Continuum-discretized Coupled-channels Research Articles

Inclusive breakup measurements of the 7Li+ 119Sn reaction

We present preliminary data of elastic scattering and inclusive breakup cross sections for the 7Li+ 119Sn reaction, recently measured at the Laboratori Nazionali del Sud (LNS-INFN) (Catania, Italy) at energies around the Coulomb barrier (E lab = 21.2 and 26.5 MeV). The experimental data have been analyzed under the Optical Model and Continuum-Discretized Coupled-Channels methods.

Determining B(E1) distributions of weakly bound nuclei from breakup cross sections using Continuum Discretized Coupled Channels calculations. Application to 11Be

A novel method to extract the B(E1) strength of a weakly bound nucleus from experimental Coulomb dissociation data is proposed. The method makes use of continuum discretized coupled channels (CDCC) calculations, in which both nuclear and Coulomb forces are taken into account to all orders. This is a crucial advantage with respect to the standard procedure based on the Equivalent Photon Method (EPM) which does not properly take into account nuclear distortion, higher order coupling effects, or Coulomb-nuclear interference terms. The systematic and statistical uncertainties of this procedure are evaluated. The procedure is applied to the 11Be nucleus using two sets of available experimental data at different energies, for which seemingly incompatible B(E1) have been reported using the EPM. We show that the present procedure gives consistent B(E1) strengths, thus solving the aforementioned long-standing discrepancy between the two measurements.

Investigation of the Calculation of Coupled Channels for Some Halo Systems

The fusion reaction for systems involving halo nuclei are investigated by two- and multicoupled channel calculations for the systems 8B+58Ni, 11Be+209Bi, and 15C+232Th. The effect of coupling between the breakup channel and the elastic channel have been considered using the Continuum Discretized Coupled Channels (CDCC) method in full quantum and semiclassical approaches. The calculation of the fusion cross-section qfus (mb), fusion barrier distribution Dfus (mb/MeV) and fusion probability Pfus reproduces the measured data for the systems under study quite well above and below the Coulomb barrier VB. In the case of two-channel coupling both in semiclassical and quantum mechanical approaches, the measured data above the Coulomb barrier VB are overestimated.

Scattering of the halo nucleus 11Be from a lead target at 3.5 times the Coulomb barrier energy

Angular distributions of quasielastic scattering and breakup of the neutron-rich halo nucleus 11Be on a 208Pb target at an incident energy of 140 MeV (about 3.5 times the Coulomb barrier) were measured at HIRFL-RIBLL. A strong suppression of the Coulomb nuclear interference peak is observed in the measured quasielastic scattering angular distribution. The result demonstrates for the first time the persistence of the strong breakup coupling effect reported so far for reaction systems involving neutron-halo nuclei at this relatively high incident energy. The measured quasielastic scattering cross sections are satisfactorily reproduced by continuum discretized coupled channel (CDCC) calculations as well as by the XCDCC calculations where the deformation of the 10Be core is taken into account. The angular and energy distributions of the 10Be fragments could also be well reproduced considering elastic breakup (CDCC and XCDCC) plus nonelastic breakup contributions, with the latter evaluated with the model by Ichimura, Austern and Vincent [1]. The comparison of the 10Be energy distributions with simple kinematical estimates evidence the presence of a significant post-acceleration effect which, in the (X)CDCC frameworks, is accounted for by continuum-continuum couplings.

Coupled-reaction-channel study of the C12(α,Be8) reaction and the Be8+Be8 optical potential

Background: Given the established $2\ensuremath{\alpha}$ structure of $^{8}\mathrm{Be}$, a realistic model of four interacting $\ensuremath{\alpha}$ clusters must be used to obtain a $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ interaction potential. Such a four-body problem poses a challenge for the determination of the $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ optical potential (OP) that is still unknown due to the lack of the elastic $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ scattering data.Purpose: To probe the complex $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ optical potential in the coupled-reaction-channel (CRC) study of the $\ensuremath{\alpha}$ transfer $^{12}\mathrm{C}(\ensuremath{\alpha},^{8}\mathrm{Be})$ reaction measured at ${E}_{\ensuremath{\alpha}}=65$ MeV and to obtain the spectroscopic information on the $\ensuremath{\alpha}+^{8}\mathrm{Be}$ cluster configuration of $^{12}\mathrm{C}$.Method: The three- and four-body continuum-discretized coupled-channel (CDCC) methods are used to calculate the elastic $\ensuremath{\alpha}+^{8}\mathrm{Be}$ and $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ scattering at the energy around 16 MeV/nucleon, with the breakup effect taken into account explicitly. Based on the elastic cross section predicted by the CDCC calculation, the local equivalent OP's for these systems are deduced for the CRC study of the $^{12}\mathrm{C}(\ensuremath{\alpha},^{8}\mathrm{Be})$ reaction.Results: Using the CDCC-based OP's and $\ensuremath{\alpha}$ spectroscopic factors given by the cluster model calculation, a good CRC description of the $\ensuremath{\alpha}$ transfer data for both the $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ and $^{8}\mathrm{Be}+^{8}\mathrm{Be}_{{2}^{+}}^{*}$ exit channels is obtained without any adjustment of the (complex) potential strength.Conclusion: The $\ensuremath{\alpha}+^{8}\mathrm{Be}$ and $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ interaction potential can be described by the three- and four-body CDCC methods, respectively, starting from a realistic $\ensuremath{\alpha}+\ensuremath{\alpha}$ interaction. The $\ensuremath{\alpha}$ transfer $^{12}\mathrm{C}(\ensuremath{\alpha},^{8}\mathrm{Be})$ reaction should be further investigated not only to probe of the $4\ensuremath{\alpha}$ interaction but also the cluster structure of $^{12}\mathrm{C}$.

Coupled channel analysis of fusion excitation function for 9Be+64Zn system at near and above barrier energies

We have calculated excitation functions of incomplete fusion, complete fusion and total fusion processes for [Formula: see text] system at near and above barrier energies. In particular, breakup effects of weakly bound projectile [Formula: see text], which has been considered as a two body system [Formula: see text] with a breakup threshold of 1.667 MeV, have been studied. The calculations are performed by using the code FRESCO, which is based on Continuum Discretized Coupled Channel (CDCC) approach. The present analysis of the total fusion excitation function for the system [Formula: see text] shows that it is suppressed at above barrier energies and enhanced at sub barrier energies when the breakup effects are taken into account. In addition, the comparison of the probabilities of incomplete fusion from neutron capture and that from alpha capture shows the dominance of former over later.

Elastic scattering for 6Li+51V and systematic study of breakup threshold anomaly

Elastic scattering for 6Li+51V system is measured around Coulomb barrier energies. The behavior of the nuclear potential is extracted from elastic scattering angular distributions measured in wide angular range. The data have been analyzed using phenomenological Woods-Saxon shaped optical potential and microscopic double folding potential frameworks. Sensitivity radius was determined using optical model and potential behavior thus analyzed shows breakup threshold anomaly (BTA). Continuum discretized coupled channel (CDCC) calculations give a good description of the measured elastic scattering data with breakup coupling effects. The contribution of breakup coupling through resonance states is significant. The potential behavior has been analyzed in the double folding framework using density distribution calculated from Hartree-Fock-Bogoliubov (HFB) method to understand the dependence of BTA in a wide mass range. It is observed that BTA exist from lower to higher mass targets for 6Li projectile. The systematic target dependence of the reaction cross-sections for 6Li projectile follows an universal scaling behavior. An enhancement in reaction cross section is observed for exotic compared to weakly and strongly bound projectiles with 51V target.

Low-energy Li11+p and Li11+d scattering in a multicluster model

The 11Li + p and 11Li + d reactions are investigated in the Continuum Discretized Coupled Channel (CDCC) method with a three-body description (9Li + n + n) of 11Li. I first discuss the properties of 11Li, and focus on E1 transition probabilities to the continuum. The existence of a 1- resonance at low excitation energies is confirmed, but the associated E1 transition from the ground state does not have an isoscalar character, as suggested in a recent experiment. In a second step, I study the 11Li + p elastic cross section at Elab = 66 MeV in the CDCC framework. I obtain a fair agreement with experiment, and show that breakup effects are maximal at large angles. The breakup cross section is shown to be dominated by the 1- dipole state in 11Li, but the role of this resonance is minor in elastic scattering. From CDCC equivalent 11Li + p and 11Li + n potentials, I explore the 11Li + d cross section within a standard three-body 11Li +(p + n) model. At small angles, the experimental cross section is close to the Rutherford scattering cross section, which is not supported by the CDCC. A five-body (9Li+n+n)+(p+n) is then performed. Including breakup states in 11Li and in the deuteron represents a numerical challenge for theory, owing to the large number of channels. Although a full convergence could not be reached, the CDCC model tends to overestimate the data at small angles. I suggest that measurements of the 9Li + p elastic scattering would be helpful to determine more accurate optical potentials. The current disagreement between experiment and theory on 11Li + d scattering also deserves new experiments at other energies.

Effect of the repulsive core in the proton-neutron potential on deuteron elastic breakup cross sections

The role of the short-range part (repulsive core) of the proton-neutron ($pn$) potential in deuteron elastic breakup processes is investigated. A simplified one-range Gaussian potential and the Argonne V4' (AV4') central potential are adopted in the continuum-discretized coupled-channels (CDCC) method. The deuteron breakup cross sections calculated with these two potentials are compared. The repulsive core is found not to affect the deuteron breakup cross sections at energies from 40 MeV to 1 GeV. To understand this result, an analysis of the peripherality of the elastic breakup processes concerning the $p$-$n$ relative coordinate is performed. It is found that for the breakup processes populating the $pn$ continua with orbital angular momentum $\ell$ different from 0, the reaction process is peripheral, whereas it is not for the breakup to the $\ell=0$ continua (the s-wave breakup). The result of the peripherality analysis indicates that the whole spatial region of deuteron contributes to the s-wave breakup.

Theoretical analysis of 8Li + 208Pb reaction and the critical angular momentum for complete fusion

In a theoretical approach, the complete and incomplete fusions are investigated by considering the Li8+208Pb reaction, within a three-body model where the projectile is described as n−7Li with binding energy εb. By decreasing εb from its known experimental value, the complete fusion is shown to have no meaningful dependence on such variations, whereas the incomplete fusion strongly depends on that. The complete and incomplete fusion cross sections are calculated by using a combination of both continuum-discretized coupled-channel and sum-rule models. To this end, an incident-energy dependent cut-off angular momentum Lc is first obtained by using the available complete fusion experimental data, within an approach which is extended to model results obtained for other incident-energies. An approximated fitted expression linking Lc to the well-known critical value Lcrit derived by Wilczyński (1973) [28] suggests that the sum-rule model could be generalized to energies around and below the Coulomb barrier.

The refractive scattering of 17F+12C

The experimental data of the elastic scattering angular distribution of 17F+12C at 170 MeV is analyzed by the continuum-discretized coupled channels (CDCC) method and the optical model (OM). In the CDCC calculation, the unambiguous optical potential of 16O+12C is used as the input to give the coupling potentials. A very refractive feature is found and two evident Airy minima are predicted at large angles. The one-channel calculation is also performed and gives nearly the same result. In the OM calculations, this optical potential of 16O+12C is used again and adjusted to reproduce the angular distribution of 17F+12C. The Airy oscillation appears again in the calculated angular distribution. These results indicate that the elastic scattering of 17F+12C at 170 MeV has the possibility of the nuclear rainbow phenomenon, which is probably due to the contribution from the 16O core.

Soft giant resonance in two neutron halo nucleus 11Li

Lithium-11 is a showcase of neutron halos and has been providing new insight to nuclear structure researches. Recently, an isoscalar resonance at low excitation energy ($ E_\mathrm{x} \sim 1$ MeV) has been confirmed by the development of a low-energy high-intensity beam of 11Li at TRIUMF. By inelastic scattering measurements $ (\mathrm{p}, \mathrm{p}^{\prime})$ and $ (\mathrm{d}, \mathrm{d}^{\prime})$ with inverse kinematics, the first excited state of 11Li has been studied in detail and an isoscalar nature of the transitions has been confirmed and a strong transition amplitude has been observed indicating the soft-resonance of 11Li. Those recent experimental results on the excitation of the soft resonance are described and then recent theoretical developments based on the four-body continuum-discretized coupled-channels 11Li + p system are presented together with a brief history of the resonance search in 11Li.

Strong coupling effect in the elastic scattering of the C10+Ni58 system near barrier

The elastic scattering of the radioactive proton-rich carbon isotope $^{10}\mathrm{C}$ has been investigated. A full differential angular distribution for the elastic scattering of $^{10}\mathrm{C}$ on a $^{58}\mathrm{Ni}$ target has been measured at ${E}_{\mathrm{Lab}}=35.3$ MeV, which is just above the Coulomb barrier for this system (${V}_{B}=27$ MeV). The obtained angular distribution was analyzed in terms of coupled-channels, coupled-reaction-channels, and continuum-discretized coupled-channels calculations. In the coupled-channels calculation, several inelastic transitions of the target and the first (${2}^{+}$) excited state of the $^{10}\mathrm{C}$ projectile were considered. The coupling to the first (${2}^{+}$) excited state of $^{10}\mathrm{C}$ was shown to be very important to describe the rising of the cross section at backward angles. We also performed an analysis with the continuum-discretized coupled channels, considering the $^{9}\mathrm{B}+p$ and $^{6}\mathrm{Be}+\ensuremath{\alpha}$ channels, which indicated a strong cluster configuration for the $^{10}\mathrm{C}$ projectile.

Perey-effect in continuum-discretized coupled-channel description of (d, p) reactions

The Perey effect in two-body channels of (d, p) reactions has been known for a long time. It arises when the nonlocal two-body deuteron-target and/or proton-target problem is approximated by a local one, manifesting itself in a reduction of the scattering channel wave functions in the nuclear interior. However, the (d, p) reaction mechanism requires explicit accounting for three-body dynamics involving the target and the neutron and proton in the deuteron. Treating nonlocality of the nucleon-target interactions within a three-body context requires significant effort and demands going beyond the widely-used adiabatic approximation, which can be done using a continuum-discretized coupled-channel (CDCC) method. However, the inclusion of nonlocal interactions into the CDCC description of (d, p) reactions has not been developed yet. Here, we point out that, similarly to the two-body nonlocal case, nonlocality in a three-body channel can be accounted for by introducing the Perey factors. We explain this procedure and present the first CDCC calculations to our knowledge including the Perey effect.

The breakup coupling effects on the rainbow scattering of 6Li at 35 AMeV

To investigate the breakup coupling effects on the formation of the nuclear rainbow, the existing experimental data of the refractive elastic scattering of 6Li on 12C, 40Ca, 58Ni and 90Zr targets at 35 AMeV are analyzed. The continuum discretized coupled-channel (CDCC) method is adopted to calculate the elastic scattering angular distributions including the coupling effects from the breakup of 6Li into α and d. The one-channel (1-ch) calculations that switch off the breakup coupling are also performed for comparison. In the calculated angular distributions given by both approaches, the first Airy (A1) minimum shows a trend of moving to larger angles as the target mass increases. Comparing the calculated results through two approaches, one can find that the breakup coupling shifts the A1 minima to larger angles. This shows that the breakup coupling can boost the nuclear rainbow, although it also damps the elastic scattering cross sections. We also find that the stronger the breakup coupling is, the larger the A1 shift becomes.

Comparative study of the effect of resonances of the weakly bound nuclei Li6,7 on total fusion with light to heavy mass targets

A systematic study of total fusion involving the weakly bound nuclei 6,7Li with several light to heavy mass targets at Coulomb energies is presented. Emphasis is given to the role of resonance states (l=2,Jπ=3+,2+,1+ of 6Li and l=3,Jπ=7/2−,5/2− of 7Li) on the total fusion excitation function. A comparative analysis of the effects of resonant breakup on total fusion is performed for both projectiles, using the Continuum-Discretized Coupled-Channel (CDCC) framework. The calculations demonstrate that (i) resonant breakup couplings play a more important role in total fusion than non-resonant couplings, (ii) resonance states with short half-lives are very important for total fusion, as incident energies decreases towards the Coulomb barrier energy where incomplete fusion dominates, and (iii) resonance states with long half-life act as quasi-bound inelastic states, playing a crucial role in complete fusion.

Breakup mechanisms in the He6+Zn64 reaction at near-barrier energies

New experimental results for the elastic scattering of 6He on 64Zn at incident energies of 15.0 and 18.0 MeV and 4He at 17.5 MeV along with results already published at 10.0 and 13.6 MeV, are presented. Elastic and alpha experimental cross sections are compared with coupled-reaction-channel, continuum-discretized coupledchannel, and DWBA inclusive-breakup models. The large yield of alpha particles observed at all measured energies can be explained by considering a nonelastic breakup mechanism.

Precision measurement of the angular distribution for the 16O(d, p)17O transfer reaction to the ground state of 17O

The mechanism of the (d, p) reaction, which has been proven a powerful spectroscopic tool, is believed to be reasonably well understood. However, the 16O(d, p)17O reaction leading to the ground state in 17O seems to be a possible exception. It was found in the previous experiments that the 16O(d, p)17O angular distribution exhibits a rapid decline below the peak at the angle of 15 degrees. To date this abnormal behavior has not been reproduced by theoretical models. In this work we present a re-measurement of the 16O(d, p)Og.s.17 angular distribution by using a high-precision magnetic spectrograph. Our new angular distribution shows a slower decline than the previous data do. A comparative analysis with the distorted Born approximation (DWBA), the adiabatic distorted wave approximation (ADWA) and the continuum discretized coupled channels (CDCC) method suggests that the drop of the differential cross sections at the forward angles is due to the deuteron breakup coupling effects. In addition, we extracted the spectroscopic factor (SF) and the asymptotic normalization coefficient (ANC) for the 17O ground state.

Microscopic Description of $${^{8}{\hbox {Li}}{+}}$$ 8 Li + Nucleus and of $${^{8}{\hbox {B}}{+}}$$ 8 B + Nucleus Scattering

We apply a microscopic version of the Continuum Discretized Coupled Channel (CDCC) method, referred to as MCDCC, to $$^{8}{\hbox {Li}}$$ and $$^{8}{\hbox {B}}$$ scattering on different targets. The $$^{8}{\hbox {Li}}$$ and $$^{8}{\hbox {B}}$$ nuclei are described in a microscopic three-cluster model ( $$\alpha +t+n$$ and $$\alpha + {^{3}}\mathrm{He}+p$$ ), using the hyperspherical coordinates. We first present spectroscopic properties of these nuclei. Then, we determine $$^{8}{\hbox {Li}}+$$ nucleus and $$^{8}{\hbox {B}}+$$ nucleus potentials by using proton $$+$$ target and neutron $$+$$ target interactions. We compute various elastic-scattering cross sections and confirm that breakup effects are important, in particular at low energies. In general, we find a fair agreement with experiment, except for $${^{8}}\mathrm{B}\,+^{58}\text{ Ni }$$ where we suggest that the data might be overestimated.

Elastic scattering, inelastic excitation, and 1n pick-up transfer cross sections for B10 + Sn120 at energies near the Coulomb barrier

The $^{10}\mathrm{B}+^{120}\mathrm{Sn}$ reaction has been systematically studied at laboratory energies around the Coulomb barrier: ${E}_{\mathrm{LAB}}=31.5$, 33.5, 35.0, and 37.5 MeV. Cross sections for the elastic scattering and some reaction processes have been measured: excitation to the ${1}^{+}$ state of $^{10}\mathrm{B}$; excitation to the ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states of $^{120}\mathrm{Sn}$; and the one-neutron pick-up transfer $^{120}\mathrm{Sn}(^{10}\mathrm{B},^{11}\mathrm{B})^{119}\mathrm{Sn}$. Coupled reaction channel (CRC) calculations have been performed in the context of the double-folding S\~ao Paulo potential. The theoretical calculations result in a good overall description of the experimental angular distributions. The effect on the theoretical elastic-scattering angular distributions of couplings to the inelastic and transfer states (through the CRC calculations) and to the continuum states (through continuum-discretized coupled-channels calculations) has been investigated.