Search Results (73 total)

An excitation function for the fusion reaction ²⁸Si + ³⁰Si (Q=14.3MeV) has been measured down to 40μb. Deviations from the behavior predicted by the optical model and standard coupled-channels calculations have been observed in this system. The fusion cross sections can be reproduced by a shallow potential model well, which was originally developed to explain the hindrance of heavy-ion fusion for systems with negative Q-values.

Fusion data for ¹⁶O+¹⁶O 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 that 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.

We analyze the fusion data for ¹⁶O+²⁰⁸Pb using coupled-channels calculations. We include couplings to the low-lying surface excitations of the projectile and target and study the effect of the (¹⁶O,¹⁷O) one-neutron pickup. The hindrance of the fusion data that is observed at energies far below the Coulomb barrier cannot be explained by a conventional ion-ion potential and defining the fusion in terms of ingoing-wave boundary conditions (IWBC). We show that the hindrance can be explained fairly well by applying the M3Y double-folding potential which has been corrected with a calibrated, repulsive term that simulates the effect of nuclear incompressibility. We show that the coupling to one-neutron transfer channels plays a crucial role in improving the fit to the data. The best fit is achieved by increasing the transfer strength by 25% relative to the strength that is required to reproduce the one-neutron transfer data. The larger strength is not unrealistic because the calculated inelastic plus transfer cross section is in good agreement with the measured quasielastic cross section. We finally discuss the problem of reproducing the fusion data at energies far above the Coulomb barrier. Here we do not account for the data when we apply the IWBC but the discrepancy is essentially eliminated by applying the M3Y+repulsion potential and a weak, short-ranged imaginary potential.

We investigate the consistency of the measured charge radius and dipole response of ¹¹Li within a three-body model. We show how these observables are related to the mean-square distance between the ⁹Li 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 1.5σ. We also investigate the sensitivity to the three-body structure of ¹¹Li 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.

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 data the 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 sub-barrier fusion of ⁵⁸Ni+⁵⁸Ni, which should be tested experimentally.

A Reply to the Comment by Moshe Gai.

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 ⁶⁴Ni+⁶⁴Ni combination using the double-folding potential with Michigan-3-Yukawa-Reid effective N-N forces supplemented with a repulsive core that reproduces the nuclear incompressibility for total overlap.

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.

Measured cross sections for the fusion of ⁶⁴Ni with ⁶⁴Ni, ⁷⁴Ge, and ¹⁰⁰Mo targets are analyzed in a coupled-channels approach. The data for the ⁶⁴Ni 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 to reproduce the data for the ⁶⁴Ni+⁷⁴Ge system. Similar calculations for ⁶⁴Ni+¹⁰⁰Mo, and also for the symmetric ⁷⁴Ge+⁷⁴Ge system, show large discrepancies with the data. Possible ways to improve the calculations are discussed.

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 falloff 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 fusion hindrance on nuclear structure.

We calculate the energy spectrum for ⁸B dissociation on a Pb target to all orders in the Coulomb and nuclear fields, and show that the slope of S₁₇(E) obtained in previous analyses of Coulomb dissociation data is too steep, due to deficiencies in the conventional first-order analysis that was used. With a more complete theory that avoids the far-field approximation and includes E2, nuclear and dynamical projectile polarization, the disagreement between indirect and direct methods for determining the S₁₇(E) slope and the extrapolated S₁₇(0) values is reduced significantly.

Cross sections for the dipole radiative capture reactions ⁷Li(n,γ)⁸Li and ⁷Be(p,γ)⁸B are calculated in a two-body model, which is based on a Woods-Saxon parametrization of the nuclear interaction. The well depth is adjusted for each reaction channel so that the measured separation energies and s-wave scattering lengths are reproduced. The calculations are repeated for a wide range of the radius and the diffuseness of the interaction. The predicted S factor for the radiative proton capture on ⁷Be falls within a surprisingly narrow range of values when the model is calibrated to reproduce measurements of the mirror reaction ⁷Li(n,γ)⁸Li. The simplified model used here is consistent with the shell model approach for proton capture on ⁷Be but it gives a significantly smaller cross section for neutron capture on ⁷Li.

Fusion-evaporation cross sections for ⁶⁴Ni+⁶⁴Ni 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 ⁵⁸Ni+⁵⁸Ni, ⁵⁸Ni+⁶⁰Ni, and ⁵⁸Ni+⁶⁴Ni systems indicates a strong dependence of the energy where the hindrance occurs on the stiffness of the interacting nuclei.

The decay rate of a triaxially deformed proton emitter is calculated in a particle-rotor model, which is based on a deformed Woods-Saxon potential and includes a deformed spin-orbit interaction. The wave function of the I=7∕2⁻ ground state of the deformed proton emitter ¹⁴¹Ho is obtained in the adiabatic limit, and a Green’s function technique is used to calculate the decay rate and branching ratio to the first excited 2⁺ state of the daughter nucleus. Only for values of the triaxial angle γ<5° is good agreement obtained for both the total decay rate and the 2⁺ branching ratio.

A coupled-channels analysis has been carried out for fusion reactions in the system ⁶⁰Ni+⁸⁹Y. It demonstrates that conventional coupled-channels calculations are unable to reproduce the unexpected steep falloff of the recently measured 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 parametrized with a simple empirical formula. The parametrization, which is derived here for rather stiff heavy-ion systems, provides an upper limit for reactions involving softer nuclei.

A Reply to the Comment by C. J. Lin.

Measurements of the fusion of ¹⁶O and ²⁷Al with a series of germanium isotopes are analyzed within a coupled-channels approach. It is found that couplings based interactions that are linear in the deformation amplitudes are insufficient in reproducing the data. In order to obtain reasonable fits, it is necessary also to include couplings based on quadratic interactions. The analysis suggests that the nuclear radius of ⁷²Ge is significantly smaller than predicted from a smooth interpolation between other germanium isotopes. The large prolate deformation of ⁷⁴Ge, which has been proposed as the preferred solution to measurements of the quadrupole moment of the 2⁺ state, is not supported by the analysis; the near spherical solution is more likely.

Angular distributions of oxygen produced in the breakup of ¹⁷F incident on a ²⁰⁸Pb target have been measured at angles from 75° to 113° and 39° to 79° for beam energies of 98 and 120 MeV, respectively. 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.

The Coulomb dissociation of ⁸B on high-Z targets can be described by first-order perturbation theory at high beam energies but the far-field approximation, which is commonly used, becomes inaccurate at impact parameters less than ∼25 fm. The leading-order correction at lower beam energies is a dynamic polarization effect, which reduces the dissociation probability. The relative significance of the effect scales roughly as Z/E in terms of the target charge Z and beam energy E. The reduction due to a destructive Coulomb-nuclear interference, on the other hand, is rather modest.

In this work we study the problem of a charged particle, bound in a harmonic-oscillator potential, being excited by the Coulomb field from a fast charged projectile. Based on a classical solution to the problem and using the squeezed-state formalism we are able to treat exactly both dipole and quadrupole Coulomb field components. Addressing various transition amplitudes and processes of multiphonon excitation, we study different aspects resulting from the interplay between E1 and E2 fields, ranging from classical dynamic polarization effects to questions of quantum interference. We compare exact calculations with approximate methods. Results of this work and the formalism we present can be useful in studies of nuclear reaction physics and in atomic stopping theory.

The excitation function for fusion evaporation in the   ︀⁶⁰Ni+  ︀⁸⁹Y system was measured over a range in cross section covering 6 orders of magnitude. The cross section exhibits an abrupt decrease at extreme sub-barrier energies. This behavior, which is also present in a few other systems found in the literature, cannot be reproduced with present models, including those based on a coupled-channels approach. Possible causes are discussed, including a dependence on the intrinsic structure of the participants.

Angular distributions of fluorine and oxygen produced from 170 MeV ¹⁷F incident on ²⁰⁸Pb 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 ¹⁶O+²⁰⁸Pb. A large yield of oxygen was observed near θ_lab=36°. It is reproduced fairly well by a calculation of the (¹⁷F,¹⁶O) 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.

We derive a general expression for the multipole expansion of the electromagnetic 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.

A particle-vibration coupling model is applied to explain the spectroscopic factors and decay rates of odd-A and odd-odd near-spherical proton emitters, as well as the branching ratio for the recently observed fine structure in the decay of ¹⁴⁵Tm. In addition, a deformed solution for ¹⁴⁵Tm with K=5/2^- is presented. Using particle-vibration coupling, good agreement is achieved with observed spectroscopic factors for the near-spherical emitters, including d_3/2 cases. For the odd-odd emitters, the unpaired neutron is treated as a spectator. The single-particle potential used in this work has the same parameters as that used to successfully describe the decay rates of the deformed proton emitters ¹³¹Eu and ¹⁴¹Ho.

Projectile fragmentation reactions are well suited to structure studies of weakly bound nuclei, but an accurate reaction theory is necessary to extract quantitative spectroscopic properties. We examine here the accuracy of the commonly used eikonal approximation for the nuclear-induced breakup of halo nuclei. Comparing to numerical solutions of the full time-dependent Schrödinger equation, we find that the eikonal remains fairly accurate for calculating breakup probabilities of halo nuclei even down to 20 MeV/nucleon, reproducing relative spectroscopic strengths to within a few percent. Absolute reaction probabilities tend to be underpredicted by the eikonal, which would make extracted spectroscopic strengths somewhat too high. We discuss other features that are seen in the full calculation but are missing in the eikonal approximation such as the “towing” mode.