Dynamic Polarization Potential Research Articles

Channel coupling effect and important role of imaginary part of coupling potential for high-energy heavy-ion scatterings

The recent works by the present authors and their collaborator predicted that the real part of heavy-ion optical potentials changes its character from attraction to repulsion around the incident energy per nucleon $E =$ 200 -- 300 MeV/u on the basis of the complex $G$-matrix interaction and the double-folding model (DFM) and revealed that the three-body force plays an important role there. In the present paper, we have analyzed the energy dependence of the coupling effect with the Microscopic Coupled Channel (MCC) method and its relation to the elastic and inelastic-scattering angular distributions in detail in the case of the $^{12}$C + $^{12}$C system in the energy range of $E =$ 100 -- 400 MeV/u. The large channel coupling effect is clearly seen in the elastic cross section although the incident energies are enough high. The dynamical polarization potential is derived to investigate the channel coupling effect. Moreover, we analyze the effect of imaginary part of the coupling potential on elastic and inelastic cross sections.

Increase in|SL|induced by channel coupling: The case of deuteron breakup

For deuteron scattering from ${}^{58}$Ni at laboratory energies of 56, 79, and 120 MeV, we study the dynamic polarization potentials (DPPs) induced by $S$-wave and $D$-wave breakup (BU), separately and together, in order to gain insight into the nature of the DPP as well as a counterintuitive property: the existence of $L$ values for which the BU coupling increases $|{S}_{L}|$, a `wrong-way' effect. The effect is associated with the existence of emissive regions in the imaginary DPP, suggesting a connection with the nonlocal nature of the DPP. The same relationship was previously found for ${}^{6}$Li scattering, indicating a generic effect bearing on the dynamics of nuclear reactions.

Complete fusion enhancement and suppression of weakly bound nuclei at near barrier energies

We consider the influence of breakup channels on the complete fusion of weakly bound systems in terms of dynamic polarization potentials. It is argued that the enhancement of the cross section at sub-barrier energies may be consistent with recent experimental observations that nucleon transfer, often leading to breakup, is dominant compared to direct breakup. The main trends of the experimental complete fusion cross sections are analyzed in the framework of the DPP approach. The qualitative conclusions are supported by CDCC calculations including a sequential breakup channel, the one neutron stripping of 7Li followed by the breakup of 6Li.

Coupling effects in proton scattering from40Ca

Recent studies showed that neutron pickup makes a substantial contribution to the proton optical model potential (OMP) for light, mostly halo, target nuclei. Here, we extend those studies to a more ``normal'' target nucleus: ${}^{40}$Ca. We present coupled reaction channel (CRC) calculations with the coupling of 30.3 MeV incident protons to deuterons and up to 12 states of ${}^{39}$Ca. The proton elastic scattering $S$ matrix from the CRC calculation is subject to ${S}_{lj}\ensuremath{\rightarrow}V(r)+\mathbf{l}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{s}\phantom{\rule{4pt}{0ex}}{V}_{\mathrm{SO}}(r)$ inversion and the bare potential of the CRC calculation is subtracted, directly yielding a local and $L$-independent representation of the dynamic polarization potential (DPP). This is appropriate for comparison with phenomenological OMPs and local OMPs derived in local density folding models. The real-central part of the DPP is repulsive and cannot be represented as a uniform normalization of the bare potential, changing the rms radius. A series of model calculations reveal the dependence of the DPP on a range of parameters illuminating (i) departures of nucleon potentials of specific nuclei from global properties, (ii) the generation of repulsion, and (iii) the requirements for all-order CRC and deuteron breakup. Light is thrown on the nonlocality of the underlying DPP.

EFFECTS OF NUCLEAR INDUCED BREAKUP ON THE FUSION OF 6Li+12C AND 6He+12C SYSTEMS AROUND BARRIER ENERGIES

We have studied the effects of nuclear induced breakup channel coupling on the fusion cross-section for 6 Li +12 C and 6 He +12 C systems in the near barrier energy regime using the dynamic polarization potential (DPP) approach. It has been found that there is enhancement in the fusion cross-section with respect to standard one-dimensional barrier penetration model in the below barrier energy regime while at energies above the barrier there is suppression of fusion cross-section with respect to simple barrier penetration model is observed. The agreement between data and predictions for 6 Li +12 C system improves significantly as a result of the inclusion of nuclear induced DPP.

Dynamic polarization potential due to6Li breakup on12C

For ${}^{6}$Li scattering from ${}^{12}$C at five laboratory energies from 90 to 318 MeV, we study the dynamic polarization potential, DPP, due to the breakup of the projectile. The breakup is evaluated using standard continuum discretized coupled-channels formalism applied to a two-body cluster model of the projectile. The DPP is evaluated over a wide radial range using both direct $S$-matrix-to-potential inversion and trivially equivalent local potential methods which yield substantially and systematically different results. The radius at which the real DPP changes from external repulsion to interior attraction varies systematically with energy. This should be experimentally testable because, according to notch tests, this crossover radius is within a radial range to which elastic scattering should be sensitive. The imaginary DPP has an emissive (generative) region at the lower energies; this may be associated with counterintuitive properties of $|{S}_{L}|$.

Dynamic polarization potential due to pickup coupling for proton scattering fromHe6

We present dynamic polarization potentials (DPPs) arising from neutron pickup coupled reaction channels, contributing to the proton-nucleus interaction for 71 MeV/nucleon protons scattering from $^{6}\mathrm{He}$. The DPPs do not represent a uniform renormalization of the potential and result in a change in the rms radius of the real part. The inclusion of breakup of the deuteron somewhat reduces the repulsive effect of the coupling and enhances the absorption. The linearity of the coupling effect suggests a method of incorporating it into a computationally feasible phenomenological scheme.

Reaction mechanisms involving weakly boundLi6andBi209at energies near the Coulomb barrier

The elastic, inelastic, and transfer cross sections are measured for the ${}^{6}\mathrm{Li}+{}^{209}\mathrm{Bi}$ reaction at energies around the Coulomb barrier. The optical model analysis of elastic scattering shows a breakup threshold anomaly in the energy dependence of the real and imaginary potentials. The observed energy dependence is found to be consistent with the dynamic polarization potential obtained from the coupled-channels calculations that explain the above measured reaction channels simultaneously. A comparison of different reaction probabilities reveals that the relative contribution of breakup starts increasing at energies below the Coulomb barrier, in contrast to the behavior of other reaction channels, which get closed as energy is lowered. The large probability of projectile breakup at sub-Coulomb energies leads to the observation of a nonzero imaginary potential even at ${E}_{\text{lab}}\ensuremath{\leqslant}0.8{V}_{B}$.

Dynamic polarization potentials for 6He + 209Bi and 11Li + 208Pb systems at near-barrier energies

The Coulomb dipole induced dynamic polarization potentials for 6He + 209Bi and 11Li + 208Pb systems within the framework of Feshbach’s formalism with a motive to ascertain the presence or absence of threshold anomaly have been studied. As a result of this study, the threshold anomaly has been found to be present for both systems. It has also been found that at deep sub-barrier energies the imaginary part either starts increasing or at least remains unchanged which indicates the presence of the breakup threshold anomaly. In addition, the Coulomb breakup transmission factors for both systems have been found to have maximum value below and near-barrier energies, but at very high energies due to closure of the breakup channel the breakup transmission coefficients quickly becomes zero.

Study of reactions with the weakly bound projectile9Be with89Y

With the aim to investigate the in∞uence of the breakup channel on difierent reaction channels, the elastic scattering and fusion of 9 Be with the medium mass target 89 Y has been stud- ied at near barrier energies. Optical model analysis of the elastic data has been carried out and a dispersion relation applied to the real and imaginary potentials to investigate their energy depen- dence from which the presence of breakup threshold anomaly has been observed. Complete fusion (CF) cross sections, obtained for 9 Be+ 89 Y system, are found to be suppressed by (20 § 5)% as compared to the coupled-channels calculations without breakup coupling. This observation has been further conflrmed by comparing these cross sections with those for the 4 He+ 93 Nb and 12 C+ 89 Y systems, where fusion is induced by a tightly bound projectile and forms a nearby compound nu- cleus to that formed by 9 Be+ 89 Y. Results from the breakup coupling done in continuum discretized coupled-channels calculations show that the elastic cross sections thus obtained, which also flt the experimental elastic cross sections, are enhanced compared to the uncoupled calculations which im- plies a reduction in absorption/fusion cross sections. These enhanced cross sections suggest that the dynamic polarization potential produced due to breakup coupling is repulsive in nature. Thus the efiective (bare+polarization) potential around the barrier becomes less attractive leading to the absence of the normal threshold anomaly.

Strong nuclear couplings as a source of Coulomb rainbow suppression

A recent measurement of the $^{11}\mathrm{Be}+^{64}\mathrm{Zn}$ quasielastic scattering angular distribution exhibits a non-Fresnel-type pattern, in contrast to $^{6}\mathrm{He}+^{64}\mathrm{Zn}$ elastic scattering but similar to that for the elastic scattering of $^{6}\mathrm{He}$ from heavy targets. We show by means of continuum discretized coupled-channels (CDCC) calculations that this unusual behavior of $^{11}\mathrm{Be}$ is caused by the much greater importance of nuclear coupling to the continuum in $^{11}\mathrm{Be}$ compared to $^{6}\mathrm{He}$, where Coulomb dipole coupling is mainly responsible for the non-Fresnel-like shape, when present. We also show that the dynamic polarization potentials derived from the CDCC calculations seem to follow a universal form as a function of radius.

Dynamic polarization potential effects on vector analyzing powers of 6Li–28Si elastic scattering from non-monotonic potentials

Experimental cross section (CS) and vector analyzing power (VAP) data of the 6Li–28Si elastic scattering at 22.8 MeV are analyzed in the coupled-channels (CC) and coupled discretized continuum channels (CDCC) methods. Non-monotonic (NM) 6Li and α potentials of microscopic origin are employed, respectively, in the CC calculations and to generate folding potentials for the CDCC calculations. The study demonstrates that the use of central NM potentials can generate an appropriate dynamic polarization potential (DPP) required to describe both the CS and VAP data without the necessity of renormalization. This also produces an effective spin–orbit (SO) potential to account for the iT11 data without the requirement of an additional static SO potential at the incident energy considered.

Strong coupling effects in proton scattering fromHe8

We present dynamic polarization potentials (DPPs), due to both neutron and neutron-pair pickup coupled reaction channels, contributing to the proton-nucleus interaction for the case of $^{8}\mathrm{He}$ at 15.66, 25, and 61.3 MeV/nucleon. The available elastic scattering and transfer data were fitted in coupled reaction channels calculations that allowed full interpartition couplings. In addition, the contributions with various different combinations of coupled reaction channels were considered; we show that this can throw light on the nonlocality of the underlying DPP, for which we determine the local and $L$-independent equivalent.

Effect of breakup in the fusion ofLi7withHo165

The effect of $^{7}\mathrm{Li}$ breakup on the fusion of the $^{7}\mathrm{Li}+^{165}\mathrm{Ho}$ system has been investigated using the continuum-discretized coupled channels (CDCC) calculations. Coupling of the breakup channel leads to a large enhancement in the total fusion cross sections at energies below the Coulomb barrier, while it leads to a small reduction of the fusion cross sections at above barrier energies. A large contribution to this enhancement is found because of dipole couplings arising from the $L=0$ continuum excitation of $^{7}\mathrm{Li}$ to its ground state. The dynamic polarization potential generated by the $^{7}\mathrm{Li}$ breakup couplings is found to have an attractive real part at below barrier energies, due to the dominance of dipole $(E1)$ couplings. Inelastic couplings due to the target deformation are found to have negligible effects on the fusion cross section.

Polarization potentials due to inelastic excitations

Dynamic polarization potentials generated by inelastic excitations of the projectile or target nuclei for three scattering systems are compared. Effects due to excitations to bound/unbound states as well as due to different multipolarities are studied. It is shown that the potentials exhibit similar radial dependence at large projectile-target separations; real parts change with the increased radius from repulsive to attractive while imaginary parts, close to zero or even emissive at the nuclear surface, are becoming absorptive at large distances. This general tendency is a consequence of the interplay between Coulomb and nuclear forces.

Elastic scattering and breakup effect analysis ofBe11+C12at 38.4 MeV/nucleon

{sup 11}Be+{sup 12}C elastic-scattering data at 38.4 MeV/nucleon has been analyzed using the optical model. The optical potential is calculated in the framework of the double folding model using M3Y effective nucleon-nucleon interaction. Different models of {sup 11}Be density are tested and the model that does not include the halo structure gives poor fitting with data. The breakup effect is studied by introducing a complex dynamical polarization potential (DPP) that is added to the ''bare'' potential. The DPP is taken in different forms that have been obtained from simple phenomenological, semiclassical approximation, and microscopic methods. The simple phenomenological DPP is related to the semiclassical approximation method. The sensitivity of the differential and reaction cross sections to these polarization potentials is tested. The microscopic DPP that has been constructed from the derivative of the folding potential describes the breakup effect well. It gives an explicit justification for the long range of the polarization potential.

Analytical potential for the elastic scattering of light halo nuclei below and close to the Coulomb barrier

An analytical expression for the dynamic polarization potential is derived for the elastic scattering of light halo nuclei in the Coulomb field of heavy targets. The derivation is based on the adiabatic motion of the projectile below and close to the Coulomb barrier together with a uniform approximation for the Coulomb functions. Detailed computations have been carried out for the elastic scattering of d+{sup 208}Pb and {sup 6}He+{sup 208}Pb at collision energies of 8 and 17.8 MeV and are compared with measurements as far as available. The obtained expression for the dynamic polarization potential is simple and can be applied for any arbitrary system with a dineutron configuration.

Pickup coupling effects in deuteron scattering: The case ofd+Ca40

The dynamic polarization potential (DPP) contribution to the effective deuteron-nucleus interaction is evaluated by means of coupled reaction channel (CRC) calculations followed by $S$-matrix-to-potential inversion. The full coupled channel $S$ matrix ${S}_{{l}^{'}l}^{J}$ is inverted using the iterative-perturbative algorithm to yield a potential that includes a complex ${T}_{R}$ tensor term as well as central and spin-orbit components. The differences between the various components of the inverted potential and the corresponding terms in the bare potential of the CRC calculation constitute a local equivalent representation of the complete DPP that is generated by the reaction channel coupling. The magnitude of the DPP, the real part in particular, is much less than that found in earlier calculations in which the nonorthogonality terms were omitted. The characteristic features of the tensor part of the DPP were traced to breakup and reorientation processes in the entrance deuteron channel that had been included with the pickup. The contribution of stripping to the deuteron-nucleus interaction is also discussed.

FOLDING MODEL ANALYSIS OF 6He + 12C ELASTIC SCATTERING

Elastic scattering of the two-neutron halo nucleus, 6 He , on 12 C target at 38.3 and 41.6 MeV/nucleon has been analyzed in the framework of the double-folding optical model. Real double-folded potentials based on the realistic density-dependent DDM3Y and JLM effective nucleon–nucleon interactions are generated using different forms of the nuclear matter density distribution of 6 He . The imaginary optical potentials are taken in the conventional Woods–Saxon form. The bare (unnormalized) real folded potentials derived from the JLM interaction are more successful in reproducing the data at both energies than those derived from the DDM3Y interaction. The effect of contribution of the dynamic polarization potential is also studied. A semimicroscopic approximation is proposed to simulate this potential by introducing a repulsive real part extracted from the generated folded potential. Fits to data have been slightly improved by considering this approximation.

Two causes of nonlocalities in nucleon-nucleus potentials and their effects in nucleon-nucleus scattering

Two causes of nonlocality inherent in nucleon-nucleus scattering are considered. They are the results of two-nucleon antisymmetry of the projectile with each nucleon in the nucleus and the dynamic polarization potential representation of channel coupling. For energies ∼ 40 -300MeV, a g -folding model of the optical potential is used to show the influence of the knock-out process that is a result of the two-nucleon antisymmetry. To explore the dynamic polarization potential caused by channel coupling, a multichannel algebraic scattering model has been used for low-energy scattering.