Total Breakup Cross Section Research Articles

Breakup of 8B+natZr at the sub-barrier energy of 26.5 MeV

In our systematic research on reactions with weakly bound nuclei at suband nearbarrier energies, we have studied the system 8B+natZr at the sub-barrier energy of 26.5 MeV. Our measurements, performed at the TriSol radioactive beam facility of the University of Notre Dame, include angular distributions of both elastic scattering and breakup, for the determination of the total reaction and breakup cross sections as well as the direct-to-total reaction cross section ratio. Preliminary results of the breakup analysis will be presented, supported by Continuum Discretized Coupling Channel calculations.

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-nuclear dynamics in the breakup of the weakly bound Li8 nucleus

A detailed study of total, Coulomb, and nuclear breakup cross sections dependence on the projectile ground-state binding energy ${\ensuremath{\varepsilon}}_{b}$ is presented by considering the $^{8}\mathrm{Li}+^{12}\mathrm{C}$ and $^{8}\mathrm{Li}+^{208}\mathrm{Pb}$ breakup reactions. To this end, apart from the experimental one-neutron separation energy of $^{8}\mathrm{Li}$ nucleus $({\ensuremath{\varepsilon}}_{b}=2.03\phantom{\rule{0.16em}{0ex}}\mathrm{MeV})$, lower values of ${\ensuremath{\varepsilon}}_{b}$ down to ${\ensuremath{\varepsilon}}_{b}=0.01\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, are also being considered. It is shown that all breakup processes become peripheral as ${\ensuremath{\varepsilon}}_{b}\ensuremath{\rightarrow}0.01\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, which is understood as due to the well-known large spacial extension of ground-state wave functions associated to weakly bound projectiles. The Coulomb breakup cross section is found to be more strongly dependent on ${\ensuremath{\varepsilon}}_{b}$ than the nuclear breakup cross section, such that the Coulomb breakup becomes more significant as ${\ensuremath{\varepsilon}}_{b}$ decreases, even in a naturally nuclear-dominated reaction. This is mainly due to the long-range nature of the Coulomb forces, leading to a direct dependence of the Coulomb breakup on the electromagnetic transition matrix. It is also highlighted the fact that the nuclear absorption plays a minor role for small binding when the breakup becomes more peripheral.

Detailed study of the eikonal reaction theory for the breakup of one-neutron halo nuclei

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 the relative energy or parallel momentum between the core and halo neutron. Method: ERT predictions of these cross sections are compared to state-of-the-art calculations. Results: The hypotheses upon which the ERT is based are confirmed and their range of validity is made clearer. The actual ordering of the evolution operators {affects ERT differential} cross sections and a specific choice leads to excellent agreement with the reference calculation. Dynamical effects in the treatment of the neutron-target interaction can be significant in the parallel-momentum observable. Conclusions: The role of the different interactions in the dynamics of breakup reactions of one-neutron halo nuclei are better understood and improvements to the ERT are suggested.

Proton-halo breakup dynamics for the breakup threshold in the ε 0 → 0 limit

Proton-halo breakup behavior in the limit (where is the ground-state binding energy) is studied around the Coulomb barrier in the reaction for the first time. For practical purposes, apart from the experimental binding energy of 137 keV, three more arbitrarily chosen values (1, 0.1, 0.01 keV) are considered. It is first shown that the Coulomb barrier between the core and the proton prevents the system from reaching the state of an open proton-halo system, which, among other factors, would require the ground-state wave function to extend to infinity in the asymptotic region, as . The elastic scattering cross section, which depends on the density of the ground-state wave function, is found to have a negligible dependence on the binding energy in this limit. The total, Coulomb and nuclear breakup cross sections are all reported to increase significantly from to 1.0 keV, and converge to their maximum values as . This increase is mainly understood as coming from a longer tail of the ground-state wave function for keV, compared to that for keV. It is also found that the effect of the continuum-continuum couplings is to slightly delay the convergence of the breakup cross section. The analysis of the reaction cross section indicates a convergence of all the breakup observables as . These results provide a better sense of the dependence of the breakup process on the breakup threshold.

Comparative analysis of proton- and neutron-halo breakups

A detailed analysis of the proton- and neutron-halo breakup cross sections is presented. Larger neutron-halo breakup cross sections than proton-halo breakup cross sections are obtained. This is found to be mainly due to the projectile structure, namely the ground state wave function and the dipole electric response function. It is also found that the continuum–continuum couplings are stronger in the proton-halo breakup than in the neutron-halo breakup. The increase of proton- and neutron-halo ground state separation energy slightly strengthens these couplings in the proton- and neutron-halo total and nuclear breakups, while they are weakened in the proton- and neutron-halo Coulomb breakups. The Coulomb-nuclear interference remains strongly destructive in both proton- and neutron-halo breakups and this is independent of the ground state separation energy. The results also show that the increase of the neutron-halo ground state separation energy decreases significantly the agreement between the proton- and neutron-halo breakup cross sections, both qualitatively and quantitatively. It is obtained that when the proton-halo ground state separation energy is increased by a factor of 4.380, the proton-halo breakup cross section is reduced by a factor of 4.392, indicating a clear proportionality. However, when the neutron-halo ground state separation energy is increased by the same factor, the neutron-halo total breakup cross section is reduced by a factor of 8.522.

Partial-wave analysis and multipole transition interferences in the breakup of 6Li on 152Sm target

We have performed a detailed partial-wave analysis in order to analyze each partial-wave contribution to the breakup cross-sections as well as multipole interference effects in the [Formula: see text] breakup reaction. The results show that [Formula: see text]-waves contribute up to 67.03% of the overall integrated total breakup cross-section, distributed as follows: 10.43% for the [Formula: see text] partial-wave, 21.94% for the [Formula: see text] partial-wave and 34.66% for the [Formula: see text] partial-wave. A similar trend is observed for both Coulomb and nuclear breakup cross-sections. The importance of [Formula: see text]-waves over the non-[Formula: see text]-waves in the breakup process is mainly due to the higher-order multipole interferences. It is also obtained that the combination of [Formula: see text]-waves and [Formula: see text]-waves accounts for 84.77%, 89.95% and 73.58% of the total, Coulomb and nuclear breakup cross-sections, respectively. Considering the results obtained for the [Formula: see text] and [Formula: see text] partial-waves, we conclude that the [Formula: see text] and [Formula: see text] resonant breakup cross-sections, which can be obtained by integrating over the resonant energy range, could not be negligible compare to the [Formula: see text] resonant breakup cross-section. As far as this reaction is concerned, we can conclude that in the sequential breakup of [Formula: see text], excitations to all its three resonant states should be considered for a fair description of such process.

Importance of the continuum–continuum couplings in the 6Li elastic breakup on different target masses

A theoretical study of Li6 breakup on target masses ranging from A=58 to 208 is performed. It is obtained that when continuum–continuum couplings are included in the potential coupling matrix, they substantially reduce the total and nuclear breakup cross sections, while the Coulomb breakup cross sections for the medium and heavy target masses are increased. When these couplings are excluded, we show that the total and nuclear breakup cross sections depend linearly on AT1/3, namely they decrease linearly as the mass of the target increases. In the same case, the Coulomb breakup cross section depends linearly with the charge of the target ZT (decreases as ZT increases). We found that this linearity is destroyed when these couplings are included. However, in this case, it is the Coulomb-nuclear interference that also depends linearly with the target charge (increase with ZT).

Coulomb and nuclear effects in breakup and reaction cross sections

We use a three-body Continuum Discretized Coupled Channel (CDCC) model to investigate Coulomb and nuclear effects in breakup and reaction cross sections. The breakup of the projectile is simulated by a finite number of square integrable wave functions. First we show that the scattering matrices can be split in a nuclear term, and in a Coulomb term. This decomposition is based on the Lippmann-Schwinger equation, and requires the scattering wave functions. We present two different methods to separate both effects. Then, we apply this separation to breakup and reaction cross sections of 7Li + 208Pb. For breakup, we investigate various aspects, such as the role of the alpha + t continuum, the angular-momentum distribution, and the balance between Coulomb and nuclear effects. We show that there is a large ambiguity in defining the 'Coulomb' and 'nuclear' breakup cross sections, since both techniques, although providing the same total breakup cross sections, strongly differ for the individual components. We suggest a third method which could be efficiently used to address convergence problems at large angular momentum. For reaction cross sections, interference effects are smaller, and the nuclear contribution is dominant above the Coulomb barrier. We also draw attention on different definitions of the reaction cross section which exist in the literature, and which may induce small, but significant, differences in the numerical values.

Effects of projectile resonances on the total, Coulomb, and nuclear breakup cross sections in theLi6+Sm152reaction

In this paper we analyze the effects of the projectile resonances on the total, Coulomb, and nuclear breakup cross sections as well as on the Coulomb-nuclear interferences at different arbitrary incident energies. It is found that these resonances have non-negligible effects on the total, Coulomb, and nuclear breakup cross sections. Qualitatively, they have no effects on the constructiveness or destructiveness of the Coulomb-nuclear interferences. Quantitatively, we obtained that these resonances increase by 7.38%, 7.58%, and 20.30% the integrated total, Coulomb, and nuclear breakup cross sections, respectively at ${E}_{\mathrm{lab}}=35\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$. This shows that the nuclear breakup cross sections are more affected by the effects of the projectile resonances than their total and Coulomb breakup counterparts. We also obtain that the effects of the resonances on the total, Coulomb, and nuclear breakup cross sections decrease as the incident energy increases.

First-order and higher-order interferences in theC15+Pb208andBe11+Pb208reactions

First-order and higher-order interferences effects on the total, Coulomb, and nuclear breakup cross sections in the $^{15}\mathrm{C}+^{208}\mathrm{Pb}$ and $^{11}\mathrm{Be}+^{208}\mathrm{Pb}$ reactions are studied at 68 $\mathrm{MeV}/\mathrm{u}$ incident energy. A partial-wave analysis is first performed, and shows that the differential total breakup cross sections are dominated by the $p$ waves. However, considered alone, they largely underestimate the data, hence the importance of the other partial-wave contributions. It is also shown that the first-order interference reduces by more than $60%$ the total breakup cross sections, by less than $3%$ the Coulomb breakup cross sections, and by more than $85%$ the nuclear breakup cross sections, for both reactions. On the other hand, the higher-order interferences are found to reduce by less than $9%$ the total breakup cross section, less than $1%$ the Coulomb breakup cross section, and less than $7%$ the nuclear breakup cross section for the $^{15}\mathrm{C}+^{208}\mathrm{Pb}$ reaction. For the $^{11}\mathrm{Be}+^{208}\mathrm{Pb}$ reaction however, the higher-order interference reduces by less than $7%$ the total breakup cross section, by less than $1%$ the Coulomb breakup cross section, and by less than $4%$ the nuclear breakup cross section. It is finally shown that even at first order, the incoherent sum of the nuclear breakup cross sections is more important than the incoherent sum of the Coulomb breakup cross sections for the two reactions.

Modern nuclear force predictions forn−H3scattering above the three- and four-nucleon breakup thresholds

Background: Description of the collision process, which includes breakup, is one of the most challenging problems of the quantum mechanics. Recently I have developed a formalism based on the complex-scaling method, which describes accurately nuclear collisions in three- and four-body systems.Purpose: To provide accurate calculations for $n\ensuremath{-}^{3}\mathrm{H}$ scattering above the three- and four-nucleon breakup thresholds.Method: A four-nucleon system is described in configuration space employing Faddeev-Yakubovsky equations. The complex-scaling method is applied to overcome the difficulties related with the complicated boundary conditions.Results: Elastic observables as well as total breakup cross sections are calculated for neutron scattering on tritium at 14.1, 18, and 22.1 MeV using realistic $\mathit{NN}$ interactions. Excellent agreement is found with the pioneering calculations of this process reported by A. Deltuva et al. [Phys. Rev. C 86, 011001 (2012)]. Strong correlation of the calculated cross sections is established with model-predicted trinucleon binding energy. The forementioned observables reveal little sensitivity to the short-range details of $\mathit{NN}$ interaction.Conclusion: Reliable and accurate methods are now available to study four-nucleon scattering including the breakup.

Nuclear and Coulomb breakup of the weakly bound6Li nucleus with targets in the range fromA=59to 208

We have performed CDCC calculations for the $^{6}$Li + $^{59}$Co, $^{144}$Sm and $^{208}$Pb systems, to investigate the dependence of the relative importance of nuclear and Coulomb breakup on the target charge (mass) at near barrier energies. The calculations were in good agreement with the experimental elastic scattering angular distributions for these systems and then, their predictions to the nuclear, Coulomb and total breakup were investigated. Although the relative importance of the nuclear breakup is, as expected, larger for lighter targets, this effect is not very pronounced. We also investigate a scaling of the nuclear breakup with the target mass and we compare the predictions for the integrated total breakup cross sections with experimental fusion cross sections at similar energies.

Physics with low energy radioactive beams

This is a review of the basic mechanisms leading to high energy breakup reactions, of the formalisms used to describe them and of some of the methods to obtain the optical potentials necessary in calculations involving exotic nuclei. Semiclassical reductions of the DWBA approximation for inclusive and exclusive breakup will be presented. The observables that can be calculated are projectile’s core parallel momentum distributions, angular distributions of nucleons from the breakup, total breakup cross sections. Methods to study resonances at threshold in unbound nuclei are also introduced. In this case the exclusive observable calculated is the neutron-core relative energy spectrum. Finally, we study the two neutron transfer to the continuum reaction between two “normal” nuclei. The observable is the continuum excitation energy spectrum of the “exotic” residual nucleus created.

Dynamical effects in proton breakup from exotic nuclei

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 between 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 equivalent neutron of higher 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, proton angular distributions, and total breakup cross sections are calculated. With respect to nuclear breakup it is found that a proton behaves exactly as a neutron of higher binding energy. The extra ``effective energy'' is caused by the combined core-target Coulomb barrier. In Coulomb breakup we distinguish the effect of the core-target Coulomb potential (called the recoil effect), with respect to which the proton behaves, again, as a more bound neutron, from the direct proton-target Coulomb potential. The latter gives cross sections about an order of magnitude larger than the recoil term. The two effects give rise to complicated interferences in the parallel momentum distributions. They are instead easily separable in the proton angular distributions, which are therefore suggested as a very useful observable for future experimental studies.

Asymmetry in resonant breakup peaks in 6Li+ 209Bi reaction

The exclusive cross section for the breakup of 6Li by 209Bi has been measured at E l a b = 40 and 36 MeV. Sequential breakup, via the resonant state ( 3 + ) of 6Li in the continuum, dominates the total breakup cross section. The two sequential breakup peaks corresponding to the above resonant state, in both alpha and deuteron spectra, were found to be asymmetric. Continuum discretized coupled-channel (CDCC) calculations show the influence of both the Coulomb as well as the nuclear field on breakup.

Four-body calculation ofHe6breakup with the Coulomb-corrected eikonal method

The elastic breakup of a three-body projectile on a target is studied within the eikonal approximation with full account of final-state interactions. Bound and scattering states are calculated in hyperspherical coordinates on a Lagrange mesh. A correction is introduced to avoid the divergence of breakup cross sections due to the Coulomb interaction. The eikonal approximation allows the direct calculation of various cross sections, and in particular multidifferential cross sections can be obtained. The model is applied to the breakup of {sup 6}He on {sup 208}Pb. The {sup 6}He halo nucleus is described within a three-body {alpha}+n+n model involving effective {alpha}n and nn interactions. The eikonal phase is obtained from optical potentials between {alpha} and n, and the target. Around 0.8 MeV, the total breakup cross sections exhibit a narrow 2{sup +} resonant peak superimposed over a broad bump corresponding to a 1{sup -} resonance. These results suffer from a disagreement with experimental data at 240 MeV/nucleon, where cross sections are much smaller at low energies. The obtained E1 strength distribution resembles other theoretical results and reopens a long-standing problem about the existence of a 1{sup -} low-energy resonance in the {sup 6}He continuum.

CDCC Approaches and Roles of Closed Channels in d-Nucleus Reactions

The effect of deuteron breakup in d-nucleus reaction is treated with the continuum discretized coupled channels (CDCC) approach, and the effects on the total reaction cross sections and elastic scattering angular distributions are studied by comparing the calculations of CDCC and spherical optical model with our global deuteron optical potential [Phys. Rev. C 73 (2006) 054605] below 200 MeV, for target nuclei ranging from 12C to 208Pb. The contributions from the closed channels to the total reaction and breakup cross sections, and angular distributions of elastic scattering are also seriously discussed.

Breakup ofHe6incident onBi209near the Coulomb barrier

A neutron-\ensuremath{\alpha}-particle coincidence experiment was performed to study breakup of $^{6}\mathrm{He}$ on a $^{209}\mathrm{Bi}$ target at an incident energy of 22.5 MeV. Direct breakup, as well as breakup through the ${2}^{+}$ excited state of $^{6}\mathrm{He}$ and also the $^{5}\mathrm{He}$$+n$ channel, could be distinguished. A total breakup cross section of $205\ifmmode\pm\else\textpm\fi{}65$ mb was measured. The data compare well with a coupled-channels calculation that assumes a 50% reduction in the B(E1) computed from a pure $^{4}\mathrm{He}$$+2n$ cluster configuration, in agreement with results obtained at much higher energies. A value of $\mathrm{B}(\mathrm{E}2\ensuremath{\Uparrow})=5.4\ifmmode\pm\else\textpm\fi{}0.7{e}^{2}{\mathrm{fm}}^{4}$ is deduced for the ${2}^{+}$ state in $^{6}\mathrm{He}$.

Coupling-in-the-continuum effects in Coulomb dissociation of halo nuclei

Higher-order effects in the Coulomb dissociation of halo nuclei are investigated by comparing the first-order perturbation theory to the numerical resolution of a time-dependent Schr\odinger equation. The calculations are performed for the breakup on a lead target of $^{11}\mathrm{Be}$ and $^{8}\mathrm{B}$. The populations of the different partial waves composing the $^{10}\mathrm{Be}$-neutron or $^{7}\mathrm{Be}$-proton continuum reveal that couplings in the continuum remain significant even at high impact parameters and high projectile-target relative velocities. Although the total breakup cross section is fairly well described by a first-order approximation, its partial-wave components reached by the first-order transitions are significantly depleted toward other partial waves after the closest approach. The information extracted by assuming the validity of the first-order approximation is affected by an energy distortion. Another distortion is caused by the presence of a resonance as exemplified by the $5/{2}^{+}$ resonance of $^{11}\mathrm{Be}$. Such effects may partly explain discrepancies between direct and indirect measurements of the astrophysical S factor of the $^{7}\mathrm{Be}(\text{p},\ensuremath{\gamma})^{8}\mathrm{B}$ reaction at stellar energies.