newly developed MUSIC detector. MUSIC is a highly efficient, active target-detector system designed to measure fusion excitation functions with radioactive beams. The present measurements are relevant for understanding x-ray superbursts. The results of the first MUSIC campaign as well as the astrophysical implications are presented in this work.

The sub-barrier fusion excitation function of Ca-40 + Zr-96 has been measured down to cross sections similar or equal to 2.4 mu b, i.e. two orders of magnitude smaller than obtained in the previous experiment, where the sub-barrier fusion of this system was found to be greatly enhanced with respect to Ca-40 + Zr-90, and the need of coupling to transfer channels was suggested. The purpose of this work was to investigate the behavior of Ca-40 + Zr-96 fusion far below the barrier. The smooth trend of the excitation function has been found to continue, and the logarithmic slope increases very slowly. No indication of hindrance shows up, and a comparison with Ca-48 + Zr-96 is very useful in this respect. A new CC analysis of the complete excitation function has been performed, including explicitly one- and two-nucleon Q > 0 transfer channels. Such transfer couplings bring significant cross section enhancements, even at the level of a few mu b. Locating the hindrance threshold, if any, in Ca-40 + Zr-96 would require challenging measurements of cross sections in the sub-mu b range.

The two-body breakup 17 F → 16 O + p on Ni and Pb targets at 10–40 MeV/u is calculated by solving the time-dependent Schrodinger equation numerically. Both Coulomb and the nuclear potentials are important in these reactions, but the Coulomb contribution cannot be calculated reliably in first-order perturbation theory. The most dramatic feature is a dynamic polarization effect, which reduces the Coulomb dissociation probability compared to first-order perturbation theory. Over most of the energy range, the correction is proportional to Z 3 , the cube of the target charge, and the relative importance is nearly inversely proportional to the beam energy. At the lowest energies in the range considered, higher-order effects ( Z 3 ) become significant as well. At the impact parameters where nuclear induced breakup is dominant, the diffraction dissociation is reduced whereas stripping is enhanced compared to the eikonal approximation. Here too the deviations decrease inversely with beam energy over most of the range considered.  2002 Elsevier Science B.V. All rights reserved.

We present preliminary results of a kinematically complete measurement of the Coulomb dissociation of 83 MeV/u 8B on a Pb target. A dipole magnet separated the unreacted beam from the breakup fragments. We measured the Coulomb dissociation cross section at low relative energies in order to extract the astrophysical S factor for the 7Be(p, γ )8B reaction.

We discuss new theoretical results on the decay of deformed and near-spherical nuclei. We interpret the latest experimental results on deformed odd-A proton emitters, including fine structure, and discuss the use of particle-vibration coupling to calculate the decay rates of near-spherical emitters.

Fragmentation reactions offer a useful tool to study the spectroscopy of halo nuclei, but the large extent of the halo wave function makes the reaction theory more difficult. The simple reaction models based on the eikonal approximation for the nuclear interaction or first-order perturbation theory for the Coulomb interaction have systematic errors that they investigate here, comparing to the predictions of complete dynamical calculations. They find that stripping probabilities are underpredicted by the eikonal model, leading to extracted spectroscopy strengths that are two large. In contrast, the Coulomb excitation is overpredicted by the simple theory. They attribute this to a screening effect, as is well known in the Barkas effect on stopping powers. The errors decrease with beam energy as E{sub beam}{sup -1}, and are not significant at beam energies above 50 MeV/u. At lower beam energies, the effects should be taken into account when extracting quantitative spectroscopic strengths.

Background: The fusion excitation function of the system $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ at energies near and below the Coulomb barrier is known only down to $\ensuremath{\simeq}15$ mb. This precludes any information on both coupling effects on sub-barrier cross sections and the possible appearance of hindrance. For $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$ even if the fusion cross section is measured down to $\ensuremath{\simeq}50$ $\ensuremath{\mu}\mathrm{b}$, the evidence of hindrance is marginal. Both systems have positive fusion $Q$ values. While $^{28}\mathrm{Si}$ has a deformed oblate shape, $^{30}\mathrm{Si}$ is spherical.Purpose: We investigate 1. the possible influence of the different structure of the two Si isotopes on the fusion excitation functions in the deep sub-barrier region and 2. whether hindrance exists in the $\text{Si}\phantom{\rule{4.pt}{0ex}}+\phantom{\rule{4.pt}{0ex}}\text{Si}$ systems and whether it is strong enough to generate an $S$-factor maximum, thus allowing a comparison with lighter heavy-ion systems of astrophysical interest.Methods: $^{28}\mathrm{Si}$ beams from the XTU Tandem accelerator of the INFN Laboratori Nazionali di Legnaro were used. The setup was based on an electrostatic beam separator, and fusion evaporation residues (ER) were detected at very forward angles. Angular distributions of ER were measured.Results: Fusion cross sections of $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ have been obtained down to $\ensuremath{\simeq}600$ nb. The slope of the excitation function has a clear irregularity below the barrier, but no indication of a $S$-factor maximum is found. For $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$ the previous data have been confirmed and two smaller cross sections have been measured down to $\ensuremath{\simeq}4$ $\ensuremath{\mu}\mathrm{b}$. The trend of the $S$-factor reinforces the previous weak evidence of hindrance.Conclusions: The sub-barrier cross sections for $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ are overestimated by coupled-channels calculations based on a standard Woods-Saxon potential, except for the lowest energies. Calculations using the M3Y+repulsion potential are adjusted to fit the $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ and the existing $^{30}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$ data. An additional weak imaginary potential (probably simulating the effect of the oblate $^{28}\mathrm{Si}$ deformation) is required to fit the low-energy trend of $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$. The parameters of these calculations are applied to predict the ion-ion potential for $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$. Its cross sections are well reproduced by also including one- and successive two-neutron transfer channels, besides the low-lying surface excitations.

Measurements of the excitation function for the fusion of $^{24}\mathrm{Mg}+^{30}\mathrm{Si}$ $(Q=17.89\text{ }\text{ }\mathrm{MeV})$have been extended toward lower energies with respect to previous experimental data. The $S$-factor maximum observed in this large, positive-$Q$-value system is the most pronounced among such systems studied thus far. The significance and the systematics of an $S$-factor maximum in systems with positive fusion $Q$ values are discussed. This result would strongly impact the extrapolated cross sections and reaction rates in the carbon and oxygen burnings and, thus, the study of the history of stellar evolution.

The interaction between neutron-rich nuclei plays an important role for understanding the reaction mechanism of the fusion process as well as for the energy production through pycnonuclear reactions in the crust of neutron stars. We have performed the first measurements of the total fusion cross sections in the systems (10,14,15)C+(12)C using a new active target-detector system. In the energy region accessible with existing radioactive beams, a good agreement between the experimental and theoretical cross sections is observed. This gives confidence in our ability to calculate fusion cross sections for systems which are outside the range of today's radioactive beam facilities.

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., RevteX, 8 Postscript Figures

We discuss theoretical studies of the Giant Dipole (GDR) and Giant Quadrupole (GQR) Resonances in nuclei far from stability, based on self-consistent Hartree–Fock and RPA calculations. The soft dipole mode that has been observed in light halo nuclei is predicted to diminish in skin nuclei, due to couplings to the isovector GDR. However, some low-lying dipole strength is predicted to exist in the isoscalar channel as a compression mode. The isoscalar GQR is expected to be much broader in skin nuclei than in stable nuclei, and substantial strength is predicted below the isoscalar GQR. The isovector GQR strength is spread over a wide range of excitation energies, both in skin and stable nuclei.

A kinematically complete measurement was made of the Coulomb dissociation of ${}^{8}\mathrm{B}$ 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 ${}^{7}\mathrm{Be}(p,\ensuremath{\gamma}{)}^{8}\mathrm{B}$ reaction. A first-order perturbation theory analysis 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 ${E}_{\mathrm{rel}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}130$ to 400 keV, we find ${S}_{17}(0){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}17.8}_{\ensuremath{-}1.2}^{+1.4}\phantom{\rule{0ex}{0ex}}\mathrm{eV}\mathrm{b}$.

The breakup of radioactive 17 F into a proton and 16 O was measured by bombarding 208 Pb with 170 MeV 17 F. The angular correlations of the fragments and the energy distributions of the protons suggest that the dominant breakup mechanism is a direct process in which a proton is excited into the low energy continuum above the breakup threshold. The breakup cross section measured near the grazing angle is 6.6±0.7 mb/sr for analysis with postacceleration considered and 3.9±0.4 mb/sr without postacceleration. This cross section is small compared to the fusion cross section at energies near the Coulomb barrier, so the breakup can have little influence on the fusion process.

We calculate the different nuclear breakup cross sections (diffraction, stripping and absorption) within the Serber model for single-nucleon as well as two-neutron halos (so-called Borromean nuclei). In contrast to calculations up to now, we use realistic wave functions as well as a realistic model for the interaction with the target. We show results of our calculations for total as well as differential cross sections.

We investigate the validity of approximations that are sometimes made in calculating the nuclear induced breakup of halo nuclei. We find that a truncated coupled-channels calculations, in which the nuclear couplings between continuum states are ignored, gives almost the same result as a first-order calculation. However, the couplings are much too strong to justify these approximations. This is demonstrated in the frozen limit of a semiclassical description, where one can compare to exact results. We find in this limit that the one-neutron removal cross section of {sup 11}Be obtained in the approximate treatment is much larger than the exact result. This trend is also indicated at low energy by comparing a perturbative calculation of the breakup of {sup 8}B to the result of a more realistic treatment, which evolves the wave function of the valence proton essentially to all orders in the target fields. {copyright} {ital 1999} {ital The American Physical Society}

The electronic properties of nanoscale-size fibers can be studied by electron energy-loss spectroscopy with electron beams that pass near the fiber but do not penetrate it. We derive the formulas for the differential energy spectrum assuming that the fiber can be treated as a dielectric cylinder. The formula can be evaluated in closed form for a conducting wire; the spectrum displays the surface plasmon and a low-energy peak associated with charge-conduction modes that diverges inversely as the energy loss.

Cross sections for multineutron transfer reactions in {sup 58}Ni+{sup 124}Sn collisions have been measured with good particle identification at four energies around the Coulomb barrier. The angle- and energy-integrated multineutron transfer cross sections exhibit an exponential falloff with increasing number of transferred neutrons. The elastic scattering and one-nucleon transfer reaction data can be reproduced well by coupled-channels calculations and distorted-wave Born approximation calculations, respectively, using the same optical potential. The transfer probabilities for each transfer channel, plotted as a function of the distance of closest approach, fall on a common exponential curve; the slopes of these exponential falloff curves are discussed. {copyright} {ital 1998} {ital The American Physical Society}

The sub-barrier fusion excitation function of 40 Ca + 96 Zr has been measured down to cross sections ≃2.4 μb, i.e. two orders of magnitude smaller than obtained in a previous experiment, where the sub-barrier fusion of this system was found to be greatly enhanced with respect to 40 Ca + 90 Zr, and the need of coupling to transfer channels was suggested relying on coupled-channels calculations. The purpose of this work has been to investigate the behavior of 40 Ca + 96 Zr fusion far below the barrier, thereby disentangling the elusive interplay of effects due to inelastic couplings, transfer couplings and, possibly, the appearance of the fusion hindrance. The smooth trend of the excitation function has been found to continue, and the logarithmic slope increases very slowly. No indication of hindrance shows up, and a comparison with 48 Ca + 96 Zr is illuminating in this respect. A new CC analysis of the complete excitation function has been performed, including explicitly one- and two-nucleon Q>0 transfer channels. Such transfer couplings bring significant cross section enhancements, even at the level of a few μb. Locating the hindrance threshold, if any, in 40 Ca + 96 Zr would require challenging measurements of cross sections in the sub-μb range.

The influence of inelastic excitations on heavy-ion fusion is well established and can be quantitativly described by coupled-channels calculations. The influence of transfer channels, however, is still under debate. We have analyzed a large set of heavy-ion-induced fusion excitation functions involving nuclei with similar structures and show that there is a universal correlation between the shape (and enhancement) of the excitation function and the strength of the total neutron-transfer cross sections for systems ranging from light to heavy masses.

${}^{11}$Li and ${}^{6}$He are described as three-body systems using different approaches. We compare our technique, based on a density-dependent, cutoff, contact interaction between the valence neutrons, with a Faddeev approach which is based on realistic interactions. The ground state properties of a weakly bound two-neutron halo are described fairly well once the contact interaction has been adjusted and calibrated to produce a realistic scattering length and effective range.

The state dependent pairing gap is calculated for a Wigner cell lying in the inner crust of a neutron star, allowing neutrons to interact through the Argonne v14 potential. Although the values of the pairing gap will be renormalized by the induced interaction, the result found, that the pairing gap is sensitive to the presence of the finite atomic nucleus in the sea of free neutrons, is expected to be quite general.

The fusion excitation function of 60 Ni + 100 Mo has been measured from above the Coulomb barrier down to a cross section around 2 μb, looking for coupling and hindrance effects in this soft medium-mass system with positive Q-values for several neutron transfer channels. A comparison is made with previous results for 64 Ni + 100 Mo where no Q > 0 transfer channels exist and the hindrance effect is quite clear. The two excitation functions are very similar, as well as the corresponding logarithmic derivatives showing analogous saturations below the barrier. It appears that transfer couplings to Q > 0 channels seem to play a marginal role near and below the barrier for 60 Ni + 100 Mo , even if measurements of cross sections lower than 1 μb would be needed also for this system. Coupled-channels calculations confirm these observations and indicate that multi-phonon excitations dominate the fusion dynamics in the whole measured energy range.

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

Distributions of parallel and transverse momenta for {sup 7}Be fragments formed in the breakup of {sup 8}B have been measured at 41A MeV. The {ital p}{sub {parallel}} distributions are narrow (81{plus_minus}4 and 62{plus_minus}3MeV/{ital c} FWHM for Be and Au targets, respectively), comparable to those of neutron halo nuclei. Reaction mechanisms influence the {sup 7}Be momentum distributions, so they do not directly reflect the valence proton momentum wave function. We present reaction models that reproduce the distributions. {copyright} {ital 1996 The American Physical Society.}

We calculate the nuclear induced breakup of {sup 11}Be and {sup 8}B using a more realistic treatment of the diffraction and stripping processes than in previous work. The breakup is treated in the eikonal approximation with a profile function calculated from a realistic optical potential at low energies and from free nucleon-nucleon cross sections at high energies. This treatment gives a good description of measured breakup cross sections, as well as the longitudinal momentum distribution of the corelike fragments, which is narrower than predicted in the transparent limit. The real part of the potential is found to be significant and enhances the diffractive breakup at low energies. {copyright} {ital 1996 The American Physical Society.}

Total reaction cross sections, ${\mathrm{\ensuremath{\sigma}}}_{\mathit{R}}$, of 20--60A MeV $^{4,6,8}\mathrm{He}$, $^{6--9,11}\mathrm{Li}$, and $^{10}\mathrm{Be}$ were measured by injecting magnetically separated, focused, monoenergetic, identified secondary beams of those projectiles into a Si detector telescope and measuring their energy-deposition spectra. These ${\mathrm{\ensuremath{\sigma}}}_{\mathit{R}}$'s, accurate to about 3%, were compared with predictions of optical, strong absorption, and microscopic models. The latter gave the best overall fit to the data, providing long-tailed matter densities were assumed. The best available optical potentials generally overpredicted the data by about 10%. Strong absorption calculations, in which the isospin-dependent term is quite important, were often unsuccessful, especially for projectiles with large neutron excess. Two-neutron removal cross sections were measured for $^{6}\mathrm{He}$ and $^{11}\mathrm{Li}$; the $^{11}\mathrm{Li}$ data were slightly overpredicted by a microscopic model which includes correlation effects for the $^{11}\mathrm{Li}$ valence neutrons. Both 2n and 4n removal from $^{8}\mathrm{He}$ were observed, in about a 2:1 ratio. Subtraction analysis of the data indicates that $^{4}\mathrm{He}$ is a good core within $^{6}\mathrm{He}$ and $^{8}\mathrm{He}$, as is $^{9}\mathrm{Li}$ within $^{11}\mathrm{Li}$. \textcopyright{} 1996 The American Physical Society.

We examine the Coulomb dissociation of aB in a model that has both E1 and E2 matrix elements. We find that the interference between El and E2 amplitudes produces large asymmetries in the angular and momentum distributions of the emitted protons and 7Be fragments. By measuring these asymmetries one may be able to put constraints on the E2 component and thereby improve the accuracy of the E1 strength that can be extracted from Coulomb dissociation experiments. We also investigate the effect of higher-order dynamical processes and find that they reduce the asymmetries in reactions on high-Z targets. They also reduee the effect of E2 transitions on the dissociation probability and on the peak height of the decay energy spectrum compared to predictions of first-order perturbation theory.

The fusion excitation function of ${}^{32}$S + ${}^{48}$Ca has been experimentally studied in a wide energy range, from above the Coulomb barrier down to cross sections in the sub-$\ensuremath{\mu}$b region. The measurements were done at INFN--Laboratori Nazionali di Legnaro, using the ${}^{32}$S beam from the XTU Tandem accelerator. The excitation function has a smooth behavior below the barrier, and no evident hindrance character shows up in the measured energy region. The fusion barrier distribution has a peculiar shape with two distinct peaks of similar height, lower and higher than the Aky\"uz-Winther barrier. Coupled-channels calculations using the M3Y + repulsion potential are presented for this system and for ${}^{36}$S + ${}^{48}$Ca. The results of these calculations give a good account of the data, and indicate the influence of one- and two-nucleon transfer channels with positive $Q$ values, which are only open for ${}^{32}$S + ${}^{48}$Ca.

The fusion excitation function of 32S + 48Ca has been experimentally studied in a wide energy range, from above the Coulomb barrier down to cross sections in the sub- b region. The measurements were done at INFN-Laboratori Nazionali di Legnaro, using the 32S beam from the XTU Tandem accelerator. The excitation function has a smooth behavior below the barrier with a rather flat slope, and no maximum of astrophysical factor S vs. energy has been observed. However, other interesting features of the dynamics of this system can be noted. In particular, the fusion barrier distribution has an unusual shape with two peaks of similar height, lower and higher than the Akyuz-Winther barrier. Preliminary coupled- channels calculations and a comparison with nearby systems have been performed to get information on the possible influence of nucleon transfer channels with positive Q-value.

The interference between E1 and E2 in the Coulomb breakup of 8B strongly affects the angular distribution of the decay proton. Thus this measurement could provide empirical information on the magnitude of the E2 contribution, which has been the subject of recent controversy.

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., 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)

The fusion excitation function of ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ has been measured from well above the Coulomb barrier, down to low energies where the cross section is as small as $\ensuremath{\simeq}$20 $\ensuremath{\mu}$b, and the astrophysical $S$ factor possibly reaches a maximum vs energy. The results of coupled-channels calculations using the $\mathrm{M}3\mathrm{Y}+\mathrm{repulsion}$ potential are presented. A detailed comparison is made with recently published data on the fusion of ${}^{40}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ and of ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, including the excitation functions, their low-energy slopes and the barrier distributions. The presence of the fusion hindrance phenomenon in all cases is pointed out, as well as the influence of the strong octupole excitation in ${}^{40}$Ca and of nucleon transfer channels with positive $Q$ values in ${}^{40}\mathrm{Ca}+{}^{48}\mathrm{Ca}$.