Coupled Reaction Channel Calculations Research Articles

Breakup effects on alpha spectroscopic factors of 16O

The triton angular distribution for the 12C(7Li,t)16O* reaction is measured at 20 MeV, populating discrete states of 16O. Continuum discretized coupled reaction channel calculations are used to to extract the alpha spectroscopic properties of 16O states instead of the distorted wave born approximation theory to include the effects of breakup on the transfer process. The alpha reduced width, spectroscopic factors and the asymptotic normalization constant (ANC) of 16O states are extracted. The error in the spectroscopic factor is about 35% and in that of the ANC about 27%.

Elastic and inelastic angular distributions of the 7Li+120Sn system for energies near the Coulomb barrier

The reaction of 7Li+120Sn has been measured at bombarding energies of 21, 24 and 27 MeV. The -ray transition in 120Sn was observed and the angular distribution for the 2+ excited state was obtained. Coupled channels and coupled-reaction channels calculations, including the dynamical polarization potential due to the projectile break-up, obtained from continuum discretized coupled channel calculations, were performed. The comparison between the existing experimental elastic angular distribution with the coupled-reaction channels calculations indicates that the 1n stripping transfer is the most intense channel to be coupled and the 2n stripping reaction occurs sequentially rather than directly, however, further data must be analyzed to confirm this indication. The experimental elastic and inelastic scattering data were well described by the calculations, but some discrepancies in these channels may indicate the need for corrections to the nuclear potential and/or the necessity to incorporate further channels.

One-neutron stripping fromBe9toTm169,Ta181, andRe187at near-barrier energies

We report the measurement of one-neutron stripping of $^{9}\text{Be}$ to the $^{169}\text{Tm},\phantom{\rule{0.16em}{0ex}}^{181}\text{Ta}$, and $^{187}\text{Re}$ nuclei, in the range from subbarrier to above-barrier energies. The activation technique was used, with the detection of off-line $\ensuremath{\gamma}$ rays. The results show that the transfer cross sections for the three systems investigated are very similar and are much larger than the corresponding fusion cross sections at subbarrier energies, whereas fusion predominates at energies above the barrier. Data are in good agreement with our coupled reaction channel calculations. We also investigate the ratio, as a function of energy, between experimental transfer and fusion cross sections. The role of transfer couplings on the fusion excitation functions is also discussed.

One-neutron stripping processes to excited states of theLi6+Zr96reaction at near-barrier energies

We report the measurement of one-neutron stripping to excited-state cross sections from the weakly bound projectile $^{6}\mathrm{Li}$ to the $^{96}\mathrm{Zr}$ target at near-barrier energies by the online $\ensuremath{\gamma}$-ray spectroscopy method. Transitions of the $^{97}\mathrm{Zr}$ nucleus were clearly identified by $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidences. This cross section was found to be much smaller than the previously reported complete-fusion cross section for this system at energies above the barrier, whereas it becomes of the same magnitude around the Coulomb-barrier energy. No evidence of two-neutron transfer was found. We also performed coupled reaction channel calculations for the one-neutron stripping process. The calculation results are discussed.

Understanding the two neutron transfer reaction mechanism in 206Pb(18O,16O)208Pb

The absolute cross sections for elastic scattering and two-neutron transfer reaction for 18O + 206Pb system have been measured at an incident energy near the Coulomb barrier. Detailed coupled reaction channel calculations have been carried out for description of the measured angular distributions for the elastic scattering and transfer reactions simultaneously. The two-neutron transfer reaction 206Pb(18O, 16O)208Pb in the g.s. → g.s. transition is analyzed in (i) extreme cluster model assuming a di-neutron transfer, (ii) two-step successive transfer, and (iii) microscopic approach (independent coordinate scheme) of simultaneous transfer of two neutrons. The relative importance of one step simultaneous transfer versus two-step successive transfer has been studied. Present analysis suggests dominance of cluster transfer of a di-neutron. The contribution from the two-step sequential processes is less significant, however, the combined “two-step plus simultaneous (microscopic)” calculations give a reasonably good agreement with the measurement. The possibility of multi-step route via projectile and target excitations and contribution from such indirect transfer paths to the present two-neutron transfer cross section has been investigated.

Barrier distribution functions for the systemLi6+Ni64and the effect of channel coupling

Background: The barrier distribution function is an important observable in low-energy nucleus-nucleus collisions because it carries the distinct signature of the channel-coupling effect that is dominant at low energies. It can be derived from the fusion excitation function as well as from the back-angle quasi-elastic excitation function. The barrier distribution functions derived from the two complimentary measurements, in general, appear to peak at an energy close to the Coulomb barrier for strongly bound systems. But for weakly bound projectiles, like $^{6}\mathrm{Li}$, a relative shift is observed between the distributions.Purpose: The present work investigates the barrier distribution functions from fusion as well as from the back-angle quasi-elastic excitation function for the $^{6}\mathrm{Li}+^{64}\mathrm{Ni}$ system. The purpose is to look for the existence of a shift, if any, between the two measured distribution functions, as reported for $^{6}\mathrm{Li}$ collision with heavy targets. A detailed coupled-channel calculation to probe the behavior of the distribution functions and their relative shift has been attempted.Measurement: A simultaneous measurement of fusion and back-angle quasi-elastic excitation functions for the system $^{6}\mathrm{Li}+^{64}\mathrm{Ni}$ was performed. The fusion excitation function was measured for the energy range of 11 to 28 MeV while the quasi-elastic excitation function measurement extended from 11 to 20 MeV. The barrier distribution functions were subsequently extracted from both the excitation functions and compared.Results: A small shift of around 450 keV peak to peak is observed between the barrier distribution functions derived from the complementary measurements. Detailed coupled channel and coupled reaction channel calculations reproduced both the excitation functions and barrier distributions. The shift of about 550 keV resulted from the model predictions corroborate the experimentally observed value for $^{6}\mathrm{Li}+^{64}\mathrm{Ni}$ system.Conclusions: The coupling to inelastic channels are found to be sufficient to describe the fusion-barrier distribution. The positive $Q$-value one-proton and one-neutron stripping channels, leading to three-body final states, on the other hand, play dominant roles in reproducing the barrier distribution from the back-angle quasi-elastic excitation function.

Spectroscopy of narrow, high-lying, low-spin states inNe20

The excited states of the $^{20}\mathrm{Ne}$ nucleus from the ground state to ${E}_{x}$ = 25 MeV were investigated with the $^{22}\mathrm{Ne}$($p,t$)$^{20}\mathrm{Ne}$ reaction at a beam energy of ${E}_{p}$ = 60 MeV using the QDD magnetic spectrometer at iThemba LABS. Narrow, low-spin ${J}^{\ensuremath{\pi}}={0}^{+},{1}^{\ensuremath{-}}$, and ${2}^{+}$ states have been observed for the first time at high-excitation energies in $^{20}\mathrm{Ne}$, namely at ${E}_{x}$ = 17.67, 18.84, 20.59, 21.16, 21.80, and 22.5 MeV. Shell-model and coupled reaction channel calculations were performed to determine the nature of the newly observed states. Candidates for $T$ = 2 states are proposed at 3.86(5), 4.43(5) MeV and 5.07(5) MeV above the lowest ${0}^{+},T$ = 2 state at ${E}_{x}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}16.73$ MeV. Two of these $T$ = 2 candidates appear to result from core excitations in the $0p$ shell. The state at ${E}_{x}$ = 22.5 MeV, which could not be interpreted by the shell-model calculations, is a tentative candidate for the 5-$\ensuremath{\alpha}$ cluster state.

1n-transfer reaction using6Li with heavy mass target

Influence of 1n-transfer coupling on quasi-elastic scattering excitation function has been investigated for 6 Li + 209 Bi system. Coupled Reaction Channels Calculations have been carried out for the energies around the Coulomb barrier. Corresponding barrier distributions obtained with and without including 1n-transfer cou- pling, have been compared with experimental data. 1n-transfer effect on quasi-elastic excitation function has been observed to be insignificant for the present system. In the reaction of 6 Li with 208 Pb and 209 Bi, an ex- perimental relative contributions for breakup and 1n-transfer channels have been reproduced by simultaneous calculation using CDCC and CRC formalism.

One neutron transfer reaction in the9Be+89Y system

One neutron transfer cross sections from the interaction of 9 Be with 89 Y have been measured at energies greater than the fusion barrier. The present measured 1n-transfer cross sections saturate at well above energies in comparison with the available experimental data at lower energies. Results of Coupled Reaction Channels Calculations (CRC) show very good agreement with the present measured cross sections.

Neutron asymptotic normalization coefficients and halo radii of the first excited states of13C and11Be

We have performed coupled reaction channels calculations of the (d,p) reactions on 12 C and 10 Be at laboratory energies of 12, 25, and 30 MeV leading to the ground and first excited states of 13 C and 11 Be. We found spectroscopic factors Sexp, asymptotic normalization coefficients (ANCs) and root mean square radii of the last neutron in these states. Our calculations confirm the existence of neutron halos in the first excited state of 13 C, as well as in the ground and the first excited states of 11 Be. We found that the neutron transfer dominates at energies about 12 and 25 MeV and demonstrated that the states with enlarged radii are formed in the reactions of a peripheral type, which satisfy the criterion of a peripherality: C 2 =Sexpb 2 =const, where C is the ANC and b is the single-particle ANC.

Quantitative analysis of two-neutron correlations in the12C(18O,16O)14C reaction

The ${}^{12}$C(${}^{18}$O,${}^{16}$O)${}^{14}$C and ${}^{12,13}$C(${}^{18}$O,${}^{17}$O)${}^{13,14}$C reactions are studied at 84 MeV. Mass distributions and energy spectra of the ejectiles are measured, indicating the selectivity of these reactions to populate two- and one-neutron configurations in the states of the residual nucleus, respectively. The measured absolute cross-section angular distributions are analyzed by exact finite range coupled reaction channel calculations based on a parameter free double-folding optical potential. The form factors for the (${}^{18}$O,${}^{16}$O) reaction are extracted within an extreme cluster and independent particles scheme with shell-model-derived coupling strengths. The results show that the measured cross sections are accurately described for the first time without the need for any arbitrary scaling factor. The (${}^{18}$O,${}^{16}$O) reaction is thus found to be a powerful tool for quantitative spectroscopic studies of pair configurations in nuclear states.

BACKWARD ANGLE STRUCTURE IN THE 20Ne+28Si QUASIELASTIC SCATTERING

New data for the quasielastic scattering of 20 Ne from a 28 Si target at incident energies of 42.5 MeV and 52.3 MeV and for the 28 Si (20 Ne , 24 Mg )24 Mg , 28 Si (20 Ne , 16 O )32S and 28 Si (20 Ne , 12 C )36 Ar transfer reactions at 52.3 MeV are reported. Oscillations are observed in the backward angle quasielastic scattering data at 52.3 MeV and the 28 Si (20 Ne , 12 C )36 Ar transfer cross-sections are of the same magnitude as those for single-α stripping. Coupled reaction channels (CRC) calculations are unable to describe either the quasielastic or the 28 Si (20 Ne , 12 C )36 Ar transfer data assuming a sequential α transfer process with α-particle form factors from the literature. The addition of direct 8 Be cluster transfer can provide a reasonable description of both data sets, but only with much larger spectroscopic factors than suggested by simple structure calculations or the large 8 Be emission thresholds of 20 Ne , 28 Si and 36 Ar , suggesting that the observed structure is of resonance-like origin. An optical model analysis of the quasielastic scattering data is also reported.

Breakup and neutron-transfer effects on6He+206Pb elastic scattering below the Coulomb barrier

The elastic scattering and inclusive α-particle yield for the 6He+206Pb system at an incident energy of 18 MeV, just below the nominal Coulomb barrier, have been measured. The α-particle yield at forward angles is also reported. The data are analyzed by means of continuum-discretized coupled-channels, distorted wave Born approximation, and coupled reaction channels calculations. Couplings to the one-neutron- and two-neutron-transfer reactions are found to be able to account for most of the absorption in the entrance channel. © 2013 American Physical Society.

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.

Fusion of the most neutron-rich nucleus8He: Recent results from GANIL

Re-accelerated radioactive ions beams of 8He from the SPIRAL facility at GANIL have been used to perform the first experimental investigations at energies around the Coulomb barrier of fusion and direct reactions with the most neutron rich 8He. Two experiments (in the 8He+65Cu and 8He+197Au systems) have been performed, using the complementarity of in-beam and off-beam techniques, to measure integral and differential cross sections for elastic scattering, fusion and neutron(s) transfer. These results, compared with Coupled Reaction Channels calculations as well as phenomenological approaches allowed to probe and understand the different facets of the interplay between the intrinsic structure of 8He and reaction mechanisms.

Reactions with the double-Borromean nucleusHe8

Differential cross sections for elastic-scattering and neutron-transfer reactions along with cross sections for fusion in the $^{8}\mathrm{He}$$+$$^{65}\mathrm{Cu}$ system are reported at energies above the Coulomb barrier (${E}_{\mathrm{lab}}=$ $19.9$ and $30.6$ MeV). The present work demonstrates the feasibility of using inclusive measurements of characteristic in-beam $\ensuremath{\gamma}$ rays with low-intensity ($~$$10$${}^{5}$ pps) radioactive ion beams to obtain the residue cross sections for fusion and neutron transfer. Exclusive measurements of $\ensuremath{\gamma}$ rays in coincidence with light charged particles have been used to further characterize the direct reactions induced by this double-Borromean nucleus. Coupled reaction channels calculations are used to illustrate the important role played by the transfer channels and to help in understanding the influence of the structure of $^{8}\mathrm{He}$ on the reaction mechanism.

Simultaneous analysis of elastic scattering and transfer/breakup channels for the 6He + 208Pb reaction at energies near the Coulomb barrier

The elastic and α-production channels for the He 6 + Pb 208 reaction are investigated at energies around the Coulomb barrier ( E lab = 14 , 16, 18, 22, and 27 MeV). The effect of the two-neutron transfer channels on the elastic scattering has been studied within the Coupled-Reaction-Channels (CRC) method. We find that the explicit inclusion of these channels allows a simultaneous description of the elastic data and the inclusive α cross sections at backward angles. Three-body Continuum-Discretized Coupled-Channels (CDCC) calculations are found to reproduce the elastic data, but not the transfer/breakup data. The trivial local polarization potential (TLP) derived from the CRC and CDCC calculations are found to explain the features found in previous phenomenological optical model calculations for this system.

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.

Li6andHe6elastic scattering fromC12and the effect of direct reaction couplings

Similarities in the $^{6}\mathrm{Li}$ and $^{6}\mathrm{He}$ elastic scattering from $^{12}\mathrm{C}$ at about 35 MeV/nucleon are manifested in the ability of an optical model potential that differs only in having a weaker imaginary strength for $^{6}\mathrm{He}$ than for $^{6}\mathrm{Li}$ to describe both data sets equally well. However, the weaker absorption seen in the $^{6}\mathrm{He}+^{12}\mathrm{C}$ data is counter to expectations of the effect of coupling to breakup channels, confirmed by continuum discretized coupled channels calculations. Coupled reaction channels calculations including couplings to the strongest transfer channels are also unable to account for this phenomenon.

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.