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We give an overview of the theoretical description of nuclear reactions involving weakly-bound nuclei. Some of the more widespread reaction formalisms employed in the analysis of these reactions are briefly introduced, including various recent developments. We put special emphasis on the continuum-discretized coupled-channel (CDCC) method and its extensions to incorporate core and target excitations as well as its application to three-body projectiles. The role of the continuum for one-nucleon transfer reactions is also discussed. The problem of the evaluation of inclusive breakup cross sections is addressed within the Ichimura-Austern-Vincent (IAV) model. Other methods, such as those based on a semiclasical description of the scattering process, are also briefly introduced and some of their applications are discussed and a brief discussion on topics of current interest, such as nucleon-nucleon correlations, uncertainty evaluation and non-locality is presented., Comment: review paper; submitted to EPJA

Background: An important aspect of reducing nuclear many-body problems to few-body models is the presence of Pauli forbidden (PF) states, which are excluded in fully antisymmetrized calculations. Insufficient treatments of PF states in deformed halo nuclei underscore the need for model refinement. Purpose: We propose a new method utilizing Nilsson states as PF states in the orthogonality condition model, and investigate the impact of PF states on the properties of resonant states. Method: We investigate the scattering states of ${}^8\mathrm{B}$ within the Particle Rotor Model (PRM) framework based on a deformed ${}^7\mathrm{Be}$ core and $p$ two-body model. We compare several methods for eliminating PF states and test them with the experimental data. Results: Our model successfully reproduces the experimental excitation function for elastic scattering cross section by properly eliminating PF states. The same calculation predicts the presence of a low-energy bump in the inelastic scattering excitation function, although its position is overestimated by about 1 MeV compared to experimental data. Conclusion: This study extends the applicability of the PRM, offering a comprehensive approach for exploring structures and reactions of loosely bound nuclei like ${}^8$B. Future integration with the continuum discretized coupled channels (CDCC) method promises to further advance the research., Comment: 8 pages, 6 figures

The measurement of the $^7$Be($d$,$^3$He)$^6$Li* transfer cross section at 5 MeV/u is carried out. The population of the 2.186 MeV excited state of $^6$Li in this reaction channel is observed for the first time. The experimental angular distributions have been analyzed in the finite range DWBA and coupled-channel frameworks. The effect of the $^7$Be($d$,$^3$He)$^6$Li reaction on both the $^6$Li and $^7$Li abundances are investigated at the relevant big-bang nucleosynthesis energies. The excitation function is calculated by TALYS and normalized to the experimental data. The $S$ factor of the ($d$,$^3$He) channel from the present work is about 50$\%$ lower than existing data at nearby energies. At big-bang energies, the $S$ factor is about three orders of magnitude smaller than that of the ($d,p$) channel. The ($d$,$^3$He) reaction rate is found to have a less than 0.1$\%$ effect on the $^{6,7}$Li abundances., Comment: 7 pages, 5 figures

The dineutron correlation is systematically studied in three different Borromean nuclei near the neutron dripline, 11Li, 14Be and 17B, via the (p, pn) knockout reaction measured at the RIBF facility in RIKEN. For the three nuclei, the correlation angle between the valence neutrons is found to be largest in the same range of intrinsic momenta, which can be associated to the nuclear surface. This result reinforces the prediction that the formation of the dineutron is universal in environments with low neutron density, such as the surface of neutron-rich Borromean nuclei.

Background: Reactions with halo nuclei from deformed regions exhibit important deviations from the inert core+valence picture. Structure and reaction formalisms have recently been extended or adapted to explore the possibility of exciting the underlying core. Purpose: We will study up to what extent transfer reactions involving halo nuclei $^{11}$Be and $^{17}$C can be reproduced with two different models that have previously shown a good success reproducing the role of the core in light halo nuclei. Methods: We focus on the structure of $^{11}$Be and $^{17}$C with two core+valence models: Nilsson and a semi-microscopic particle-rotor model using Antisymmetrized Molecular Dinamic calculations of the cores. These models are later used to study $^{16}$C(d,p)$^{17}$C and $^{11}$Be(p,d)$^{10}$Be transfer reactions within the Adiabatic Distorted Wave Approximation. Results are compared with three different experimental data sets. Results: A good reproduction of both the structure and transfer reactions of $^{10}$Be and $^{17}$C is found. The Nilsson model provides an overall better agreement for the spectrum and reactions involving $^{17}$C while the semi-microscopic model is more adequate for $^{11}$Be, as expected, since the $^{17}$C core is closer to an ideal rotor. Conclusions: Both models show promising results for the study of transfer reactions with halo nuclei. We expect that including microscopic information in the Nilsson model, following the spirit of the semi-microscopic model, can provide a useful, yet simple framework for studying newly discovered halo nuclei., Comment: 11 pages, 11 figures

Inclusive breakup is an important reaction mechanism of reactions induced by weakly bound nuclei. The Ichimura, Austern, and Vincent (IAV) model is widely used to analyze inclusive breakup processes and is based on a Distorted Wave Born Approximation (DWBA). However, the validity of the DWBA form for inclusive breakup requires further exploration. In this study, we present a derivation of the IAV model, using the continuum-discretized coupled-channels (CDCC) wave function, and apply it to the $d+^{93}$Nb reaction. We examine the differences between the CDCC-IAV and DWBA-IAV models by artificially modifying the binding energy of the deuteron using two distinct types of optical potential. Our findings indicate that the CDCC method potentially provides a more fundamental description of the $d$+$A$ interaction and may provide a more realistic description of the interior part of the wave function. This study offers significant potential in increasing the precision and dependability of weakly bound nuclei inclusive breakup process estimation within a fully quantum mechanical model., Comment: 16 pages, 7 figures, submitted for publication

The discrepancy between experimental data and theoretical calculations in one-nucleon removal reactions at intermediate energies (quantified by the so-called "quenching factors") and its dependence on the isospin asymmetry of the nuclei has been an open problem in nuclear physics for the last fifteen years. In this work, we propose an explanation for this long-standing problem, which relies on the inclusion of the process of core destruction due to its interaction with the removed nucleon. To include this effect, we extend the commonly used eikonal formalism via an effective nucleon density, and apply it to a series of nucleon knockout reactions. The effect of core destruction is found to depend strongly on the binding energy of the removed nucleon, leading to a significant reduction of the cross section for deeply bound nucleons, which reduces the isospin dependence of the "quenching factors", making them more consistent with the trends found in transfer and (p,pN) reactions., Comment: 7 pages, 4 figures, Submitted to Physical Review Letters

The elastic and inelastic scattering of $^7$Be from $^{12}$C have been measured at an incident energy of 35 MeV. The inelastic scattering leading to the 4.439 MeV excited state of $^{12}$C has been measured for the first time. The experimental data cover an angular range of $\theta_{cm}$ = 15$^{\circ}$-120$^{\circ}$. Optical model analyses were carried out with Woods-Saxon and double-folding potential using the density dependent M3Y (DDM3Y) effective interaction. The microscopic analysis of the elastic data indicates breakup channel coupling effect. A coupled-channel analysis of the inelastic scattering, based on collective form factors, show that mutual excitation of both $^7$Be and $^{12}$C is significantly smaller than the single excitation of $^{12}$C. The larger deformation length obtained from the DWBA analysis could be explained by including the excitation of $^7$Be in a coupled-channel analysis. The breakup cross section of $^7$Be is estimated to be less than 10$\%$ of the reaction cross section. The intrinsic deformation length obtained for the $^{12}$C$^*$ (4.439 MeV) state is $\delta _2$ = 1.37 fm. The total reaction cross section deduced from the analysis agrees very well with Wong's calculations for similar weakly bound light nuclei on $^{12}$C target., Comment: 8 pages, 5 figures

Atomic nuclei are composite systems, and they may be dynamically excited during nuclear reactions. Such excitations are not only relevant to inelastic scattering but they also affect other reaction processes such as elastic scattering and fusion. The coupled-channels approach is a framework which can describe these reaction processes in a unified manner. It expands the total wave function of the system in terms of the ground and excited states of the colliding nuclei, and solves the coupled Shr\"odinger equations to obtain the $S$-matrix, from which several cross sections can be constructed. This approach has been a standard tool to analyze experimental data for nuclear reactions. In this paper, we review the present status and the recent developments of the coupled-channels approach. This includes the microscopic coupled-channels method and its application to cluster physics, the continuum discretized coupled-channels (CDCC) method for breakup reactions, the semi-microscopic approach to heavy-ion subbarrier fusion reactions, the channel coupling effects on nuclear astrophysics and syntheses of superheavy elements, and inclusive breakup and incomplete fusion reactions of weakly-bound nuclei., Comment: 90 pages, 37 figures. Accepted for publication in Progress in Particle and Nuclear Physics

The properties of nuclei with extreme neutron-to-proton ratios, far from those naturally occurring on Earth, are key to understand nuclear forces and how nucleons hold together to form nuclei. $^7$H, with six neutrons and a single proton, is the nuclear system with the most unbalanced neutron-to-proton ratio known so far. However, its sheer existence and properties are still a challenge for experimental efforts and theoretical models. Here we report experimental evidences on the formation of $^7$H as a resonance, detected with independent observables, and the first measurement of the structure of its ground state. The resonance is found at $\sim$0.7 MeV above the $^3$H+4n mass, with a narrow width of $\sim$0.2 MeV and a $1/2^+$ spin and parity. These data are consistent with a $^7$H as a $^3$H core surrounded by an extended four-neutron halo, with a unique four-neutron decay and a relatively long half-life thanks to neutron pairing; a prime example of new phenomena occurring in what would be the most pure-neutron nuclear matter we can access in the laboratory.

A measurement of proton inelastic scattering of $^8$He at $8.25A$~MeV at TRIUMF shows a resonance at 3.54(6)~MeV with a width of 0.89(11)~MeV. The energy of the state is in good agreement with coupled cluster and no-core shell model with continuum calculations, with the latter successfully describing the measured resonance width as well. Its differential cross section analyzed with phenomenological collective excitation form factor and microscopic coupled reaction channels framework consistently reveals a large deformation parameter $\beta_2$ = 0.40(3), consistent with no-core shell model predictions of a large neutron deformation. This deformed double-closed shell at the neutron drip-line opens a new paradigm., Comment: 9 pages, 5 figures. Accepted for publication in Physics Letters B

In 1985, Hussein and McVoy [Nuc. Phys. A445 (1985) 124] elucidated a formula for the evaluation of the nonelastic breakup ("stripping") contribution in inclusive breakup reactions. The formula, based on the spectator core model, acquires a particularly simple and appealing form in the eikonal limit, to the extent that it has become the standard procedure to analyze single-nucleon knockout reactions at intermediate energies. In this contribution, a critical assessment of this formula is presented and its connection with other, noneikonal expressions discussed. Some calculations comparing the different formulae are also presented for the one-nucleon removal of $^{14}$O+$^{9}$Be reaction at several incident energies., Comment: To be published in EPJA in the special issue "Cluster Structure and Dynamics of Nuclei - A Tribute to Mahir Hussein"

In this review article we discuss the present status of direct nuclear reactions and the nuclear structure aspects one can study with them. We discuss the spectroscopic information we can assess in experiments involving transfer reactions, heavy-ion-induced knockout reactions and quasifree scattering with (p,2p), (p,pn), and (e,e'p) reactions. In particular, we focus on the proton-to-neutron asymmetry of the quenching of the spectroscopic strength., Comment: 138 pages, 63 figures

Nucleon-knockout reactions on proton targets (p, pN ) have experienced a renewed interest due to the availability of inverse-kinematics experiment with exotic nuclei. Various theoretical descriptions have been used to describe these reactions, such as the Distorted-Wave Impulse Approximation (DWIA), the Faddeev-type formalism and the Transfer to the Continuum method. Our goal is to benchmark the observables computed with the Faddeev and Transfer to the Continuum formalisms in the intermediate energy regime relevant for the experimental (p, pn) and (p, 2p) studies. In this paper, we analyze the 11 Be(p,pn)10Be reaction for different beam energies, binding energies and orbital quantum numbers with both formalisms to assess their agreement for different observables. We obtain a good agreement in all cases considered, within 10%, when the input potentials are taken consistently and realistically., Comment: 9 pages, 15 figures, accepted in Physical Review C

The first investigation of the single-particle structure of the bound states of 17C, via the d(16C, p) transfer reaction, has been undertaken. The measured angular distributions confirm the spin-parity assignments of 1/2+ and 5/2+ for the excited states located at 217 and 335 keV, respectively. The spectroscopic factors deduced for these states exhibit a marked single-particle character, in agreement with shell model and particle-core model calculations, and combined with their near degeneracy in energy provide clear evidence for the absence of the N = 14 sub-shell closure. The very small spectroscopic factor found for the 3/2+ ground state is consistent with theoretical predictions and indicates that the {\nu}1d3/2 strength is carried by unbound states. With a dominant l = 0 valence neutron configuration and a very low separation energy, the 1/2+ excited state is a one-neutron halo candidate., Comment: 7 pages, 5 figures, Accepted for publication in Physics Letters B

We study the evolution of a single-particle wave function during the collision of a one dimensional potential well by another well, which can be regarded as a simple model for the problem of the scattering of a one-neutron halo nucleus by another nucleus. This constitutes an effective three-body problem, whose solution in three dimensions can be extremely complicated, particularly when breakup and rearrangement channels are to be considered. Our one-dimensional model provides the essential three-body nature of this problem, and allows for a much simpler application and assessment of different methods of solution. To simplify further the problem, we assume that the potential well representing the projectile moves according to a predetermined classical trajectory, although the internal motion of the "valence" particle is treated fully quantum-mechanically. This corresponds to a semiclassical approach of the scattering problem. Different approaches are investigated to understand the dynamics involving one-body halo-like systems: the "exact" time-dependent solution of the Schr\"odinger equation is compared to a numerical continuum-discretized coupled-channels (CC) calculation presenting various model cases including different reaction channels. This framework allows us to discuss the reaction mechanism and the role of continuum, whose inclusion in the CC calculation results to be crucial to reproduce the "exact" solution, even when the initial and final states are well bound. We also link each dynamical situation with analogous problem solved in a three dimensional (3D) CC framework, discussing the main challenges experienced in the usual 3D models.

New experimental results for the elastic scattering of 6He on 64Zn at incident energies of 15.0 and 18.0 MeV and 4He at 17.5 MeV along with results already published at 10.0 and 13.6 MeV, are presented. Elastic and alpha experimental cross sections are compared with coupled-reaction-channel, continuum-discretized coupledchannel, and DWBA inclusive-breakup models. The large yield of alpha particles observed at all measured energies can be explained by considering a nonelastic breakup mechanism.

A novel method to extract the $B(E1)$ strength of a weakly bound nucleus from experimental Coulomb dissociation data is proposed. The method makes use of continuum discretized coupled channels (CDCC) calculations, in which both nuclear and Coulomb forces are taken into account to all orders. This is a crucial advantage with respect to the standard procedure based on the Equivalent Photon Method (EPM) which does not properly take into account nuclear distortion, higher order coupling effects, or Coulomb-nuclear interference terms. The procedure is applied to the $^{11}$Be nucleus using two sets of available experimental data at different energies, for which seemingly incompatible $B(E1)$ have been reported using the EPM. We show that the present procedure gives consistent $B(E1)$ strengths, thus solving the aforementioned long-standing discrepancy between the two measurements., Comment: Submitted for publication

Collisions between complex nuclei may give rise to their total or partial fusion. The latter case is found experimentally to gain importance when one of the colliding nuclei is weakly bound. It has been commonly assumed that the partial fusion mechanism is a two-step process, whose first step is the dissociation of the weakly bound nucleus, followed by the capture of one of the fragments. To assess this interpretation, we present the first implementation of the three-body model of inclusive breakup proposed in the 1980s by Austern et al. [Phys. Rep. 154, 125 (1987)] that accounts for both the direct, one-step, partial fusion and the two-step mechanism proceeding via the projectile continuum states. Contrary to the widely assumed picture, we find that, at least for the investigated cases, the partial fusion is largely dominated by the direct capture from the projectile ground-state., Comment: Accepted for publication in Phys. Rev. Letters

The Continuum-Discretized Coupled-Channels (CDCC) has been successfully employed to describe elastic and breakup of nuclear reactions induced by weakly bound projectiles. In this contribution, we review some other, less widespread applications of the CDCC wavefunction, some of them in combination with other reaction formalisms, which are being currently employed in the analysis of reactions involving three or more fragments in the initial or final state., Comment: Invited contribution to INPC 2019 (Glasgow, UK, July 2019)

The Transfer to the Continuum method has been applied to describe the $^{11}\text{Li}(p,pn)$ and $^{14}\text{Be}(p,pn)$ reactions in inverse kinematics, using structure overlaps computed within a full three-body model for the projectile. Calculations agree with the available experimental data on the unbound $^{10}$Li and $^{13}$Be nuclei., Comment: 5 pages; proceedings of the INPC2019

We present an investigation of the structure of 13Be obtained via a kinematically complete measurement of the (p; pn) reaction in inverse kinematics at 265 MeV/nucleon. The relative energy spectrum of 13Be is compared to Transfer-to-the-Continuum calculations which use as structure inputs the overlaps of the 14Be ground-state wave function, computed in a three-body model, with the unbound states of the 13Be residual nucleus. The key role of neutron p-wave orbital in the interpretation of the low-relative-energy part of the spectrum is discussed.

The continuum structure of the unbound system $^{10}$Li, inferred from the $^{9}$Li$(d,p)^{10}$Li transfer reaction, is reexamined. Experimental data for this reaction, measured at two different energies, are analyzed with the same reaction framework and structure models. It is shown that the seemingly different features observed in the measured excitation energy spectra can be understood as due to the different incident energy and angular range covered by the two experiments. The present results support the persistence of the $N=7$ parity inversion beyond the neutron dripline as well as the splitting of the well-known low-lying $p$-wave resonance. Furthermore, they provide indirect evidence that most of the $\ell=2$ single-particle strength, including possible $d_{5/2}$ resonances, lies at relatively high excitations energies., Comment: accepted for publication in Physics Letters B

The main of this paper is to prove that in terms of normalized density, a space-time block code based on an irreducible quadratic polynomial over the Eisenstein integers is an optimal space-time block code compared with any quadratic space-time block code over the ring of integers of imaginary quadratic fields. In addition we find the optimal design of space-time block codes based on an irreducible quadratic polynomial over some rings of imaginary quadratic fields., Comment: 15 pages

Experimental studies of nuclear collisions involving light weakly-bound nuclei show a systematic suppression of the complete fusion cross section by $\sim$30\% with respect to the expectation for tightly bound nuclei, at energies above the Coulomb barrier. Although it is widely accepted that the phenomenon is related to the weak binding of these nuclei, the origin of this suppression is not fully understood. In here, we present a novel approach that provides the complete fusion for weakly bound nuclei and relates its suppression to the competition between the different mechanisms contributing to the reaction cross section. The method is applied to the $^{6,7}$Li+$^{209}$Bi reactions, where we find that the suppression of complete fusion is mostly caused by the flux associated with non-elastic breakup modes, such as the partial capture of the projectile (incomplete fusion), whereas the elastic breakup mode is found to play a minor role. Finally, we demonstrate that the large $\alpha$ yields observed in these reactions can be naturally explained as a consequence of a {\it Trojan Horse} mechanism., Comment: 6 pages, 4 figures. Accepted for publication in Phys. Rev. Letters

A campaign of intermediate energy (300-450 MeV/u) proton-induced nucleon knockout measurements in inverse kinematics has been recently undertaken at the R 3 B/LAND setup at GSI. We present a systematic theoretical analysis of these data with the aim of studying the quenching of the single-particle strengths and its binding-energy dependence. For that, the measured semi-inclusive (p, 2p) and (p, pn) cross sections are compared with theoretical predictions based on single-particle cross sections derived from a novel coupled-channels formalism and shell-model spectroscopic factors. A systematic reduction of about 20-30% is found, with a very limited dependence on proton-neutron asymmetry., Comment: 8 pages, 3 figures

In this contribution, I present a short overview of the theory of direct nuclear reactions, with special emphasis on the case of reactions induced by weakly-bound nuclei. After introducing some general results of quantum scattering theory, I present specific applications to elastic, inelastic, transfer and breakup reactions. For each of them, I first introduce the most standard framework, followed by some alternative models or extensions suitable for the case of weakly bound nuclei. A short discussion on semiclassical theory of Coulomb excitation and its application to breakup of halo nuclei is also provided., Comment: Proceedings of the International School of Physics Enrico Fermi: "Nuclear Physics with Stable and Radioactive Ion Beams". Several typos fixed in this version

Using a combination of scanning tunneling spectroscopy and atomic lateral manipulation, we obtained a systematic variation of the Kondo temperature ($T_\mathrm K$) of Co atoms on Ag(111) as a function of the surface state contribution to the total density of states at the atom adsorption site ($\rho_s$). By sampling the $T_\mathrm K$ of a Co atom on positions where $\rho_s$ was spatially resolved beforehand, we obtain a nearly linear relationship between both magnitudes. We interpret the data on the basis of an Anderson model including orbital and spin degrees of freedom (SU(4)) in good agreement with the experimental findings. The fact that the onset of the surface band is near the Fermi level is crucial to lead to the observed linear behavior. In the light of this model, the quantitative analysis of the experimental data evidences that at least a quarter of the coupling of Co impurities with extended states takes place through the hybridization to surface states. This result is of fundamental relevance in the understanding of Kondo screening of magnetic impurities on noble metal surfaces, where bulk and surface electronic states coexist.

In this paper, we address the problem of the post-prior equivalence in the calculation of inclusive breakup and transfer cross sections. For that, we employ the model proposed by Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)], conveniently generalized to include the part of the cross section corresponding the transfer to bound states. We pay particular attention to the case in which the unobserved particle is left in a bound state of the residual nucleus, in which case the theory prescribes the use of a complex potential, responsible for the spreading width of the populated single-particle states. We see that the introduction of this complex potential gives rise to an additional term in the prior cross section formula, not present in the usual case of real binding potentials. The equivalence is numerically tested for reaction induced by deuterons., Comment: 5 pages, 1 figure. Submitted for publication