Comparative assessment of the total breakup proton-emission cross sections measured for 56 MeV deuteron interaction with target nuclei from $^{12}$C to $^{209}$Bi, with an empirical parametrization and recently calculated microscopic neutron-removal cross sections has been done at the same time with similar data measured at 15, 25.5, 70, and 80 MeV. Comparable mass dependances of the elastic-breakup (EB) cross sections provided by the empirical parametrization and the microscopic results have been also found at the deuteron energy of 56 MeV, while the assessment of absolute-values variance up to a factor of two has been not possible due to the lack of EB measurements at energies higher than 25.5 MeV. While the similarities represent an additional validation of the microscopic calculations, the cross-section difference should be considered within the objectives of further measurements.
The Kohn variational principle is formulated for calculating elastic proton-deuteron scattering amplitudes at energies above the deuteron breakup threshold. The use of such a principle with an expansion of the wave function on the (correlated) hyperspherical harmonic basis is discussed.
We present calculations of deuteron elastic and inelastic breakup cross sections and angular distributions at deuteron energies below 100 MeV obtained using the post-form DWBA approximation. The elastic breakup cross section was extensively studied in the past. Very few calculations of inelastic breakup have been performed, however. We also analyze the angular momentum - energy distributions of the cross section for formation of the compound nucleus after inelastic breakup.
We investigate the effect of the deuteron breakup on the optical potential for the elastic scattering of 56 MeV deuterons from $^{51}$V. The breakup probabilities calculated within the post-form distorted wave Born-approximation theory of breakup reactions are fitted to derive the contribution to the optical potential from the breakup channels. The breakup potentials are found to have large real as well as imaginary parts. Thus the dynamical polarization potential due to the breakup process is expected to modify strongly the real part of the optical potential calculated by the double folding m…
The complex Kohn variational principle and the (correlated) hyperspherical harmonics method are applied to study the proton-deuteron elastic scattering at energies above the deuteron breakup threshold. Results for the elastic cross section and various elastic polarization observables have been obtained by fully taking into account the long-range effect of the Coulomb interaction and using a realistic nucleon-nucleon interaction model. Detailed comparison between the theoretical predictions and the accurate and abundant proton-deuteron experimental data can now be performed.
The hadron-deuteron correlation function has attracted many interests as a potential method to access the three-hadron interactions. However, the weakly-bound nature of deuteron has not been considered in the preceding studies. In this study, the breakup effect of deuteron on the deuteron-$Ξ^-$ ($d$-$Ξ^-$) correlation function $C_{dΞ^-}$ is investigated. The $d$-$Ξ^-$ scattering is described by a nucleon-nucleon-$Ξ$ three-body reaction model. The continuum-discretized coupled-channels method, which is a fully quantum-mechanical and non-perturbative reaction model, is adopted. $C_{dΞ^-}$ turns …
We discuss deuteron $A(d,p)X$ breakup and cumulative pion production $A(d,π)X$ in the framework of constituent quark model of the deuteron. We demonstrate that consideration of the Pauli principle at the quark level, as well as multiple scattering, affect drastically cross section and polarization observables of these reactions and provide good description of the experimental data.
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 conc…
Theoretical predictions for the nucleon induced deuteron breakup process based on solutions of the three-nucleon Faddeev equation including such relativistic features as the relativistic kinematics and boost effects are presented. Large changes of the breakup cross section in some complete configurations are found at higher energies. The predicted relativistic effects, which are mostly of dynamical origin, seem to be supported by existing data.
We re-examine the deuteron elastic breakup cross sections on 12C and 10Be at low incident energies, for which a serious discrepancy between the continuum-discretized coupled-channels method (CDCC) and the Faddeev-Alt-Grassberger-Sandhas theory (FAGS) was pointed out. We show the closed-channels neglected in the preceding study affect significantly the breakup cross section calculated with CDCC, resulting in good agreement with the result of FAGS.
A microscopic formalism for describing observed cross sections for deuteron breakup by three-nucleon nuclei was developed on the basis of the diffraction nuclear model. A general formula that describes the amplitude for the reaction d+3He->3He+p+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 He-3 nuclei at the projectile energy of 89.4 MeV. The importance of employing, in calculations, a deuteron…
We extend our approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) Faddeev calculations from elastic proton-deuteron (pd) scattering to the breakup process. The main new ingredient is a 3-dimensional screened pp Coulomb t-matrix obtained by a numerical solution of the 3-dimensional Lippmann-Schwinger equation. We demonstrate numerically that the proton-deuteron breakup observables can be determined from the resulting on-shell 3N amplitudes increasing the screening radius. However, contrary to the pd elastic scattering, the screening limit exists only after r…
The low-energy breakup differential cross sections of the neutron-deuteron (nd) scattering are studied by employing the energy-independent version of the quark-model baryon-baryon interaction fss2. This interaction reproduces almost all the breakup differential cross sections predicted by the meson-exchange potentials for the neutron incident energies $E_n \leq$ 65 MeV. The space star anomaly of 13 MeV nd scattering is not improved even in our model. Some overestimation of the breakup differential cross sections at $E_n$=22.7 - 65 MeV implies that systematic studies of various breakup configur…
The differential cross section, the tensor analyzing power, $T_{20}$, and the polarization transfer, $κ_0$, in $^{12}C(d,p)$ breakup at relativistic energy are calculated within a model which incorporates multiple scattering and Pauli principle at quark level. It is shown that the rescattering and quark exchange affect drastically the polarization observables for kinematical region corresponding to high internal momentum in the deuteron.
We examine a description of available cross section data for symmetric space star (SST) configurations in the neutron-deuteron (nd) and proton-deuteron (pd) breakup reaction using numerically exact solutions of the three-nucleon (3N) Faddeev equation based on two- and three-nucleon (semi)phenomenological and chiral forces. The predicted SST cross sections are very stable with respect to the underlying dynamics for incoming nucleon laboratory energies below $\approx 25$ MeV. We discuss possible origins of the surprising discrepancies between theory and data found in low-energy nd and pd SST bre…
The contributions to the reaction cross section from the elastic and inelastic breakup processes, calculated within the post-form distorted wave Born-approximation theory, are used as constraints to determine the contributions to the imaginary part of the deuteron optical potentials (IPDOP) due to the breakup channels. The Coulomb part of this potential due to the elastic breakup process is seen to account for the long range absorption in the optical potential. The nuclear parts of the IPDOP due to the elastic and inelastic breakup modes peak in different regions of the nuclear surface, with t…
A new computational method for solving the nucleon-deuteron breakup scattering problem has been applied to study the inelastic neutron-deuteron scattering on the basis of the configuration-space Faddeev equations. This method is based on the spline-decomposition in the angular variable and on a generalization of the Numerov method for the hyperradius. The Merkuriev-Gignoux-Laverne approach has been generalized for arbitrary nucleon-nucleon potentials and with an arbitrary number of partial waves. Neutron-deuteron observables at the incident nucleon energy 14.1 MeV have been calculated using th…
The problem of the calculation of inclusive breakup cross sections in nuclear reactions is reexamined. For that purpose, the post-form theory proposed by Ichimura, Austern and Vincent [Phys. Rev. C32, 431 (1985) is revisited, and an alternative derivation of the non-elastic breakup part of the inclusive breakup is presented, making use of the coupled-channels optical theorem. Using the DWBA version of this model, several applications to deuteron and $^6$Li reactions are presented and compared with available data. The validity of the zero-range approximation of the DWBA formula is also investig…
Use of deuteron-induced spallation reactions at intermediate energies has recently been proposed for transmutation of several long-lived fission products (LLFPs). In the design study of a transmutation system using a deuteron primary beam, accurate cross section data of deuteron-induced reactions on the LLFPs are indispensable. Reliable model predictions play an important role in completing the necessary cross section data since currently available experimental data are very limited. Under the circumstances, we have been developing a code system dedicated for deuteron-induced reactions, which …
We extended the study of relativistic effects in neutron-deuteron scattering to the exclusive breakup. To this aim we solved the three-nucleon Faddeev equation including such relativistic features as relativistic kinematics and boost effects at incoming neutron lab. energies E_n^{lab}=65 MeV, 156 MeV and 200 MeV. As dynamical input a relativistic nucleon-nucleon interaction exactly on-shell equivalent to the CD Bonn potential has been used. We found that the magnitude of relativistic effects increases with the incoming neutron energy and, depending on the phase-space region, relativity can inc…
The reactions of nucleon and polarized deuteron scattered off a heavy target at large impact parameter with intermediate energies have been investigated by using the improved quantum molecular dynamics model. It is found that, due to the difference effect of isovector potential on proton and neutron, there is a significant difference between the angle distribution of elastic scattering protons and neutrons. To overcome the lack of monochromatic neutron beam, the reaction of polarized deuteron peripherally scattered off the heavy target is used to replace the reaction of individual proton and n…
Quasi-binary reaction of the deuteron breakup $p+d\to (pp)+n$ with the final proton-proton pair $(pp)$ in the $^1S_0$ state is analyzed at initial energies $0.5 - 2$ GeV in the kinematics of backward elastic pd-scattering $pd\to dp$. On the basis of the main mechanisms of the $pd\to dp$ process, including initial and final state interaction, we show that unpolarized cross section and spin observables of this reaction exhibit important properties of the half-off-shell $pp(^1S_0)$-scattering amplitude, which are relevant to the nucleon-nucleon interaction at short distances.
We discuss the quasi-adiabatic approximations to the three-body wavefunction in breakup processes, clarifying the assumptions underlying the model. This suggests alternative approximation schemes. Using different theoretical three-body models, calculated differential cross section angular distributions for the Be-11(p,d) reaction,for which new preliminary data have been reported at 35 MeV, are presented. We show that calculations are sensitive to the inclusion of deuteron breakup and to the breakup model used, particularly if used to deduce absolute spectroscopic information on the 0{+} and 2{…
An extensive study of three-nucleon force effects in the entire phase space of the nucleon-deuteron breakup process, for energies from above the deuteron breakup threshold up to 200 MeV, has been performed. 3N Faddeev equations have been solved rigorously using the modern high precision nucleon-nucleon potentials AV18, CD Bonn, Nijm I, II and Nijm 93, and also adding 3N forces. We compare predictions for cross sections and various polarization observables when NN forces are used alone or when the two pion-exchange Tucson-Melbourne 3NF was combined with each of them. In addition AV18 was combin…
An isoscalar $pn$ pair is expected to emerge in nuclei that have similar proton and neutron numbers and it may be a candidate for a deuteron ``cluster.'' There is, however, no experimental evidence for it. The purpose of this paper is to construct a new reaction model for the ($p,pd$) reaction including the deuteron breakup in the elementary process and the deuteron reformation by the final-state interactions (FSIs). How these processes contribute to the observables of the reaction is investigated. The distorted wave impulse approximation is extended in twofold. The elementary processes of the…
We present results for the three-cluster breakup in deuteron-deuteron collisions at 130 and 270 MeV deuteron beam energy. The breakup amplitude is calculated using the first term in the Neumann series expansion of the corresponding exact four-nucleon equations. In analogy with nucleon-deuteron breakup where an equivalent approximation is compared with exact calculations, we expect this single-scattering approximation to provide a rough estimation of three-body breakup observables in quasifree configurations. We predict the nucleon-deuteron and deuteron-deuteron three-cluster breakup cross sect…
The relation between the differential cross section of the charge-exchange breakup of a fast deuteron d+p -> (pp)+n and the differential cross section of the charge transfer process n+p -> p+n is discussed taking into account the effects of the proton identity and of the Coulomb and strong interactions of protons in the final state. The distribution of the relative momenta of the protons is found in the framework of the impulse approach. It is shown that the use of polarized initial deuterons and protons allows one to separate two spin-dependent terms in the amplitude of the charge transfer re…
We investigate the sensitivity of the non-exclusive nucleon induced deuteron breakup reaction to the three-nucleon interaction and distributions of three-nucleon force effects in inclusive spectra. To this end we solve the three-nucleon Faddeev equation at a number of incoming nucleon laboratory energies using the CD Bonn nucleon-nucleon interaction alone or combined with the 2π-exchange Tucson-Melbourne three-nucleon force. Based on these solutions energy spectra of an outgoing nucleon, at a specified detection angle as well as spectra integrated over that angle, are calculated. By integratin…
Deuteron-deuteron elastic scattering and transfer reactions in the energy regime above four-nucleon breakup threshold are described by solving exact four-particle equations for transition operators. Several realistic nuclear interaction models are used, including the one with effective many-nucleon forces generated by the explicit $Δ$-isobar excitation; the Coulomb force between protons is taken into account as well. Differential cross sections, deuteron analyzing powers, outgoing nucleon polarization, and deuteron-to-neutron polarization transfer coefficients are calculated at 10 MeV deuteron…
The complex Kohn variational principle and the (correlated) Hyperspherical Harmonics technique are applied to study the N--d scattering above the deuteron breakup threshold. The configuration with three outgoing nucleons is explicitly taken into account by solving a set of differential equations with outgoing boundary conditions. A convenient procedure is used to obtain the correct boundary conditions at values of the hyperradius $\approx 100$ fm. The inclusion of the Coulomb potential is straightforward and does not give additional difficulties. Numerical results have been obtained for a simp…
In view of recent neutron-deuteron (nd) breakup data for neutron-neutron (nn) and neutron-proton (np) quasi-free-scattering (QFS) arrangements and the large discrepancy found between theoretical predictions and measured nn QFS cross sections, we analyze the sensitivity of the QFS cross sections to different partial wave components of the nucleon-nucleon (NN) interaction. We found that the QFS cross section is strongly dominated by the 1S0 and 3S1-3D1 contributions. Because the standard three-nucleon force (3NF) only weakly influence the QFS region, we conjecture, that it must be the nn 1S0 for…
An analysis of the $^{231}$Pa$(d,3n)$$^{230}$U reaction excitation function at energies around the Coulomb barrier has taken into account the pre-equilibrium and compound-nucleus cross sections corrected for the deuteron-breakup decrease of the total reaction cross section, as well as the inelastic breakup enhancement. The analysis reveals the dominance of the deuteron breakup mechanism unlike a former assessment in this respect of the deuteron-induced fission process.
Selected Nd breakup data over a wide energy range are compared to solutions of Faddeev equations based on modern high precision NN interactions alone and adding current three-nucleon force models. Unfortunately currently available data probe phase space regions for the final three nucleon momenta which are rather insensitive to 3NF effects as predicted by current models. Overall there is good to fair agreement between present day theory and experiment but also some cases exist with striking discrepancies. Regions in the phase space are suggested where large 3NF effects can be expected.
The deuteron fragmentation by fast protons has been studied both near the kinematics of quasi-free proton - proton scattering and far away from it. We have concentrated on the interplay between different reaction mechanisms associated with the antisymmetrization of the initial and final states and rescattering contributions. A multiple-scattering-expansion technique has been applied to evaluate the reaction amplitude. An essential element of this approach in the momentum representation is the use of the effective nucleon- nucleon interaction constructed by Love and Franey as a two-body t-matri…
An extended analysis of the key role of direct interactions, i.e., breakup, stripping and pick-up processes, has been carried out for deuteron-induced reactions. Particular comments concern the deuteron breakup which is the dominant mechanism involved in surrogate reactions on heavy nuclei, around the Coulomb barrier.
We present in this paper a formalism for deuteron-induced inclusive reactions. We disentangle direct elastic breakup contributions from other processes (which we generically call non-elastic breakup) implying a capture of the neutron both above and below the neutron emission threshold. The reaction is described as a two step process, namely the breakup of the deuteron followed by the propagation of the neutron-target system driven by an optical potential. The final state interaction between the neutron and the target can eventually form an excited compound nucleus. Within this context, the dir…
The exclusive deuteron break-up reaction is analyzed within a covariant approach based on the Bethe-Salpeter equation with realistic meson-exchange interaction. Relativistic effects in the cross section, tensor analyzing power and polarization transfer are investigated in explicit form. Results of numerical calculations are presented for kinematical conditions in forthcoming p + D reactions at COSY.
A set of differential cross section of the three-body $^{2}$H($d$,$dp$)$n$ breakup reaction at 160 MeV deuteron beam energy are presented for 147 kinematically complete configurations near the quasi-free scattering kinematics. The experiment was performed at KVI in Groningen, the Netherlands using the BINA detector. The cross-section data have been normalized to the $^{2}$H($d$,$d$)$^{2}$H elastic scattering cross section. The data are compared to the recent single-scattering approximation (SSA) calculations for three-cluster breakup in deuteron-deuteron collisions. Confronting the SSA predict…
Recent advances in the study of electrodisintegration of 3He are presented and discussed. The pair-correlated hyperspherical harmonics method is used to calculate the initial and final state wave functions, with a realistic Hamiltonian consisting of the Argonne v18 two-nucleon and Urbana IX three-nucleon interactions. The model for the nuclear current and charge operators retains one- and many-body contributions. Particular attention is made in the construction of the two-body current operators arising from the momentum-dependent part of the two-nucleon interaction. Three-body current operator…
Available experimental data on the exclusive $pd\to pnp$ reaction at 585 MeV show a narrow peak in the proton-neutron final-state interaction region. It was supposed previously, on the basis of a phenomenological analysis of the shape of this peak, that the final spin-singlet $pn$ state provided about one third of the observed cross section. By comparing the absolute value of the measured cross section with that of $pd$ elastic scattering using the Fäldt-Wilkin extrapolation theorem, it is shown here that the $pd\to pnp$ data can be explained mainly by the spin-triplet final state with a singl…
We present a practical method to solve the proton-deuteron scattering problem at energies above the three-body breakup threshold, in which we treat three-body integral equations in coordinate space accommodating long-range proton-proton Coulomb interactions. The method is examined for phase shift parameters, and then applied to calculations of differential cross sections in elastic and breakup reactions, analyzing powers, etc. with a realistic nucleon-nucleon force and three-nucleon forces. Effects of the Coulomb force and the three-nucleon forces on these observables are discussed in comparin…
The influence of the magnetic moment interaction of nucleons on nucleon-deuteron elastic scattering and breakup cross sections and on elastic scattering polarization observables has been studied. Among the numerous elastic scattering observables only the vector analyzing powers were found to show a significant effect, and of opposite sign for the proton-deuteron and neutron-deuteron systems. This finding results in an even larger discrepancy than the one previously established between neutron-deuteron data and theoretical calculations. For the breakup reaction the largest effect was found for …
The coefficients of new analytical forms for the deuteron wave function in coordinate space for NijmI, NijmII, Nijm93, Reid93 and Argonne v18 potentials have been numerically calculated. The obtained wave functions do not contain any superfluous knots. The designed parameters of the deuteron are in good agreement with the experimental and theoretical data. The new parameterization of the deuteron wave function in momentum space is obtained. The tensor polarization t20 calculated based on the wave functions is proportionate to the earlier published results.
Neutrino emissions from electron/positron capture on the deuteron and the nucleon-nucleon fusion processes in the surface region of a supernova core are studied. These weak processes are evaluated in the standard nuclear physics approach, which consists of one-nucleon and two-nucleon-exchange currents and nuclear wave functions generated by a high precision nucleon-nucleon potential. In addition to the cross sections for these processes involving the deuteron, we present neutrino emissivities due to these processes calculated for typical profiles of core-collapsed supernovae. These novel neutr…
Field-theoretical description of the deuteron breakup in the clothed particle representation
Akhiezer Institute for Theoretical Physics of NSC KIPT（NSC KIPT 阿赫伊泽尔理论物理研究所）；M. Smoluchowski Institute of Physics, Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University（雅盖隆大学物理、天文学和应用计算机科学学院 M.Smoluchowski 物理研究所）；Doctoral School of Exact and Natural Sciences, Jagiellonian University（雅盖隆大学精确与自然科学学院博士项目）；Research Center for Nuclear Physics, Osaka University（大阪大学核物理研究中心）；Department of Physics, Kyushu Institute of Technology（九州工业大学物理系）；Department of Physics and Astronomy, The University of Iowa（爱荷华大学物理与天文系）
We analyze the momentum distributions of constituents in 3He, as well as the spin-dependent observables for (3He,d), (3He,p), and (d,p) breakup reactions. Special attention is paid to the region of small relative momenta of the helium-3 and the deuteron constituents, where a single parameter, D_2, has determining role for the spin-dependent observables. We extract also this parameter for the deuteron, basing on existing data for the tensor analyzing power of this reaction.
Deuteron breakup processes $p+d\to (NN)_{s,t}+N$ are studied in the kinematics of backward elastic pd-scattering at law relative momenta of the NN-pair $k\sim 0-50 MeV/c$ for initial energies $T_0=0.5-2.5 GeV$ in the framework of the known mechanisms of the $pd\to dp$ process including rescatterings in the initial and final states. A considerable suppression of the $Δ-$ and $N^*-$ isobar excitation mechanisms is found for the production of the singlet $(NN)_s$-pair. As a result, one nucleon exchange mechanism can be identified in the cross section and polarization observables by the node of th…
The available data on the forward charge exchange of nucleons on the deuteron up to 2GeV per nucleon are reviewed. The value of the inclusive nd->pnn/np->pn cross section ratio is sensitive to the fraction of spin-independent neutron-proton backward scattering. The measurements of the polarisation transfer in d(\vec{n},\vec{p})nn or the deuteron analysing power in p(\vec{d},pp)n in high resolution experiments, where the final nn or pp pair emerge at low excitation energy, depend upon the longitudinal and transverse spin-spin np amplitudes. The relation between these types of experiments is dis…
We analyze the $^{16}{\rm C}+p$ and $^{16}{\rm C}+d$ reactions within the four- and five-body Continuum Discretized Coupled Channel (CDCC) method. The $^{16}$C nucleus is described by a $^{14}{\rm C}+n+n$ configuration in hyperspherical coordinates. This description reproduces fairly well several $^{16}$C low-lying states. First we analyze the $2^+\rightarrow 0^+$ $E2$ transition amplitude, which confirms that an effective charge must be introduced to reproduce the experimental value. Then, proton and deuteron elastic and inelastic scattering are investigated by including $^{16}$C pseudostates…
We study the effect of the neutrino magnetic moment on the neutrino-deuteron breakup reaction, using a method called the standard nuclear physics approach, which has already been well tested for several electroweak processes involving the deuteron.
The adiabatic distorted wave approximation (ADWA) is widely used by the nuclear community to analyse deuteron stripping ($d$,$p$) experiments. It provides a quick way to take into account an important property of the reaction mechanism: deuteron breakup. In this work we provide a numerical quantification of a perturbative correction to this theory, recently proposed in [R.C. Johnson, J. Phys. G: Nucl. Part. Phys. 41 (2014) 094005] for separable rank-one nucleon-proton potentials. The correction involves an additional, nonlocal, term in the effective deuteron-target ADWA potential in the entran…
We study high energy photodisintegration of the deuteron into two $Δ$-isobars at large center of mass angles within the QCD hard rescattering model (HRM). According to the HRM, the process develops in three main steps: the photon knocks the quark from one of the nucleons in the deuteron; the struck quark rescatters off a quark from the other nucleon sharing the high energy of the photon; then the energetic quarks recombine into two outgoing baryons which have large transverse momenta. Within the HRM, the cross section is expressed through the amplitude of $pn\rightarrow ΔΔ$ scattering which we…
We discuss how to reduce theoretical uncertainties in the neutrino-deuteron breakup cross-sections crucial to the Sudbury Neutrino Observatory's efforts to measure the solar neutrino flux. In effective field theory, the dominant uncertainties in all neutrino-deuteron reactions can be expressed through a single, common, isovector axial two-body current parameterized by $L_{1,A}$. After briefly reviewing the status of fixing $L_{1,A}$ experimentally, we present a constraint on $L_{1,A}$ imposed by existing reactor antineutrino-deuteron breakup data. This constraint alone leads to an uncertainty …
A new computational method for solving the configuration-space Faddeev equations for the breakup scattering problem has been applied to nd scattering both below and above the two-body threshold.
The Continuum Discretized Coupled Channels (CDCC) method is a well established theory for direct nuclear reactions which includes breakup to all orders. Alternatively, the 3-body problem can be solved exactly within the Faddeev formalism which explicitly includes breakup and transfer channels to all orders. With the aim to understand how CDCC compares with the exact 3-body Faddeev formulation, we study deuteron induced reactions on: i) $^{10}$Be at $E_{\rm d}= 21.4, 40.9 \; {\rm and} \; 71$ MeV; ii) $^{12}$C at $E_{\rm d} = 12 \; {\rm and} \; 56$ MeV; and iii) $^{48}$Ca at $E_{\rm d} = 56$ MeV…
