Proton-neutron correlation in the deuteron breakup at 56 MeV and prior-form DWBA analysis

Proton-neutron angular correlations in the ¹²C, ⁵¹V and ¹¹⁸Sn(d, pn) reactions have been measured at 56 MeV to investigate the deuteron breakup process. The elastic breakup which leaves the target nucleus in its ground state dominates the coincident spectra. The elastic breakup cross sections are estimated to be 36–48% of the inclusive breakup yields at 15° or 17.5°. In the angular correlations the protons are emitted predominantly on the side of the beam opposite to the neutrons. The experimental data have been analyzed using the prior-form DWBA. For both nuclear and Coulomb breakup, sufficient convergence of the calculations is obtained by including the pn angular momenta up to l = 2. For the nuclear breakup calculations, the l = 0 and 2 contributions dominate the cross sections. For the Coulomb breakup the l = 1 contribution is predominant. In the calculations the effect of the Coulomb breakup is seen at forward angles of the angular correlation. The DWBA calculations reproduce fairly well the coincident energy spectra and the angular correlations in the angular region where the protons are emitted on the side of the beam opposite to the neutrons. On the other hand the calculations overestimate the break-up cross sections by a factor of 2 to 10 in the angular region where the protons are emitted on the same side of the beam as the neutrons. The distributions of deuteron c.m. angular momenta that contribute to the breakup amplitude are examined to obtain information on the region of space in which the breakup reactions takes place.     

Momentum space 3N Faddeev calculations of hadronic and electromagnetic reactions with proton-proton Coulomb and three-nucleon forces included

We extend our approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) momentum space Faddeev calculations of elastic proton-deuteron (pd) scattering and breakup to the case when also a three-nucleon force (3NF) is acting. In addition, we formulate that approach in the application to electron- and g \gamma -induced reactions on ³He . The main new ingredient is a 3-dimensional screened pp Coulomb t -matrix obtained by a numerical solution of a 3-dimensional Lippmann-Schwinger equation (LSE). The resulting equations have the same structure as the Faddeev equations which describe pd scattering without 3NF acting. That shows the practical feasibility of both presented formulations.     

Influence of breakup on elastic and α-production channels in the ~6Li+~(116)Sn reaction

The effects of breakup reactions on elastic and α-production channels for the ~6Li+~(116)Sn system have been investigated at energies below and near the Coulomb barrier. The angular distributions of α-particle production differential cross sections have been obtained at several projectile energies between 22 and 40 MeV. The measured breakup α-particle differential cross sections and elastic scattering angular distributions have been compared with the predictions of continuum-discretized coupled channels(CDCC) calculations. The influence of breakup coupling has also been investigated by extracting dynamic polarization potentials(DPP) from the CDCC calculations. From the predictions of CDCC calculations the relative importance of the nuclear, Coulomb, and total breakup contributions have also been investigated. The nuclear breakup couplings are observed to play an important role in comparison to the Coulomb breakup for the direct breakup mechanisms associated in the reaction of ~6Li projectile with ~(116)Sn target nuclei. The influence of strong nuclear breakup coupling exhibits suppression in the Coulomb-nuclear interference peak. The direct breakup cross sections from the CDCC calculations under-predict the measured α-particle differential cross sections at all energies. This suggests that the measured α particles may also have contributions from other possible breakup reaction channels.     

Large-angle quasi-free scattering in 6Li(p,pd)4He at 670 MeV

The ⁶Li(p, pd)⁴He reaction was investigated at 670 MeV by a coincidence experiment with a large-angle scattering geometry. The energy sharing and angular correlation of the reaction products were measured and the momentum distribution of the recoil nucleus was determined for transitions leading to residual nuclei in the ground and excited states. Results were analysed in terms of a simplified distorted-wave impulse approximation using cluster-model and three-body wave functions. The observed momentum distribution of the p-n pair in the p-shell of ⁶Li is in agreement with three-body calculations, while the spectroscopic factor is larger than predicted by theory. Transitions to breakup states of the α-particle also have the characteristics of quasi-free scattering on deuteron clusters.     

Elastic scattering and fusion cross-sections in 7Li + 27Al reaction

With an aim to understand the effects of breakup and transfer channels on elastic scattering and fusion cross-sections in the ⁷Li + ²⁷Al reaction, simultaneous measurement of elastic scattering angular distributions and fusion cross-sections have been carried out at various energies (E _lab?=?8.0–16.0 MeV) around the Coulomb barrier. Optical model (OM) analysis of the elastic scattering data does not show any threshold anomaly or breakup threshold anomaly behaviour in the energy dependence of the real and imaginary parts of the OM potential. Fusion cross-section at each bombarding energy is extracted from the measured α-particle evaporation energy spectra at backward angles by comparing with the statistical model prediction. Results on fusion cross-sections from the present measurements along with data from the literature have been compared with the coupled-channels predictions. Detailed coupled-channels calculations have been carried out to study the effect of coupling of breakup, inelastic and transfer, channels on elastic scattering and fusion. The effect of 1n-stripping transfer coupling was found to be significant compared to that of the projectile breakup couplings in the present system.     

A study of the odd isotopes of copper using the 58, 60, 62, 64Ni(τ, d) 59, 61, 63, 65Cu and 48Ca(τ, d)49Sc reactions

Experimental measurements are reported for the ^{58, 60, 62, 64}Ni(τ, d) ^{59, 61, 63, 65}Cu and ⁴⁸Ca(τ, d)⁴⁹Sc reactions and for the elastic scattering of ³He particles from ^{58, 60, 62, 64}Ni and ⁴⁸Ca targets at an incident energy of 18 MeV. The (τ, d) angular distributions cover the angular range from approximately θ_c.m. = 5° to 90° and the elastic scattering angular distributions range from θ_c.m. = 12° to 172°. In the (τ, d) reactions several weakly excited states, not previously seen in stripping reactions, have been identified and assignments of the transferred angular momentum made. The ⁴⁸Ca(τ, d)⁴⁹Sc reaction data are used in conjunction with the theoretical sum rules of MacFarlane and French to determine the normalization factors to be used with DWBA calculations for different sets of optical potentials. These normalization factors are used to extract spectroscopic strengths and centroid energies from the Ni(τ, d)Cu data which are compared with published model calculations for the odd copper isotopes. It is concluded that these calculations invariably fail to give a consistent picture of the odd copper isotopes mainly due to the use of centroid energies as variable parameters in the model calculations.     

Deuteron breakup with 3He at 89.4 and 118.9 MeV

Quasifree processes were studied by measuring coincident energy spectra for the ²H(³He, ³Hep)n, ²H(³He, tp)p and ²H(³He, dd)p reactions at 89.4 and 118.9MeV. The spectral shape was reproduced with two types of spectator model, that is, a three-body model (TBM) and a four-body model (FBM). The latter contains the effects of projectile breakup processes. Angular correlations of peak cross sections were explained by calculations in the FBM in contrast with those in the TBM. The absolute cross sections were not explained by either model.     

Analysis of inelastic scattering of3He on14C at 37.9 MeV

The differential cross sections of elastic and inelastic scattering of³He ions on the¹⁴C nucleus have been measured at an energy of 37.9 MeV. By fitting the shape of the measured angular distribution of the elastic scattering the parameters of the optical model have been found. These parameters have been used for the standard DWBA calculations of angular distributions corresponding to excitations of the¹⁴C levels 6.73(3^?), 7.01(2⁺) and 8.32(2⁺) MeV and for coupled channels calculations of the level 8.32(2⁺) MeV. The vibration parametersβ _L of the¹⁴C nucleus have been deduced.     

Fragment angular correlation in the breakup of 16O ions at 95 MeV/A

Fragment angular correlations in projectile breakup reactions are very sensitive to interference between different multipolarities entering in the excitation-dissociation process of the projectile. In particular, it was proposed to disentangle L = 1 and L = 2 contributions in direct breakup reactions of ¹⁶O with low relative energy between the α and ¹²C fragment, which are of astrophysical interest. We studied the experimental aspects of extracting those angular correlations in extreme kinematical conditions usually encountered in breakup experiments of astrophysical interest. The breakup of 95 MeV/A ¹⁶O projectiles induced by a ²⁰⁸Pb target was measured using the high-resolution spectrometer SPEG at Ganil for the coincident detection of the fragments. Sequential breakup via the 12.53 MeV level of ¹⁶O is analyzed in this framework and it favors an one-step M2 excitation of this level.     

The elastic scattering of 3He on 4He at medium energies

The differential cross section of the elastic scattering ³He(⁴He, ⁴He)³He has been measured at center of mass energies E_c.m. between 28 and 44 MeV and in the c.m. angular range of 20° to 160°. The ³He polarization P at E_c.m. = 42 MeV and θ_c.m. = 132° was determined in a double scattering experiment. The analysis of the cross section data with the optical and the cluster model has been described previously. The phase shifts obtained in the cluster model calculations were used as starting values in a phase shift analysis. The resulting final real phase shifts and elasticity parameters give good fits to the cross section data. At 44 MeV the elasticity parameters show a pronounced odd-even dependence on angular momentum which had been found already in the case of the real phase shifts. The result of the polarization experiment |P| < 0.22 is consistent with cluster model predictions.     

The reaction 3He + p → p + p + d studied with BOL at 69 MeV 3He incoming energy

The proton-induced ³He breakup into p and d has been studied in a kinematically complete way at 69 MeV ³He-incoming (23 MeV p-incoming) lab energy, using the spherical multi-detector array BOL.The four-dimensional cross-section data cover most of the three-body final-state phase space. By slicing and integrating the data, they have been brought into suitable one- and two-dimensional representations to reveal different aspects of the reaction process. Based on these, this paper presents information on the interplay between the different reaction modes occurring in the p³He breakup process. In particular, pp final-state interaction, pp and pd quasi-free scattering and nucléon transfer have been studied here.Anomalous effects, probably due to interference between these processes, show up in the data.     

Evidence for a deep bound-state level in the 4HeNaCl(001) potential

Through a systematic high-resolution study of the elastic bound state resonances observed in the inelastic background of the angular distributions of ⁴He scattering from the NaCl(001) surface, carried out at 90 K, we obtained clear and conclusive evidence that a deep level in the ⁴HeNaCl(001) interaction potential exists at −7.07 meV. Important deviations from the free-atom dispersion are observed, as expected for deep bound-state levels. We discuss the physical reasons why deep-level resonances, which are observed in inelastic scattering, may not be detectable in elastic scattering experiments. This finding appears to be crucial with respect to the theory of atom-surface potentials since former quantum-mechanical and close-coupling calculations excluded the existence of a deep level in ⁴HeNaCl(001) in agreement with elastic scattering studies but at odds with phenomenological predictions.     

Cross section and analyzing powers for the reaction pd→3He + γ at intermediate energies

We report the results of measurements of the differential cross section and analyzing power for the reaction pd → γ³He at six energies in the range 200 < E_p < 500 MeV. The cross-section data are in good agreement with the most recent results for the inverse process assuming detailed balance; thus no evidence for time-reversal violation is inferred. In addition, the shapes of the measured angular distributions are in general overall accord with those measured in the photodisintegration reaction. The data are compared with several theoretical calculations showing inclusion of meson-exchange current contributions to be important in reproducing the measured cross section. The analyzing powers measured at E_p = 500 MeV are not yet explained by microscopic models.     

Analysis of 6Li Scattering at 600 MeV

The elastic and inelastic scattering of ⁶Li on ¹²C, ⁵⁸Ni, ⁹⁰Zr, and ²⁰⁸Pb targets at 600 MeV are analyzed via double-folding optical model potentials based on the S1Y effective nucleon–nucleon (NN) interaction and tρρ approximation. Information is provided, by single- and coupled-channel calculations, on the effect of breakup and its feedback on the elastic scattering of ⁶Li ions. Experimental results are successfully reproduced. The in-medium NN cross-section and second-order (double-scattering) correction to the tρρ potential are taken into account. Reaction cross-sections are computed from exact and approximate solutions.     

Microscopic description of diffractive deuteron breakup by <Superscript>3</Superscript>He nuclei

A microscopic formalism for describing observed cross sections for deuteron breakup by threenucleon nuclei was developed on the basis of the diffraction nuclear model. A general formula that describes the amplitude for the reaction ²H(³He, ³Hep)n and which involves only one adjustable parameter was obtained by using expansions of the integrands involved in terms of a Gaussian basis. This formula was used to analyze experimental data on the exclusive cross sections for deuteron breakup by ³He nuclei at the projectile energy of 89.4MeV. The importance of employing, in calculations, a deuteron wave function that has a correct asymptotic behavior at large nucleon–nucleon distances was demonstrated.     

A study of the 6Be system by use of the reaction 3He(3He,p)5Li(g.s.) between 17 and 30 MeV with a polarized target

The differential cross section of the reaction ³He(³He, p)⁵Li(g.s.) has been measured at 26 MeV and the analyzing power A_γ in the energy range 17–30 MeV with the use of a polarized ³He target. The data are compared with existing microscopic multi-channel calculations to the ⁶Be system. The influence of the J^π = 4⁺ channels turned out to be too strong. The deviations from the antisymmetry to 90° c.m. of the analyzing power angular distribution _γ(θ) are discussed with respect to the purely direct transfer model for identical particles in the entrance channel.     

Proton-hole states in 115In observed in the 116Sn(d, 3He) reaction

The ¹¹⁶Sn(d, ³He)¹¹⁵In reaction has been investigated at E_d = 50 MeV. Thirteen transitions to states up to 3 MeV excitation energy were studied. The measured angular distributions were compared with DWBA calculations and transferred angular momenta and spectroscopic factors were deduced. Levels at 1.04, 2.23 and 2.52 MeV were found to be excited most likely by l = 3 angular momentum transfer in contrast to previous investigations at lower incident energies in which no l = 3 transitions have been observed.     

Reaction mechanism of <Superscript>6</Superscript>Li scattering at 600 MeV

Elastic scattering and inclusive breakup of ⁶Li particles on ¹²C, ⁵⁸Ni, ⁹⁰Zr, and ²⁰⁸Pb targets are measured at 100A MeV. The elastic scattering data are compared with single channel and Coupled Discretized Continuum Channels calculations. The coupling-effect between the elastic and the breakup channels is important even at an incident energy of 100A MeV and cannot be neglected. The inclusive breakup data are investigated for orbital dispersion effects which are found to be less significant at 100A MeV. The longitudinal momentum distributions are broader than predicted by theoretical expectations. Received: 17 December 1999 / Revised version: 9 February 2000     

DWBA analysis of (3He,d) reactions at 90MeV and contributions from the nuclear interior

Differential cross sections of ³He elastic scatterings and (³He, d) reactions have been measured at 90 MeV for ²⁸Si, ⁵⁴Fe, ⁵⁸Ni, ⁹⁰Zr and ¹²⁴Sn. From the optical-model analysis of the elastic scattering, both shallow ($\text{V ? 105}\text{MeV}$) and deep ($\text{V ? 150}\text{MeV}$) potentials of ³He were obtained. The shallow potentials correspond to the ones which were determined uniquely from other measurements extended to more backward angles. The (³He, d) reactions have been analyzed with the DWBA using the shallow and deep potentials for ³He. The calculations using the deep potentials reproduced the data well, but those using the shallow ones did not. The contributions from the nuclear interior were investigated through the radial cutoff in the DWBA. The calculations using the shallow potentials reproduced the data well when the radial cutoffs were introduced. The effects of the radial cutoff were very small when the deep potentials were used. It was found that a much greater reduction of the contributions from the nuclear interior was needed when the shallow potentials were used in the DWBA calculations.