Cluster Folding Research Articles

Reanalysis of 6Li+90Zr angular distributions using different nuclear potentials

The experimental angular distributions for 6Li elastically scattered from a 90Zr target in the energy range 14.89–240 MeV are theoretically reanalyzed using phenomenological and semi-microscopic potentials. The phenomenon of the break-up threshold anomaly (BTA) is well represented in the various used potentials. In analyzing nuclear systems induced by weakly bound projectiles such as 6Li, the well-known reduction in the strength of the real part of potential generated based on double folding (DF) and cluster folding (CF) models is also observed. The Sao Paulo potential (SPP) is used to perform double folding calculations. In order to fit the data fairly, a reduction of ∼ 42% and 45% in the strength of the microscopic real part of potential constructed using SPP and CFM, respectively, is found to be required. By including an additional dynamical polarization potential, the data are also reproduced without renormalizing the real cluster folding potential.

Analysis of alpha elastically scattered by light nuclei applying different models

This paper reports on 4He elastic scattering by [Formula: see text]Li, 9Be and [Formula: see text]B angular distributions analyzed in the optical model (OM) context using Woods–Saxon (WS) potential form and double folding (DF) with distorted-wave Born approximation (DWBA), while applying the M3Y approach to the real part and a WS shape to describe the imaginary part of the optical model potential (OMP). Cluster folding (CF) with the DWBA model has also been explored for theoretical data analysis. The coupled reaction channels (CRC) method has been applied to all nuclear systems under consideration where both inelastic scattering and the transfer with elastic scattering have been involved in the analysis of experimental data. The study highlights the overall agreement between the data under the study and the concerned theoretical approaches.

Prediction of the analyzing power for p⃗+He6 elastic scattering at 200 MeV from p⃗+He4 elastic scattering at 200 MeV

We apply the cluster-folding (CF) model for $\vec{p}+^{6}$He scattering at 200 MeV, where the potential between $\vec{p}$ and $^{4}$He is fitted to data on $\vec{p}+^{4}$He scattering at 200 MeV. For $\vec{p}+^{6}$He scattering at 200 MeV, the CF model reproduces measured differential cross section with no free parameter, We then predict the analyzing power $A_y(q)$ with the CF model, where $q$ is the transfer momentum. Johnson, Al-Khalili and Tostevin construct a theory for one-neutron halo scattering, taking (1) the adiabatic approximation and (2) neglecting the interaction between a valence neutron and a target, and yield a simple relationship between the elastic scattering of a halo nucleus and of its core under certain conditions. We improve their theory with (3) the eikonal approximation in order to determine $A_y(q)$ for $^{6}$He from the data on $A_y(q)$ for $^{4}$He. The improved theory is accurate, when approximation (1)--(3) are good. Among the three approximations, approximation (2) is most essential. The CF model shows that approximation (2) is good in $0.9 < q < 2.4$ fm$^{-1}$. In the improved theory, the $A_y(q)$ for $^{6}$He is the same as that for $^{4}$He. In $0.9 < q < 2.4$ fm$^{-1}$, we then predict $A_y(q)$ for $\vec{p}+^{6}$He scattering at 200 MeV from measured $A_y(q)$ for $\vec{p}+^{4}$He scattering at 200 MeV. We thus predict $A_y(q)$ with the model-dependent and the model-independent prescription. The ratio of differential cross sections measured for $^{6}$He to that for $^{4}$He is related to the wave function of $^{6}$He. We then determine the radius between $^{4}$He and the center-of-mass of valence two neutrons in $^{6}$He. The radius is 5.77 fm.

Peculiarities of 6Li +12C elastic scattering

Using the phenomenological optical potential and two different semi-microscopic potentials, namely double folding and cluster folding (CF), the available experimental data for 6Li elastically scattered from [Formula: see text]C nucleus at energies 50–600[Formula: see text]MeV are reanalyzed. On the basis of the well-known cluster structure of 6Li as a composite nucleus consisting of a core “alpha” with a valence particle “deuteron” orbiting this core, special attention was paid to the CF potential. Elastic scattering data for 6Li+[Formula: see text]C system plotted as a function of momentum transfer showed that the real Coulomb nuclear interference region is independent of the bombarding energy. The aforementioned structural behavior for the data could be used to define the potential with some certainty. In addition to a Woods–Saxon imaginary potential of fixed radius, the real part of the potential derived from the cluster structure of 6Li was successful in reproducing the experimental data in the whole angular range. Coupled channel (CC) calculation effects are also performed by coupling to 6Li resonant state ([Formula: see text], [Formula: see text][Formula: see text]MeV).

5He+αcluster model of9Bebreakup

We present here for the first time continuum-discretised-coupled-channels (CDCC) calculations for the elastic scattering and breakup of ${}^{9}\mathrm{Be}{+}^{12}\mathrm{C}.$ We employ a two-body cluster-folding (CF) model picture of ${}^{9}\mathrm{Be},$ which is considered as a ${}^{5}\mathrm{He}$ core plus a ${}^{4}\mathrm{He}$ cluster. The calculations agree well with data for elastic scattering and excitation of the ${5/2}^{\ensuremath{-}}$ resonance of ${}^{9}\mathrm{Be}$ at 2.43 MeV. The cross section for excitation of the ${1/2}^{+}$ resonance at 1.68 MeV is not well described by our model, the calculations being considerably smaller than the data. This is as expected from structure calculations of ${}^{9}\mathrm{Be},$ which suggest that this state is almost exclusively of ${}^{8}\mathrm{Be}+n$ cluster form.

Continuum-discretized coupled-channels analysis of6Li→+4Hescattering atEc.m.=11.1MeV

Data for the elastic scattering of 27.8 MeV polarized {sup 6}Li from {sup 4}He and new data for the {sup 6}Li{r_arrow}{alpha}+d sequential breakup have been analyzed using the coupled-channels (CC) method with potentials derived via the cluster-folding (CF) procedure. The three low-lying T=0 resonant excited states of {sup 6}Li as well as nonresonant continuum states were taken into account in the calculations by means of the continuum-discretized coupled-channels (CDCC) method. No adjustable parameters were used. The analysis shows a dominant role of the projectile breakup into {alpha}+d in the {sup 6}Li+{sup 4}He elastic scattering. The deuteron transfer process is found to be of less importance. The calculations reproduce the values of the differential cross section for the sequential breakup channels at forward scattering angles. Predictions for the direct breakup near the {sup 6}Li{r_arrow}{alpha}+d breakup threshold are made. {copyright} {ital 1997} {ital The American Physical Society}

The role of breakup in near-barrier 6Li+ 208Pb scattering

Continuum-discretized-coupled-channels (CDCC) calculations for the 6Li+ 208Pb system have been performed at several near-barrier energies using a cluster-folding (CF) model description of the 6Li-target interactions. Good agreement with the elastic scattering angular distributions is obtained without the need for re-normalization of the CF potential. Decomposition of the calculated 6Li sequential breakup cross section into Coulomb and nuclear components shows that the forward angle cross section is dominated by the Coulomb amplitude at near-barrier energies.

Coupled-channels analysis of the elastic scattering of polarized 6Li by 58Ni using cluster-folding potentials.

Angular distributions of differential cross section and the analyzing powers ${\mathit{iT}}_{11}$, ${\mathit{T}}_{20}$, and $^{\mathit{T}}$${\mathit{T}}_{20}$ have been measured for the elastic scattering of polarized $^{6}\mathrm{Li}$ by $^{58}\mathrm{Ni}$ at an incident energy of 70.5 MeV. These data have been compared with the results of coupled-channels (CC) calculations with central interaction and coupling potentials generated using the cluster-folding (CF) method. The significance of spin-dependent potentials and the D-state admixture in the $^{6}\mathrm{Li}$ ground state wave function are discussed.

Coupled channels analysis ofF19+12C elastic and inelastic scattering using a cluster-folding interaction

Angular distributions for elastic and inelastic scattering of the [sup 19]F[sup +] [sup 12]C system leading to the 1/2[sup +] (g.s.), 5/2[sup +] (0.197 MeV), 3/2[sup +] (1.554 MeV), and 9/2[sup +] (2.780 MeV) states in [sup 19]F were calculated with a coupled channels (CC) method using cluster folding (CF) interactions based on a [sup 16]O+[ital t]+[sup 12]C three-body model at [ital E][sub [ital L]]([sup 12]C)=30--60 MeV. The calculations reproduce well the experimental angular distributions for the elastic and inelastic scattering to the 5/2[sup +] and 3/2[sup +] states at all energies, although for the inelastic scattering to the 5/2[sup +] and 3/2[sup +] states the phases of the calculated angular distributions seem to be shifted slightly backward from the experimental ones. The calculations are compared with the CC calculations using Woods-Saxon interaction in order to investigate the effect of the shape of the interaction.

Coupled-channels study of polarized 6Li scattering at 44 MeV

Previously published coupled-channels (CC) analyses by Rusek et al. of polarized 6Li elastic scattering by 26Mg and 120Sn at Elab=44 MeV are analyzed. Excitations of 6Li to its three lowest T = 0 excited states are taken into account in the framework of continuum-discretized coupled-channels (CDCC). The analyses are made with the use of the projectile-target interactions based on the cluster-folding (CF) model and those on the double-folding (DF) one. It is shown that the coupling to the 6Li-excited states has large contributions to the vector and tensor analyzing powers of the elastic scattering. A test of the accuracy of the weak-binding-energy approximation (WBEA), which was used in the previous analyses, is made in comparison with the results of the CDCC calculation. It is also pointed out that there exists an ambiguity in the deuteron-target spin-orbit interaction, which affects the conclusion on the competition between the folding spin-orbit interaction and the projectile-excitation effects in the vector analyzing power.

Anomalous renormalization of cluster-folding interactions for 6Li-nucleus scattering at low energies

The validity of cluster-folding (CF) interactions for elastic scattering of 6Li by various nuclei is investigated in the α+d+target three-body model. The 6Li→α+d breakup process is taken into account in the framework of the continuum-discretized coupled-channels (CDCC). It is shown that, at low energies below E lab A p ≅10 MeV , the real part of the CF potentials has to be reduced by about (40–50)%, even when the resonant and non-resonant breakup channels are explicitly included in the CDCC calculations, while no renormalization is necessary for fits to scattering at higher energies.

Breakup effect on 6Li-nucleus scattering at intermediate energies

Elastic scattering of 6Li by a nucleus at intermediate energies has been investigated by the continuum-discretised coupled-channels method based on a cluster-folding (CF) model of 6Li-nucleus interactions. The projectile breakup effect, which was quite significant at low energies, has been found to be less important at intermediate energies. This reflects the strong energy dependence of the input optical potentials for α and d clusters. The results suggest the validity of a simple CF model in the description of 6Li-nucleus scattering at intermediate energies.

Scattering of polarized 7Li by 120Sn and projectile-target spin-dependent interactions

Scattering of 7Li by 120Sn targets at E lab = 44 MeV is investigated in the coupled-channel frame by taking account of the projectile virtual excitations to the lowest three excited states. Calculations are performed by the cluster-folding (CF) interactions and the double-folding (DF) one. Both interactions reproduce very well the experimental data on the cross section, the vector analyzing power, the second-rank tensor ones and the third-rank tensor one in elastic and projectile inelastic scattering, although some differences are found between the CF results and the DF ones. In the calculation, the virtual excitations of the projectile are important for most of the analyzing powers and the spin-orbit interaction is indispensable for the vector analyzing power. These features are in contrast to those in 7Li- 58Ni scattering at 20 MeV and are interpreted as over-Coulomb-barrier effects. The scattering amplitudes and the analyzing powers are investigated by the invariant amplitude method, which provides a key connecting the spin-dependent interactions to the analyzing powers. The method proposes an important relationship between the tensor analyzing powers, which is useful in analyses of both theoretical and experimental results. Finally, it is found that in the elastic scattering the second-rank tensor analyzing powers are proportional to the strength of the second-rank tensor interaction and the vector and third-rank tensor analyzing powers to the square or cube of the strength of this interaction, while in the inelastic scattering the cross section is proportional to the square of the strength of the tensor interaction, other quantities being weakly dependent on the strength.