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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.

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.

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.

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.

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

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.

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 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.

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

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.}

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 ${}^{40}\mathrm{Ca}+{}^{48}\mathrm{Ca}$.

The fusion cross section for ${}^{12}$C+${}^{13}$C has been measured down to ${E}_{\mathrm{c}.\mathrm{m}.}=2.6$ MeV, at which the cross section is of the order of 20 nb. By comparing the cross sections for the three carbon isotope systems, ${}^{12}$C+${}^{12}$C, ${}^{12}$C+${}^{13}$C, and ${}^{13}$C+${}^{13}$C, it is found that the cross sections for ${}^{12}$C+${}^{13}$C and ${}^{13}$C+${}^{13}$C provide an upper limit for the fusion cross section of ${}^{12}$C+${}^{12}$C over a wide energy range. After calibrating the effective nuclear potential for ${}^{12}$C+${}^{12}$C using the ${}^{12}$C+${}^{13}$C and ${}^{13}$C+${}^{13}$C fusion cross sections, it is found that a coupled-channels calculation with the ingoing wave boundary condition (IWBC) is capable of predicting the major peak cross sections in ${}^{12}$C+${}^{12}$C. A qualitative explanation for this upper limit is provided by the Nogami-Imanishi model and by level density differences among the compound nuclei. It is found that the strong resonance found at 2.14 MeV in ${}^{12}$C+${}^{12}$C exceeds this upper limit by a factor of more than 20. The preliminary result from the most recent measurement shows a much smaller cross section at this energy, which agrees with our predicted upper limit.

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

The structure of 15 C, with an s1/2 neutron weakly bound to a closed-neutron shell nucleus 14 C, 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 15 C + 232 Th at energies in the vicinity of the Coulomb barrier and compared it to the yield of the neighboring 14 C + 232 Th system measured in the same experiment. At sub-barrier energies, an enhancement of the fusion yield by factors of 2-5 was observed for 15 C, while the cross sections for 14 C match the trends measured for 12,13 C.

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., 4 pages, 2 figures, Phys. Rev. Lett. (accepted)

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

The coupled-channels technique is applied to analyze recent fusion data for {sup 48}Ca+{sup 48}Ca. The calculations include the excitations of the low-lying 2{sup +}, 3{sup -}, and 5{sup -} 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.

The complete fusion of {sup 9}Be with {sup 144}Sm and {sup 208}Pb targets is calculated in the coupled-channels approach. The calculations include couplings among the 3/2{sup -}, 5/2{sup -}, and 7/2{sup -} states in the K=3/2 ground-state rotational band of {sup 9}Be. It is shown that the B(E2) values for the excitation of these states are accurately described in the rotor model. The interaction of the strongly deformed {sup 9}Be nucleus with a spherical target is calculated using the double-folding technique and the effective M3Y interaction, which is supplemented with a repulsive term that is adjusted to optimize the fit to the data for the {sup 144}Sm target. The complete fusion is described by ingoing-wave boundary conditions. The decay of the unbound excited states in {sup 9}Be is considered explicitly in the calculations by using complex excitation energies. The model gives an excellent account of the complete fusion (CF) data for {sup 9}Be+{sup 144}Sm, and the cross sections for the decay of the excited states are in surprisingly good agreement with the incomplete fusion (ICF) data. Similar calculations for {sup 9}Be+{sup 208}Pb explain the total fusion data at high energies but fail to explain the CF data, which are suppressedmore » by 20%, and the calculated cross section for the decay of excited states is a factor of 3 smaller than the ICF data at high energies. Possible reasons for these discrepancies are discussed.« less

Fusion evaporation cross sections for the {sup 27}Al+{sup 45}Sc (Q=9.63 MeV) system are measured down to about 300 nb. Deviations from standard coupled-channels calculations were observed in this system at the lowest energies. The steep fall-off of the fusion cross sections can be reproduced by calculations using a shallow potential model, which was originally developed to explain the hindrance behavior of heavy-ion fusion in medium-mass systems with negative Q values. Comparisons of the hindrance behavior between the present experiment and other systems, for example, {sup 28}Si+{sup 30}Si (Q=14.3 MeV) and {sup 36}S+{sup 48}Ca (Q=7.55 MeV) are presented.

We have studied the effect of the spatial correlation between the valence neutrons in 11 Li on the double-charge exchange reaction 11 B(π − , π + ) 11 Li. The spatial correlation enhances the forward angle cross section by a factor of 2–3 compared to the prediction of an independent particle description.

The semiclassical, dynamical description of diffraction dissociation of weakly bound nuclei is applied to analyze the decay-energy spectra of $^{15}\mathrm{C}$ that have been measured at 68 MeV/nucleon on a Pb target. The optical potentials that are used to describe the nuclear interaction of $^{15}\mathrm{C}$ 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 $^{14}\mathrm{C}$ to the ${1/2}^{+}$ ground state of $^{15}\mathrm{C}$ is deduced from the analysis. When combined with an estimated contribution from the capture to the ${5/2}^{+}$ excited state of $^{15}\mathrm{C}$, an excellent agreement with a recent direct capture measurement is achieved.

We exploit a model describing the break-up of weakly-bound nuclei that can be used as a laboratory for testing different prescriptions that have been advanced in the literature to take into account the near-by presence of continuum states. In the model we follow the evolution of a single particle wave function in one dimension, initially bound by a Woods-Saxon type potential and then perturbed by a time- and position-dependent external field. Proper choices of this potential can simulate the effect of the interaction between reaction partners in a nuclear collision. These processes generate inelastic excitation probabilities that - distributed over the bound and continuum states of the system - lead to either a partial or a total fragmentation of the final wave function. The comparison with the exact calculations shows that standard coupled channel descriptions based on discretization of the continuum can be accurate only when a proper choice is made of the number of discrete states, of the energy mesh and of the energy cutoff. This may imply, even in simplified cases. the use of a rather large (and unpracticable) number of channels. The use of a more restricted number of channels may lead to misleading results.

We propose a two‐step model for heavy‐ion fusion reactions based on the adiabatic approach in order to account for steep fall‐off of fusion cross sections at deep subbarrier energies. The two‐step model consists of the capture process in the two‐body potential pocket, which is followed by the penetration of the adiabatic one‐body potential to reach a compound state after the touching configuration. We argue that although the sudden and adiabatic approaches provide a similar result to each other for the fusion cross section, the two approaches can be discriminated by detecting average angular momenta of a compound nuclei.

The mass distributions for giant dipole resonances in 32S and 132Sn decaying through particle emission and for deep-inelastic collisions between 16O nuclei have been investigated by implementing the Balian-Veneroni variational technique based upon a three-dimensional time-dependent Hartree-Fock code with realistic Skyrme interactions. The mass distributions obtained have been shown to be significantly larger than the standard TDHF results., 6 pages, 2 figures, Based on talk by J. M. A. Broomfield at the FUSION08 Conference, Chicago, September 22-26, 2008. Conference proceedings to be published by AIP

The exact evolution of a system coupled to a complex environment can be described by a stochastic mean-field evolution of the reduced system density. The formalism developed in Ref. [D.Lacroix, Phys. Rev. E77, 041126 (2008)] is illustrated in the Caldeira-Leggett model where a harmonic oscillator is coupled to a bath of harmonic oscillators. Similar exact reformulation could be used to extend mean-field transport theories in Many-body systems and incorporate two-body correlations beyond the mean-field one. The connection between open quantum system and closed many-body problem is discussed., Proceedings series of Proceedings of "FUSION08: New Aspects of Heavy Ion Collisions near the Coulomb Barrier", September 22-26, 2008, Chicago, USA

Nucleus-nucleus interaction potentials in heavy-ion fusion reactions are extracted from the microscopic time-dependent Hartree-Fock theory. When the center-of-mass energy is much higher than the Coulomb barrier energy, extracted potentials identify with the frozen density approximation. As the center-of-mass energy decreases to the Coulomb barrier energy, potentials become energy dependent. This dependence indicates dynamical reorganization of internal degrees of freedom and leads to a reduction of the "apparent" barrier. Including this effect leads to the Coulomb barrier energy very close to experimental one. Aspects of one-body energy dissipation extracted from the mean-field theory are discussed., 6 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

We investigate the origin of the effects observed in the fusion cross section of light weakly bound nuclei, through a review of the most recent experimental and theoretical works. In particular we focus on the well‐documented fusion suppression at energies just above the potential barrier. We show that, besides the couplings to the breakup process, effects due to the couplings to transfer need be taken into account. The magnitude of the cross section for the direct process, breakup or transfer, is not a reliable indicator of the size of the effects induced on the elastic scattering and fusion.