We investigate the Coulomb breakup of $^{11}$Be halo nuclei on a heavy target from intermediate (70 MeV/nucleon) to low energies (5 MeV/nucleon) within the non-perturbative time-dependent approach. The convergence of the computational scheme is demonstrated in this energy range including \textit{n}+$^{10}$Be low-lying resonances in different partial and spin states. We have found a considerable contribution of the $5/2^{+}$ resonance ($E_{r}$= 1.23 MeV) to the breakup cross section at 30 MeV/nucleon and lower, while at higher energies, the resonant states $3/2^{-}$ and $3/2^{+}$ (with $E_{r}$= 2.78 and 3.3 MeV) make most visible contributions. The obtained results are in good agreement with experimental data available at 69 and 72 MeV/nucleon. Comparison with the existing theoretical calculations of other authors for 20 and 30 MeV/nucleon is also made. The developed computational scheme opens new possibilities in the investigation of the Coulomb, as well as nuclear, breakup of other halo nuclei on heavy and light targets.
A classical dynamical model that treats break-up stochastically is presented for low energy reactions of weakly-bound nuclei. The three-dimensional model allows a consistent calculation of breakup, incomplete and complete fusion cross sections. The model is assessed by comparing the breakup observables with CDCC quantum mechanical predictions, which are found to be in reasonable agreement. Through the model, it is demonstrated that the breakup probability of the projectile as a function of its distance from the target is of primary importance for understanding complete and incomplete fusion at…
We study the postacceleration of charged fragments in reactions with unstable nuclear beams. For elastic breakup processes we show that the postaceleration effect can be well understood in terms of closed analytical forms derived in a quantum mechanical formulation. This gives theoretical support to the effect experimentally observed in the breakup of Li-11 projectiles at intermediate energies.
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…
The continuum-discretized coupled-channels (CDCC) method is used to study the breakup of weakly-bound nuclei at intermediate energies collisions. For large impact parameters, the Eikonal CDCC (E-CDCC) method was applied. The effects of Lorentz contraction on the nuclear and Coulomb potentials have been investigated in details. Such effects tend to increase cross sections appreciably. We also show that, for loosely-bound nuclei, the contribution of the so-called close field is small and can be neglected.
We calculate the nuclear induced breakup of Be11 and B8 using a more realistic treatment of the diffraction and stripping processes than in previous work. The breakup is treated in the eikonal approximation with a profile function calculated from a realistic optical potential at low energies and from free nucleon-nucleon cross sections at high energies. This treatment gives a good description of measured breakup cross sections, as well as the longitudinal momentum distribution of the core-like fragments, which is narrower than predicted in the transparent limit. The real part of the potential …
Application of the absorbing boundary condition is discussed to analyse breakup reactions of weakly bound nuclei. The key ingredient is an introduction of the absorbing potential outside the physical area which simulates the outgoing boundary condition approximately. The scattering problem is then recasted into the Schroedinger like equation with a source term in the interaction region and with the vanishing boundary condition at the boundary. We demonstrate usefulness of the method taking a few examples. Deuteron breakup reactions are examined comparing present results with those by the conti…
The incomplete fusion dynamics of $^6$Li + $^{209}$Bi collisions at energies above the Coulomb barrier is investigated. The classical dynamical model implemented in the {\sc platypus} code is used to understand and quantify the impact of both $^6$Li resonance states and transfer-triggered breakup modes (involving short-lived projectile-like nuclei such as $^8$Be and $^5$Li) on the formation of incomplete fusion products. Model calculations explain the experimental incomplete-fusion excitation function fairly well, indicating that (i) delayed direct breakup of $^6$Li reduces the incomplete fusi…
The mechanism of the Coulomb breakup reactions of the nuclei with neutron-halo structure is investigated in detail. A time-dependent Schrödinger equation for the halo neutron is numerically solved by treating the Coulomb field of a target as an external field. The momentum distribution and the post-acceleration effect of the final fragments are discussed in a fully quantum mechanical way to clarify the limitation of the intuitive picture based on the classical mechanics. The theory is applied to the Coulomb breakup reaction of $^{11}$Be + $^{208}$Pb. The breakup mechanism is found to be differ…
The open issues in the development of models for the breakup of exotic nuclei and the link with the extraction of structure information from experimental data are reviewed. The question of the improvement of the description of exotic nuclei within reaction models is approached in the perspective of previous analyses of the sensitivity of these models to that description. Future developments of reaction models are suggested, such as the inclusion of various channels within one model. The search for new reaction observables that can emphasise more details of exotic nuclear structure is also prop…
We investigate the Coulomb breakup of neutron rich nuclei 11Be and (19,17,15)C within a theory developed in the framework of Distorted Wave Born Approximation. Finite range effects are included by a local momentum approximation, which allows incorporation of realistic wave functions for these nuclei in our calculations. Energy and angular as well as parallel momentum distributions of the fragments emitted in the breakup of these nuclei on heavy targets have been calculated using several structure models for their ground state. Comparison with the available experimental data shows that the resu…
We discuss the effect of the coupling to the break-up channel on the total fusion involving a halo nucleus with a heavy target. We show that there is a competition between the hindrance arising from this coupling, mostly at above barrier energies, and the enhancement which ensues at sub-barrier energies owing to the static effect of the extended matter distribution and the coupling to the soft modes.
How to extract an electric dipole (E1) breakup cross section σ(E1) from one- neutron removal cross sections measured by using 12C and 208Pb targets, σ_(-1n)^C and σ_(-1n)^Pb, respectively, is discussed. It is shown that within about 5% error, σ(E1) can be obtained by subtracting Γσ_(-1n)^C from σ_(- 1n)^Pb, as assumed in preceding studies. However, for the reaction of weakly-bound projectiles, the scaling factor Γis found to be two times as large as that usually adopted. As a result, we obtain 13-20% smaller σ(E1) of 31Ne at 250 MeV/nucleon than extracted in a previous analysis of experimental…
All possible dissociation cross sections for the loosely bound three-body halo nuclei $^6$He (n+n+$α$) and $^{11}$Li (n+n+$^{9}$Li) are computed as functions of target and beam energy. Both Coulomb and nuclear interactions are included in the same theoretical framework. The measurements agree with the calculations for energies above 100 Mev/nucleon. The largest cross sections correspond to final states with zero or three particles for heavy and with two neutrons for light targets.
We study the eikonal model for the nuclear-induced breakup of Borromean nuclei, using Li11 and He6 as examples. The full eikonal model is difficult to realize because of six-dimensional integrals, but a number of simplifying approximations are found to be accurate. The integrated diffractive and one-nucleon stripping cross sections are rather insensitive to the neutron-neutron correlation, but the two-nucleon stripping does show some dependence on the correlation. The distribution of excitation energy in the neutron-core final state in one-neutron stripping reactions is quite sensitive to the …
We propose a simple schematic model for two-neutron halo nuclei. In this model, the two valence neutrons move in a one-dimensional mean field, interacting with each other via a density-dependent contact interaction. We first investigate the ground state properties, and demonstrate that the dineutron correlation can be realized with this simple model due to the admixture of even- and odd-parity single-particle states. We then solve the time-dependent two-particle Schrödinger equation under the influence of a time-dependent one-body external field, in order to discuss the effect of dineutron cor…
Background: One-neutron removal reactions are used to study the single-particle structure of unstable nuclei, and in particular the exotic halo nuclei. The Eikonal Reaction Theory (ERT) has been developed by Yahiro, Ogata and Minomo in Prog. Theor. Phys. 126, 167 (2011) to include dynamical effects, which are missing in the usual eikonal description of these reactions. Encouraging results have been obtained for total breakup cross sections in comparison to more elaborate reaction models. Purpose: We extend these comparisons to more differential breakup cross sections expressed as functions of …
We investigate dissociation reactions of loosely bound and spatially extended three-body systems. We formulate a practical method for simultaneous treatment of long-range Coulomb and short-range nuclear interactions. We use $^6$He (n+n+$α$) and $^{11}$Li (n+n+$^{9}$Li) as examples and study the two-neutron separation cross sections as functions of target and beam energy. Individual Coulomb and nuclear as well as interference contributions are also extracted.
Optical potentials for elastic p-d scattering and the coupled processes p+$^3$He $\rightarrow$ p+$^3$He and p+$^3$He $\rightarrow$ d+d are derived in the Faddeev-Yakubovsky framework with special emphasis on leading order terms, which are expected to be valid at intermediate energies. In addition, equations for the fragmentations $^3$He(p,ppp)n and $^3$He(p,pp)d are derived within the same framework. Again leading order terms for intermediate energies are considered.
We use the three-body model and the sudden approximation to compute angular correlations in high-energy fragmentation reactions of two-neutron halos on light targets. The contribution from one-neutron absorption by far dominates over that of neutron scattering. We use 6He (n+n+alpha) and 11Li (n+n+9Li) as examples and study the dependence of the predictions of this model on different physical assumptions and parameters. PACS number(s): 25.60.-t, 25.60.Gc, 21.45.+v}
A self-contained Fortran-90 program based on a classical trajectory model with stochastic breakup is presented, which should be a powerful tool for quantifying complete and incomplete fusion, and breakup in reactions induced by weakly-bound two-body projectiles near the Coulomb barrier. The code calculates complete and incomplete fusion cross sections and their angular momentum distribution, as well as breakup observables (angle, kinetic energy and relative energy distributions).
We investigate the breakup of the one-neutron halo nuclei 11Be and 19C within a dynamical model of the continuum excitation of the projectile. The time evolution of the projectile in coordinate space is described by solving the three-dimensional time dependent Schroedinger equation, treating the projectile-target (both Coulomb and nuclear) interaction as a time dependent external perturbation. The pure Coulomb breakup dominates the relative energy spectra of the fragments in the peak region, while the nuclear breakup is important at higher relative energies. The coherent sum of the two contrib…
The $^9$C nucleus and related capture reaction, ${^8\mathrm{B}}(p,γ){^9\mathrm{C}}$, have been intensively studied with an astrophysical interest. Due to the weakly-bound nature of $^9$C, its structure is likely to be described as the three-body (${^7\mathrm{Be}}+p+p$). Its continuum structure is also important to describe reaction processes of $^9$C, with which the reaction rate of the ${^8\mathrm{B}}(p,γ){^9\mathrm{C}}$ process have been extracted indirectly. We perform three-body calculations on $^9$C and discuss properties of its ground and low-lying states via breakup reactions. We employ…
We review the current status of obtaining the spectroscopic information on the one-neutron halo nuclei from the Coulomb breakup reactions. The theory of these reactions formulated in the framework of the Distorted Wave Born Approximation, allows the use of the realistic wave functions corresponding to any orbital angular momentum structure for the core-valence neutron relative motion in the ground state of the projectile. The energy, angular and parallel momentum distributions of the projectile fragments calculated within this theory are selective about the ground state wave function of the pr…
Breakup reactions of loosely-bound nuclei are often used to extract structure and/or astrophysical information. Here we compare three non-perturbative reaction theories often used when analyzing breakup experiments, namely the continuum discretized coupled channel model, the time-dependent approach relying on a semiclassical approximation, and the dynamical eikonal approximation. Our test case consists of the breakup of 15C on Pb at 68 MeV/nucleon and 20 MeV/nucleon.
The eikonal description of breakup reactions diverges because of the Coulomb interaction between the projectile and the target. This divergence is due to the adiabatic, or sudden, approximation usually made, which is incompatible with the infinite range of the Coulomb interaction. A correction for this divergence is analysed by comparison with the Dynamical Eikonal Approximation, which is derived without the adiabatic approximation. The correction consists in replacing the first-order term of the eikonal Coulomb phase by the first-order of the perturbation theory. This allows taking into accou…
An interesting physical process has been unveiled: dynamical core excitation during a breakup reaction of loosely bound $core+N$ systems. These reactions are typically used to extract spectroscopic information and/or astrophysical information. A new method, the eXtended Continuum Discretized Coupled Channel (XCDCC) method, was developed to incorporate, in a consistent way and to all orders, core excitation in the bound and scattering states of the projectile, as well as dynamical excitation of the core as it interacts with the target. The model predicts cross sections to specific states of the…
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.
Recent developments on the understanding of low energy reactions are highlighted. Emphasis is given to the CDCC framework where the breakup channels of the projectile are included explicitly. Properties of the breakup couplings are presented. Comments are given with regard to the separation between the nuclear and the Coulomb contributions to breakup cross sections as well as the dependence on the optical potentials. A discussion on the sensitivity of the CDCC basis is discussed, by comparing pure breakup results with transfer to the continuum calculations. Finally, some remaining controversie…
The formal theory of breakup reactions is reviewed. The direct breakup mechanism which is formulated within the framework of the post form distorted wave Born approximation is discussed in detail. In this theory, which requires the information about only the ground state wave function of the projectile, the fragment-target interactions are included to all orders while fragment-fragment interaction is treated only in the first order. The general applicability of this theory to describe the breakup of halo nuclei is demonstrated by comparing the calculations with data for total, as well as energ…
Background: The eikonal approximation is a high-energy reaction model which is very computationally efficient and provides a simple interpretation of the collision. Unfortunately, it is not valid at energies around 10 MeV/nucleon, the range of energy of HIE-ISOLDE at CERN and the future ReA12 at MSU. Fukui etal. [Phys. Rev. C 90, 034617 (2014)] have shown that a simple semiclassical correction of the projectile-target deflection could improve the description of breakup of halo nuclei on heavy targets down to 20 MeV/nucleon. Purpose: We study two similar corrections, which aim at improving the …
The optical potential of halo and weakly bound nuclei has a long range part due to the coupling to breakup that damps the elastic scattering angular distributions. In order to describe correctly the breakup channel in the case of scattering on a heavy target, core recoil effects have to be taken into account. We show here that core recoil and nuclear breakup of the valence nucleon can be consistently taken into account. A microscopic absorptive potential is obtained within a semiclassical approach and its characteristics can be understood in terms of the properties of the halo wave function an…
The inclusive breakup of three-fragment projectiles is discussed within a four-body spectator model. Both the elastic breakup and the non-elastic breakup are obtained in a unified framework. Originally developed in the 80's for two-fragment projectiles such as the deuteron, in this paper the theory is successfully generalized to three-fragment projectiles. The expression obtained for the inclusive cross section allows the extraction of the incomplete fusion cross section, and accordingly generalizes the surrogate method to cases such as (t,p) and (t,n) reactions. It is found that two-fragment …
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 …
The influence on fusion of coupling to the breakup process is investigated for reactions where at least one of the colliding nuclei has a sufficiently low binding energy for breakup to become an important process. Elastic scattering, excitation functions for sub-and near-barrier fusion cross sections, and breakup yields are analyzed for $^{6,7}$Li+$^{59}$Co. Continuum-Discretized Coupled-Channels (CDCC) calculations describe well the data at and above the barrier. Elastic scattering with $^{6}$Li (as compared to $^{7}$Li) indicates the significant role of breakup for weakly bound projectiles. …
The eXtended Continuum Discretized Coupled Channel (XCDCC) method is developed to treat reactions where core degrees of freedom play a role. The projectile is treated as a multi-configuration coupled channels system generated from a valence particle coupled to a deformed core which is allowed to excite. The coupled channels initial state breaks up into a coupled channels continuum which is discretized into bins, similarly to the original CDCC method. Core collective degrees of freedom are also included in the interaction of the core and the target, so that dynamical effects can occur during th…
We present a semiclassical and mostly analytical model of elastic neutron breakup reactions for exotic projectiles. Both nuclear and Coulomb induced reactions are considered and the potentials are treated to all orders in the interactions. Furthermore we introduce a technique which allows the use of the full Coulomb potential, thus including all multipoles besides the dipole. Results for deeply bound states as well as for halo initial states are presented and it is shown that experiments on heavy targets would be well suited to study exotic nuclei with tightly bound valence nucleons.
We derive the inclusive breakup cross section of a three-fragment projectile nuclei, $a = b +x_1 + x_2$, in the spectator model. The resulting four-body cross section for observing $b$, is composed of the elastic breakup cross section which contains information about the correlation between the two participant fragments, and the inclusive non-elastic breakup cross section. This latter cross section is found to be a non-trivial four-body generalization of the Austern formula \cite{Austern1987}, which is proportional to a matrix element of the form, $\langle\hatρ_{{x_1},{x_2}}\left|\left[W_{x_1}…
Reaction theory is an essential ingredient when performing studies of nuclei far from stability. One approach for the calculation of breakup reactions of exotic nuclei into two fragments is to consider inelastic excitations into the single particle continuum of the projectile. Alternatively one can also consider the transfer to the continuum of a system composed of the light fragment and the target. In this work we make a comparative study of the two approaches, underline the different inputs, and identify the advantages and disadvantages of each approach. Our test cases consist of the breakup…
The angular distributions for elastic scattering and breakup of halo nuclei are analysed using a near-side/far-side decomposition within the framework of the dynamical eikonal approximation. This analysis is performed for 11Be impinging on Pb at 69AMeV. These distributions exhibit very similar features. In particular they are both near-side dominated, as expected from Coulomb-dominated reactions. The general shape of these distributions is sensitive mostly to the projectile-target interactions, but is also affected by the extension of the halo. This suggests that the link between elastic scatt…
We propose a new method to describe three-body breakups of nuclei, in which the Lippmann-Schwinger equation is solved combining with the complex scaling method. The complex-scaled solutions of the Lippmann-Schwinger equation (CSLS) enables us to treat boundary conditions of many-body open channels correctly and to describe a many-body breakup amplitude from the ground state. The Coulomb breakup cross section from the 6He ground state into 4He+n+n three-body decaying states as a function of the total excitation energy is calculated by using CSLS, and the result well reproduces the experimental …
Coulomb breakup of a projectile in the Coulomb field of a fully stripped heavy nucleus is at present one of the most popular experimental methods to obtain information on reactions of interest in nuclear astrophysics. Its theoretical interpretation presents, however, considerable difficulties, due to the three-body nature and the infinite range of the Coulomb forces involved. Among the uncertainties affecting present analyses, the possible modification of the dissociation cross section by three-body Coulomb final-state interactions plays a major role. Various methods which have been proposed t…
In this work, we reexamine the extension of the CDCC formalism to include target excitation and apply it to a variety of reactions to study the effect of breakup on inelastic cross sections. We use a transformed oscillator basis to discretize the continuum of the projectiles in the different reactions and use the extended CDCC method developed in this work to solve the resulting coupled differential equations. A new code has been developed to perform the calculations. Reactions 58Ni(d, d) 58Ni*, 24Mg(d, d) 24Mg* , 144Sm( 6Li, 6Li) 144Sm* and 9Be( 6Li, 6Li) 9Be* are studied. Satisfactory agreem…
The classical trajectory model with stochastic breakup for nuclear collision dynamics of weakly-bound nuclei is further developed. It allows a quantitative study of the importance of incomplete fusion dynamics in the angular distribution of direct alpha-production. Model calculations indicate that the incomplete fusion contribution diminishes with decreasing energy towards the Coulomb barrier, notably separating in angles from the contribution of no-capture breakup events. This should facilitate the experimental disentanglement of these competing reaction processes.
Complete fusion cross sections in collisions of light, weakly bound nuclei and high Z targets show above-barrier suppression of complete fusion. This has been interpreted as resulting from breakup of the weakly bound nucleus prior to reaching the fusion barrier, reducing the probability of complete fusion. This paper investigates how these conclusions are affected by lifetimes of the resonant states that are populated prior to breakup. If the mean life of a populated resonance is much longer than the fusion timescale, then its breakup cannot suppress complete fusion. For short-lived resonances…
The density distributions of $^{10}$Be and $^{11}$Be nuclei obtained within the quantum Monte Carlo (QMC) model and the generator coordinate method (GCM) are used to calculate the microscopic optical potentials (OPs) and cross sections of elastic scattering of these nuclei on protons and $^{12}$C at energies $E<100$ MeV/nucleon. The real part of the OP is calculated using the folding model with the exchange terms included, while the imaginary part of the OP that reproduces the phase of scattering is obtained in the high-energy approximation (HEA). In this hybrid model of OP the free parameters…
We derive closed expressions for the nuclear breakup cross sections in the adiabatic limit using the Austern-Blair theory. These expressions are appropriate for the breakup of weakly bound nuclei. The concept of an exit doorway that mediates the coupling between the entrance channel and the breakup continuum is used. We prove the validity of the scaling law that dictates that the nuclear breakup cross section scales linearly with the radius of the target. We also compare our results for the nuclear breakup cross section of $^{11}$Be, $^8$B on several targets with recent CDCC calculation.
We have performed CDCC calculations for collisions of $^{7}$Li projectiles on $^{59}$Co, $^{144}$Sm and $^{208}$Pb targets at near-barrier energies, to assess the importance of the Coulomb and the nuclear couplings in the breakup of $^{7}$Li, as well as the Coulomb-nuclear interference. We have also investigated scaling laws, expressing the dependence of the cross sections on the charge and the mass of the target. This work is complementary to the one previously reported by us on the breakup of $^{6}$Li. Here we explore the similarities and differences between the results for the two Lithium i…
We develop a four-body model for the inclusive breakup of two-fragment halo projectiles colliding with two-fragment targets. In the case of a short lived projectiles, such as halo nuclei, on a deuteron target, the model allows the extraction of the neutron capture cross section of such projectiles. We supply examples.
Nuclear and Coulomb breakup of halo nuclei have been treated often as incoherent processes and structure information have been extracted from their study. The aim of this paper is to clarify whether interference effects and Coulomb-nuclear couplings are important and how they could modify the simple picture previously used. We calculate the neutron angular and energy distributions by using first order perturbation theory for the Coulomb amplitude and an eikonal approach for the nuclear breakup. This allows for a simple physical interpretation of the results which are mostly analytical. Our for…
We study theoretically fusion of the light proton-rich exotic nuclei $^{17}$F and $^8$B at near-barrier energies in order to investigate the possible role of breakup processes on their fusion cross sections. To this end, coupled channel calculations are performed considering the couplings to the breakup channels of these projectiles. In case of $^{17}$F, the coupling arising out of the inelastic excitation from the ground state to the bound excited state and its couplings to the continuum have also been taken into consideration. It is found that the inelastic excitation/breakup of $^{17}$F aff…
We extend the virial equation of state to include 3H and 3He nuclei, and predict significant mass-three fractions near the neutrinosphere in supernovae. While alpha particles are often more abundant, we demonstrate that energy transfer cross-sections for muon and tau neutrinos at low densities are dominated by breakup of the loosely-bound 3H and 3He nuclei. The virial coefficients involving A=3 nuclei are calculated directly from the corresponding nucleon-3H and nucleon-3He scattering phase shifts. For the neutral-current inelastic cross-sections and the energy transfer cross sections, we perf…
A study of the kinematics of the $α$-$d$ coincidences in the $^{6}$Li + $^{59}$Co system at a bombarding energy of $E_{lab} = 29.6$ MeV is presented. With exclusive measurements performed over different angular intervals it is possible to identify the respective contributions of the sequential projectile breakup and direct projectile breakup components. A careful analysis using a semiclassical approach of these processes provides information on both their lifetime and their distance of occurrence with respect to the target. Breakup to the low-lying (near-threshold) continuum is delayed, and ha…
We extend our previous calculation of the breakup of 11Be using Halo Effective Field Theory and the Dynamical Eikonal Approximation to include an effective 10Be-n-target force. The force is constructed to account for the virtual excitation of 10Be to its low-lying 2+ excited state. In the case of breakup on a 12C target this improves the description of the neutron-energy and angular spectra, especially in the vicinity of the 11Be 5/2+ state. By fine-tuning the range parameters of the three-body force, a reasonable description of data in the region of the 3/2+ 11Be state can also be obtained. T…
Breakup reactions are one of the main tools for the study of exotic nuclei, and in particular of their continuum. In order to get valuable information from measurements, a precise reaction model coupled to a fair description of the projectile is needed. We assume that the projectile initially possesses a cluster structure, which is revealed by the dissociation process. This structure is described by a few-body Hamiltonian involving effective forces between the clusters. Within this assumption, we review various reaction models. In semiclassical models, the projectile-target relative motion is …
Complete fusion excitation functions of reactions involving breakup are studied by using the empirical coupled-channel (ECC) model with breakup effects considered. An exponential function with two parameters is adopted to describe the prompt-breakup probability in the ECC model. These two parameters are fixed by fitting the measured prompt-breakup probability or the complete fusion cross sections. The suppression of complete fusion at energies above the Coulomb barrier is studied by comparing the data with the predictions from the ECC model without the breakup channel considered. The results s…
We consider the influence of breakup channels on the complete fusion of weakly bound cluster-type systems in terms of dynamic polarization potentials. It is argued that the enhancement of the cross section at sub-barrier energies may be consistent with recent experimental observations that nucleon transfer, often leading to breakup, is dominant compared to direct breakup. The main trends of the experimental complete fusion cross sections are analyzed in the framework of the Dynamic Polarization Potential approach. The qualitative conclusions are supported by CDCC calculations including a seque…
We study dynamical effects in proton breakup from a weakly bound state in an exotic nucleus on a heavy target. The Coulomb interactions between the proton and the core and the proton and the target are treated to all orders, including also the full multipole expansion of the Coulomb potential. The dynamics of proton nuclear and Coulomb breakup is compared to that of an equiva- lent neutron of larger binding energy in order to elucidate the differences with the well understood neutron breakup mechanism. A number of experimentally measurable observables such as parallel momentum distributions, p…
The breakup of the $^{9}$Be projectile on the $^{209}$Bi target at bombarding energies above and near the Coulomb barrier is studied in the adiabatic two-center shell model approach. The effect of $^{9}$Be$% \to $n$+2α$ breakup channel on complete fusion, elastic and inelastic cross sections is investigated. Results show that the breakup of the projectile $^{9}$Be could be due to a molecular single-particle effect shortly before the colliding nuclei reach the Coulomb barrier.
