Inclusive Breakup Research Articles

Comparison of Ichimura-Austern-Vincent and Glauber models for the deuteron-induced inclusive breakup reaction in light and medium-mass nuclei

Comparison of Ichimura-Austern-Vincent and Glauber models for the deuteron-induced inclusive breakup reaction in light and medium-mass nuclei

A systematic analysis of deuteron breakup

Inclusive breakup cross sections for deuterons incident on a wide range of nuclei at different incident energies are studied. In our analysis, we use the post-form distorted-wave-Born approximation (DWBA) to calculate the elastic and nonelastic breakup cross sections. We also calculate exciton and statistical compound-nucleus model cross sections to account for pre-equilibrium and equilibrium emissions. The calculations are performed using the code EMPIRE and are compared to the available experimental data. The comparisons of the integrated cross sections reveal a generally good agreement between the calculations and the data. However, systematic discrepancies are observed between the calculated double differential neutron and proton cross sections and the data, especially for heavier targets. Possible reasons for the disagreements between the theoretical predictions and the experimental data are discussed.

Modelling inclusive breakup: application to incomplete fusion

We propose an extension of the inclusive breakup model of Ichimura, Austern and Vincent [Phys. Rev. C 32, 431 (1985)] for the evaluation of incomplete fusion (ICF) cross sections in nuclear reactions induced by two-body projectiles. The main idea, adopted in other methods, consists in the separation of the participant-target optical potential into its direct reaction and compound reaction components, the latter being responsible for the ICF contribution of the total nonelastic breakup cross section. Preliminary comparison with experimental data shows encouraging results.

Coulomb breakup reaction of loosely bound F17 with dynamic polarization potentials

We investigate the elastic scattering, inelastic scattering, breakup reaction, and total fusion reactions of the $^{17}\mathrm{F}+^{208}\mathrm{Pb}$ system using an optical model approach by including the dynamical polarization potential. In particular, we focus on the breakup reaction channels, whose effects on other reactions have been argued to be small. By exploiting two different potentials composed of a surface-type Woods-Saxon potential, which were obtained by a fitting analysis, and a Love-type optical potential, the breakup reaction cross sections are explained with other elastic and quasielastic scattering cross sections. For the breakup reaction at ${E}_{\text{lab}}=170$ MeV in the forward angle region, where only exclusive reaction data are known, inclusive breakup reaction data are deduced from available theoretical and experimental $E1$ strength values. We discuss the breakup reaction effects on the other nuclear reactions related to the $^{17}\mathrm{F}$ projectile in detail.

Inclusive breakup cross sections in reactions induced by the nuclides He6 and Li6,7 in the two-body cluster model

Calculations of inclusive ${\alpha}$ particle production are performed to interpret reaction experimental data induced by the two-neutron halo $^6$He and the isotopes $^{6,7}$Li on different target nuclei. We have implemented the zero-range post-form DWBA to compute the elastic and nonelastic breakup cross sections. Integrated cross sections, angular distributions and spectra are presented. Projectiles are approximated as two-body clusters, namely $^6$He as ${\alpha}$+dineutron and $^{6}$Li ($^{7}$Li) interpreted as ${\alpha}$+deuteron(triton). The S\~ao Paulo optical potential is employed in the calculation of the distorted wave functions for the incident channels, while standard phenomenological interactions are used for the fragment-target interactions. Calculations for $^6$Li and $^7$Li furnish a good description of the data, while the reaction involving $^6$He is found to be a complicated case, where data interpretation is still considered a major obstacle. The present analysis identifies an overall large contribution from inclusive breakup emissions for all the cases studied.

The Hussein–McVoy formula for inclusive breakup revisited

The Hussein–McVoy formula for inclusive breakup revisited

Insight into the reaction dynamics of proton drip-line nuclear system 17F+58Ni at near-barrier energies

The mechanism of reactions with weakly-bound proton-rich nuclei at energies near the Coulomb barrier is a long-standing open question owing to the paucity of experimental data. In this study, a complete kinematics measurement was performed for the proton drip-line nucleus 17F interacting with 58Ni at four energies near the Coulomb barrier. Thanks to the powerful performance of the detector array, exhaustive information on the reaction channels, such as the differential cross sections for quasielastic scattering, exclusive and inclusive breakup, as well as for fusion-evaporation protons and alphas, was derived for the first time. The angular distributions of quasielastic scattering and exclusive breakup can be described reasonably well by the continuum-discretized coupled-channels calculations. The inclusive breakup was investigated using the three-body model proposed by Ichimura, Austern, and Vincent, and results indicate the non-elastic breakup is the dominant component. The total fusion cross sections were determined by the fusion-evaporation protons and alphas. Based on the measured exclusive breakup data, the analysis of the classical dynamical simulation code PLATYPUS demonstrates that the incomplete fusion plays a minor role. Moreover, compared with 16O+58Ni, both the reaction and total fusion cross sections of 17F+58Ni exhibit an enhancement in the sub-barrier energy region, which mainly arises from couplings to the continuum states. This work indicates that the information of full reaction channels is crucially important to comprehensively understand the reaction mechanisms of weakly bound nuclear systems.

Comparison of semiclassical transfer to continuum model with Ichimura-Austern-Vincent model in medium energy knockout reactions

The full quantum mechanical (QM) model of inclusive breakup of Ichimura-Austern-Vincent (IAV) is implemented in this paper to calculate breakup from heavy radioactive nuclei on a 9Be target at intermediate energies. So far it had been implemented and applied only to low energy reactions with light projectiles. The IAV model is successful in predicting absolute cross sections among other observables. In order to get insight on the content of the model in the case of the complicated heavy-ion reactions, results are compared with those of the semiclassical transfer to the continuum (TC) model. Because the TC is based on analytical formulae the dynamics of the breakup as it is contained in the rather involved IAV formalism will become more transparent. Heavy-ion reactions at high energies (>50 A.MeV) are demanding from the computational point of view because of the high number of partial waves involved, typically around 100. The TC constitutes a useful alternative to the full QM calculations whenever predictions and/or estimates are necessary. It allows also for a systematic, fast evaluation of breakup observables. In the applications of both methods we use state-of-the art optical potentials and structure information. Excellent agreement is found between the calculated results of both methods and with available experimental data which shows that the qualitative and quantitative understanding of most aspects of one nucleon breakup is well under control.

Inclusive breakup measurements of the 7Li+ 119Sn reaction

We present preliminary data of elastic scattering and inclusive breakup cross sections for the 7Li+ 119Sn reaction, recently measured at the Laboratori Nazionali del Sud (LNS-INFN) (Catania, Italy) at energies around the Coulomb barrier (E lab = 21.2 and 26.5 MeV). The experimental data have been analyzed under the Optical Model and Continuum-Discretized Coupled-Channels methods.

The total reaction cross section of heavy-ion reactions induced by stable and unstable exotic beams: the low-energy regime

In this review paper we present a detailed account of the extraction and the calculation of the total reaction cross section of strongly bound and weakly bound, stable and unstable, exotic, nuclei. We discuss the optical model and the more general coupled channels model of direct reactions. The effect of long-range absorption due to the coupling to excited states in the target and to the breakup continuum in the projectile is also discussed. The generalized optical theorem for charged particle scattering and the resulting sum-of differences method is then discussed. The so-called "quarter-point recipe" is discussed next, and the quarter-point angle is introduced as a simple and rapid mean to obtain the total reaction cross section. The last topic discussed is the reduction of the total reaction cross section that would allow a large body of data to sit on a single universal function. Such a universal function exists in the case of the fusion data, and the aim of this last topic of the review is to extend the fusion case to the total reaction, by adding the direct reaction contribution. Also discussed is the inclusive breakup cross section and how it can be used to extract the total reaction cross section of the interacting fragment with the target. This method is also known as the Surrogate method and represents a case of hybrid reactions. The sum of the integrated inclusive breakup cross section with the complete fusion cross section supplies the total fusion cross section. The main experimental methods to determine the total reaction cross section are also discussed, with emphasis in recent techniques developed to deal with reactions induced by unstable beams.

Lagrange-mesh R -matrix method for inhomogeneous equations

The Lagrange-mesh $R$-matrix method is generalized to inhomogeneous equations. This method is numerically stable and efficient. It can be directly used for transfer reactions with the formalism discussed by Ascuitto and Glendenning [Phys. Rev. 181,1396 (1969)] and for inclusive breakup reactions modeled by Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)]. We first present a simple example to assess the method. Then the application to the $^{93}$Nb($d$,$pX$) non-elastic breakup is discussed.

Unraveling the Reaction Mechanisms Leading to Partial Fusion of Weakly Bound Nuclei.

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 etal. [Phys. Rep. 154, 125 (1987)PRPLCM0370-157310.1016/0370-1573(87)90094-9] 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.

The neutron within the deuteron as a surrogate for neutron-induced reactions

We propose the use of neutron poisons in reactions induced by radioactive beams as a test of theoretical models aiming to relate neutron capture in nuclei with neutron surrogate reactions such as ([Formula: see text]) reactions. We exploit the approximations necessary to obtain a direct relation between the two reactions: surrogate versus neutron capture. We also show how this is intimately related to the momentum distribution of the neutron within the deuteron. The models we use are based on the theory of inclusive breakup reactions commonly employed in the treatment of incomplete fusion and surrogate method. Such theories were developed in the 1980s by Ichimura, Austern and Vincent [Phys. Rev. C 32 (1985) 431], Udagawa and Tamura [Phys. Rev. C 24 (1981) 1348] and Hussein and McVoy [Nucl. Phys. A 445 (1985) 124]. We use these theories to derive an expression for the proton yield in the reaction [Formula: see text]. The capture reaction [Formula: see text] is then extracted using reasonable approximations. By recalling an old method proposed by Serber [Phys. Rev. 80 (1950) 1098; Proc. Roy. Soc. A 208 (1951) 559] we explain how the momentum distribution of neutrons within the deuteron will depend on the short-range dependence of the nucleon–nucleon force. The relevance of our work to nucleosynthesis in the rapid neutron capture process is emphasized.

Inclusive breakup calculations in angular momentum basis: Application to Li7+Ni58

The angular momentum basis method is introduced to solve the inclusive breakup within the model proposed by Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)]. This method is based on the geometric transformation between Jacobi coordinates, thus it is easy to corporate with particle spins. To test the validity of this partial wave expansion method, a benchmark calculation is done comparing with the one given in [Phys. Rev. C 92, 044616 (2015)]. Using the distorted-wave Born approximation (DWBA) version of IAV model, some applications to $^7$Li reactions are presented and compared with available data.

Post-prior equivalence for transfer reactions with complex potentials

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.

Inclusive breakup of Borromean nuclei

We derive the inclusive breakup cross section of a three-fragment projectile nuclei, a = b + x1 +x2, 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 [1], which is proportional to a matrix element of the form, . The new feature here is the three-body absorption, represented by the imaginary potential, W3b. We analyze this type of absorption and supply ideas of how to calculate its contribution.

Comprehensive analysis of large α yields observed in Li6 -induced reactions

Background: Large $\ensuremath{\alpha}$ yields have been reported over the years in reactions with $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ projectiles. Previous theoretical analyses have shown that the elastic breakup (EBU) mechanism (i.e., projectile breakup leaving the target in its ground state) is able to account only for a small fraction of the total $\ensuremath{\alpha}$-inclusive breakup cross sections, pointing toward the dominance of nonelastic breakup (NEB) mechanisms.Purpose: We aim to provide a systematic study of the $\ensuremath{\alpha}$-inclusive cross sections observed in nuclear reactions induced by $^{6}\mathrm{Li}$ projectiles. In addition to estimating the total $\ensuremath{\alpha}$ singles' cross sections, it is our goal to evaluate angular and energy distributions of these $\ensuremath{\alpha}$ particles and compare them with experimental data, when available.Method: We compute separately the EBU and NEB components of the inclusive breakup cross sections. For the former, we use the continuum-discretized coupled-channels (CDCC) method, which treats this mechanism to all orders. For the NEB part, we employ the model proposed by Ichimura et al. [Phys. Rev. C 32, 431 (1985)], within the distorted-wave Born approximation (DWBA).Results: Overall, the sum of the computed EBU and NEB cross sections is found to reproduce very well the measured singles' cross sections. In all cases analyzed, we find that the inclusive breakup cross section is largely dominated by the NEB component.Conclusions: The presented method provides a global and systematic description of inclusive breakup reactions induced by $^{6}\mathrm{Li}$ projectiles. It provides also a natural explanation of the previously observed underestimation of the measured $\ensuremath{\alpha}$ yields by CDCC calculations. The method used here can be extended to other weakly bound projectiles, including halo nuclei.

Inclusive breakup of three-fragment weakly bound nuclei

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 correlations inside the projectile affect in a conspicuous way the elastic breakup cross section. The inclusive non-elastic breakup cross section is calculated and is found to contain the contribution of a three-body absorption term that is also strongly influenced by the two-fragment correlations. This latter cross section contains the so-called incomplete fusion where more than one compound nuclei are formed. Our theory describes both stable weakly bound three-fragment projectiles and unstable ones such as the Borromean nuclei.

Inclusive Breakup Theory of Three-Body Halos

We present a recently developed theory for the inclusive breakup of three-fragment projectiles within a four-body spectator model \cite{CarPLB2017}, for the treatment of the elastic and inclusive non-elastic break up reactions involving weakly bound three-cluster nuclei in $A\,(a,b)\,X$ / $a = x_1 + x_2 + b$ collisions. The four-body theory is an extension of the three-body approaches developed in the 80's by Ichimura, Autern and Vincent (IAV) \cite{IAV1985}, Udagawa and Tamura (UT) \cite{UT1981} and Hussein and McVoy (HM) \cite{HM1985}. We expect that experimentalists shall be encouraged to search for more information about the $x_{1} + x_{2}$ system in the elastic breakup cross section and that also further developments and extensions of the surrogate method will be pursued, based on the inclusive non-elastic breakup part of the $b$ spectrum.

Determining astrophysical three-body radiative capture reaction rates from inclusive Coulomb break-up measurements

A relationship between the Coulomb inclusive break-up probability and the radiative capture reaction rate for weakly-bound three-body systems is established. This direct link provides a robust procedure to estimate the reaction rate for nuclei of astrophysical interest by measuring inclusive break-up processes at different energies and angles. This might be an advantageous alternative to the determination of reaction rates from the measurement of $B(E1)$ distributions through exclusive Coulomb break-up experiments. In addition, it provides a reference to assess the validity of different theoretical approaches that have been used to calculate reaction rates. The procedure is applied to $^{11}$Li ($^{9}$Li+n+n) and $^6$He ($^{4}$He+n+n) three-body systems for which some data exist.