Breakup Cross Section Research Articles

Direct and resonant breakup of radioactive Be7 nuclei produced in the Sn112(Li6,Be7) reaction

Cross sections for direct and resonant breakup of radioactive $^{7}\mathrm{Be}$ nuclei produced in a transfer reaction $^{112}\mathrm{Sn}(^{6}\mathrm{Li},^{7}\mathrm{Be}\ensuremath{\rightarrow}\ensuremath{\alpha}+^{3}\mathrm{He})\phantom{\rule{0.16em}{0ex}}^{111}\mathrm{In}$ have been measured. Breakup of $^{7}\mathrm{Be}$ into $\ensuremath{\alpha}$ and $^{3}\mathrm{He}$ cluster fragments via its resonant states of $7/{2}^{\ensuremath{-}}$(4.57 MeV) and $5/{2}^{\ensuremath{-}}$ (6.73 MeV) in the continuum have been identified for the first time using the measured distribution of $\ensuremath{\alpha}\text{\ensuremath{-}}^{3}\mathrm{He}$ relative energy and the reaction $Q$ value obtained from the $\ensuremath{\alpha}\text{\ensuremath{-}}^{3}\mathrm{He}$ coincident events. The breakup cross sections extracted from the efficiency corrected coincidence yield compares well with the results of the coupled-channels calculations. Significant cross sections for breakup of $^{7}\mathrm{Be}$ into its cluster fragments directly or through resonant states highlight the importance of the ground-state structure of $^{7}\mathrm{Be}$ as a cluster of $\ensuremath{\alpha}$ and $^{3}\mathrm{He}$.

PHENIX results on polarization in p+p collisions.

One of the big questions in quarkonia production is how heavy-quark pairs are produced in the initial hard scattering and hadronize into final quarkonia states. This question also affects the estimation of quarkonia breakup cross-sections and color screening in heavy ion collisions. Many existing models describe well general features of quarkonia production like cross-section and transverse momentum distributions. In order to differentiate between various models one has to study quarkonia production in more details. One of such tools is a study of angular distributions of decay leptons, usually called polarization. The PHENIX experiment has measured inclusive polar and azimuthal angular decay coefficients in the mid and forward rapidity regions in p+p collisions at 200 GeV and 510 GeV. This talk will present the analysis strategy as well as the results in different polarization frames.

Low-energy Li11+p and Li11+d scattering in a multicluster model

The 11Li + p and 11Li + d reactions are investigated in the Continuum Discretized Coupled Channel (CDCC) method with a three-body description (9Li + n + n) of 11Li. I first discuss the properties of 11Li, and focus on E1 transition probabilities to the continuum. The existence of a 1- resonance at low excitation energies is confirmed, but the associated E1 transition from the ground state does not have an isoscalar character, as suggested in a recent experiment. In a second step, I study the 11Li + p elastic cross section at Elab = 66 MeV in the CDCC framework. I obtain a fair agreement with experiment, and show that breakup effects are maximal at large angles. The breakup cross section is shown to be dominated by the 1- dipole state in 11Li, but the role of this resonance is minor in elastic scattering. From CDCC equivalent 11Li + p and 11Li + n potentials, I explore the 11Li + d cross section within a standard three-body 11Li +(p + n) model. At small angles, the experimental cross section is close to the Rutherford scattering cross section, which is not supported by the CDCC. A five-body (9Li+n+n)+(p+n) is then performed. Including breakup states in 11Li and in the deuteron represents a numerical challenge for theory, owing to the large number of channels. Although a full convergence could not be reached, the CDCC model tends to overestimate the data at small angles. I suggest that measurements of the 9Li + p elastic scattering would be helpful to determine more accurate optical potentials. The current disagreement between experiment and theory on 11Li + d scattering also deserves new experiments at other energies.

Effect of the repulsive core in the proton-neutron potential on deuteron elastic breakup cross sections

The role of the short-range part (repulsive core) of the proton-neutron ($pn$) potential in deuteron elastic breakup processes is investigated. A simplified one-range Gaussian potential and the Argonne V4' (AV4') central potential are adopted in the continuum-discretized coupled-channels (CDCC) method. The deuteron breakup cross sections calculated with these two potentials are compared. The repulsive core is found not to affect the deuteron breakup cross sections at energies from 40 MeV to 1 GeV. To understand this result, an analysis of the peripherality of the elastic breakup processes concerning the $p$-$n$ relative coordinate is performed. It is found that for the breakup processes populating the $pn$ continua with orbital angular momentum $\ell$ different from 0, the reaction process is peripheral, whereas it is not for the breakup to the $\ell=0$ continua (the s-wave breakup). The result of the peripherality analysis indicates that the whole spatial region of deuteron contributes to the s-wave breakup.

Current stage of studies of the star configurations at intermediate energies with the use of the BINA detector

The~Space Star Anomaly in proton-deuteron breakup cross-section occurs at energies of about 10~MeV. Data for higher energies are sparse. Therefore, a~systematic scan over star configurations in the~range of intermediate energies between 50 and 100 MeV/nucleon is carried out on the~basis of data collected with the~large acceptance BINA detector. The~preliminary cross section results for forward star configurations at 80 MeV/nucleon slightly surpass the~theoretical calculations, but the~systematic uncertainties are still under study. Also, a~new variable describing rotation of star configurations is proposed.

Extended optical model analyses of $$^{11}\hbox {Be+}^{197}\hbox {Au}$$ with dynamic polarization potentials

We discuss angular distributions of elastic, inelastic, and break-up cross-sections for the \(^{11}\hbox {Be} + ^{197}\hbox {Au}\) system, measured at energies below and around the Coulomb barrier. To this end, we employ Coulomb dipole excitations and a long-range nuclear (LRN) potential in order to account for long-range effects of the halo nuclear system and break-up effects of the weakly bound structure. We then analyze recent experimental data, comprising three channels, viz., elastic, inelastic, and break-up cross-sections, at \(E_{\text {c.m.}}=29.6\hbox { MeV}\) and \(E_{\text {c.m.}}=37.1\hbox { MeV}\). From the parameter sets extracted using a \(\chi ^{2}\) analysis, we successfully reproduce the experimental angular distributions of the elastic, inelastic, and break-up cross-sections for the \(^{11}\hbox {Be+}^{197}\hbox {Au}\) system simultaneously. Finally, we discuss the necessity of the LRN potential around the Coulomb barrier from a detailed analysis of the experimental data.

Sensitivity of one-neutron knockout to the nuclear structure of halo nuclei

Background: Information about the structure of halo nuclei are often inferred from one-neutron knockout reactions. Typically the parallel-momentum distribution of the remaining core is measured after a high-energy collision of the exotic projectile with a light target. Purpose: We study how the structure of halo nuclei affects knockout observables considering an eikonal model of reaction. Method: To evaluate the sensitivity of both the diffractive and stripping parallel-momentum distributions to the structure of halo nuclei, we consider several descriptions of the projectile within a halo effective field theory. We consider the case of 11Be, the archetypical one-neutron halo nucleus, impinging on 12C at 68 MeV/nucleon, which are usual experimental conditions for such measurements. The low-energy constants of the description of 11Be are fitted to experimental data as well as to predictions of an ab initio nuclear-structure model. Results: One-neutron knockout reaction is confirmed to be purely peripheral, the parallel-momentum distribution of the remaining core is only sensitive to the asymptotics of the ground-state wavefunction and not to its norm. The presence of an excited state in the projectile spectrum reduces the amplitude of the breakup cross section; the corresponding probability flux is transferred to the inelastic-scattering channel. Although the presence of a resonance in the core-neutron continuum significantly affects the energy distribution, it has no impact on the parallel-momentum distribution. Conclusions: One-neutron knockout cross section can be used to infer information about the tail of the ground-state wavefunction, viz. its asymptotic normalization coefficient (ANC). The independence of the parallel-momentum distribution on the continuum description makes the extraction of the ANC from this observable very reliable.

Convergent close-coupling calculations of positron scattering on H−

The convergent close-coupling method has been applied to positron scattering by the hydrogen negative ion. Convergence of the cross sections is achieved and internal consistency of the method is verified using both the single- and two-center approaches. Calculations were performed using accurate target wave functions obtained with the multicore approach. Obtained results for Ps formation and breakup cross sections are compared with previous calculations.

Extension of the ratio method to proton-rich nuclei

The ratio method has been developed to improve the study of one-neutron halo nuclei through reactions. By taking the ratio of angular distributions for two processes, viz. breakup and elastic scattering, this new observable is nearly independent of the reaction mechanism and hence much more sensitive to the projectile structure than the cross sections for each single process. We study the extension of the ratio method to proton-rich nuclei and also explore the optimum experimental conditions for measuring this new observable. We compare accurate dynamical calculations of reactions for proton-rich projectiles to the prediction of the ratio method. We use the dynamical eikonal approximation that provides good results for this kind of reaction at intermediate energy. Our tests for 8B, an archetypical one-proton halo nucleus, on Pb, Ni, and C targets at 44 MeV/nucleon show that, the ratio works less well than for neutron halos due to the non-negligible Coulomb interaction between the valence proton and the target. Nevertheless, thanks to its strong sensitivity to the single-particle structure of the projectile, the ratio method still provides pertinent information about nuclear structure on the proton-rich side of the valley of stability. To account for the lower quality of the method applied to charged systems, we suggest variations in its application from the original idea. Interestingly the method is not affected if energy ranges—or bins—are considered in the projectile continuum. This makes the ratio easier to measure experimentally by increasing the breakup cross section. We also extend our analysis to 17F, 25Al, and 27P, whose study is of interest to both nuclear astrophysics and nuclear structure. We show that, albeit less precise than for one-neutron halo nuclei, nuclear-structure information can be inferred from the ratio method applied to exotic proton-rich nuclei. For nuclei in which the valence proton is deeply bound and/or sits in an l ≥ 2 orbital, the method provides only estimates of nuclear-structure features, like the one-proton separation energy or the orbital angular momentum of the valence proton in the ground state. When the valence proton is loosely bound in an s or p orbital, viz. for proton halo nuclei, more detailed structure information can be obtained through this new reaction observable.

Studies of Deuteron Breakup Reactions in Deuteron\u2013Deuteron Collisions at 160\xa0MeV with BINA

A rich set of differential cross section of the three-body ^{2}H(d,dp)n breakup reaction at 160 MeV deuteron beam energy has been measured over a large range of the available phase space. The experiment was performed at KVI in Groningen, the Netherlands, using the BINA detector. The cross-section data for the breakup reaction have been normalized to the simultaneously measured ^{2}H(d,d)^{2}H elastic scattering cross section. The breakup cross sections obtained for 147 kinematically complete configurations near the quasi-free scattering kinematics are compared to the recent approximate calculations for the three-cluster breakup in deuteron–deuteron collisions. The cross sections for 294 kinematic configurations of the quasi-free scattering regime, for which no theoretical calculations exist, are also presented. Besides the three-body breakup, semi-inclusive energy distributions for the four-body ^{2}H(d,pp)nn breakup are reported.

Measurement of Differential Cross Section for Proton-induced Deuteron Breakup at 108 MeV

The experiment was performed at CCB IFJ PAN in Krakow with the use of the BINA detector. The experimental program and data analysis of proton-induced deuteron breakup reaction at 108 MeV are presented.

Deuteron breakup at zero angle in the Coulomb nuclear field

Deuteron breakup cross sections on the C and CH2 targets have been measured up to the proton internal momenta of 0.3 GeV/c. The cross-sections 12C(d, p)X and 1H(d, p)X reactions have been obtained with high precision. The obtained data are compared with previous measurements. The behavior features in the vicinity of the cross section maximum were studied in dependence on the transversal momentum in the region of 0.01 < pt < 0.16 GeV/c. The measurements have been performed at the Veksler Baldin Laboratory of High Energy Physics of the Joint Institute for Nuclear Research.

Analysis of (11Li+9Be)-reaction in the framework of the time-dependent Schrodinger equation

Neutron transfer and nucleus breakup cross sections in ( 11 Li + 9 Be) -reaction are calculated at energy range up to 32 MeV/nucleon. The evolution of probability density of external weakly bound neutrons of 11Li and the probabilities of neutron transfer and nucleus breakup are determined based on a numerical solution of the time-dependent Schrodinger equation. Our calculation results are agree with the experiment.

Simultaneous Optical Model Analysis of Elastic Scattering and Breakup Reaction Channels for 11Li + 208Pb System

Using the optical model (OM) potential, we perform simultaneous χ2 analysis of the elastic scattering and the breakup reaction data for 11Li + 208Pb system. We introduce Coulomb dipole excitation (CDE) and long-range nuclear (LRN) potentials to consider effects of long range interaction. By the simultaneous χ2 analysis, we obtain a variety of the parameter set with a large diffuseness parameter which is inferred by two valence neutrons of 11Li located in two different orbits moving into a wide region. From the extracted best parameter set, finally, we calculate the breakup, total fusion, and total reaction cross sections. The total reaction and the breakup reaction cross sections obtained from our present work well reproduced experimental data within 5% and 10%, respectively, whereas the total fusion cross sections overestimate experimental data. Detailed discussions regarding the disagreement with the fusion data are also addressed.

Resonant breakup of Be8 in Sn112(Li7,Be8→2α) reaction

Background: Reactions involving weakly bound projectiles with $\ensuremath{\alpha}+x$ cluster structure are known to produce a large number of $\ensuremath{\alpha}$ particles, where transfer-induced breakup is one of the possible origins. Detailed investigation on each of these channels is desirable to understand the underlying reaction mechanism.Purpose: Our purpose is to measure the $+1p$ transfer-induced breakup in the $^{112}\mathrm{Sn}(^{7}\mathrm{Li},^{8}\mathrm{Be}\ensuremath{\rightarrow}2\ensuremath{\alpha})$ reaction to understand the possible modes of $^{8}\mathrm{Be}$ breakup and their contribution to inclusive $\ensuremath{\alpha}$ production.Methods: $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ coincidence measurements have been carried out for the above reaction at ${E}_{\mathrm{beam}}=30$ MeV. Projectile-like fragments were detected using five sets of Si-strip-detector telescopes and five sets of single Si-detector telescopes. Optical model analysis of elastic scattering data, coupled reaction channels (CRC), and continuum discretized coupled channels (CDCC) calculations were performed to understand the measured cross sections.Results: The experimental cross sections for $+1p$ transfer-induced breakup in ($^{7}\mathrm{Li},^{8}\mathrm{Be}\ensuremath{\rightarrow}2\ensuremath{\alpha}$) reaction through different resonance states of $^{8}\mathrm{Be}$ have been obtained. Relative energy distribution and Monte Carlo simulation confirm the observation of breakup of $^{8}\mathrm{Be}$ from its ${4}^{+}$ (11.35-MeV) resonant state for the first time along with its well-known ${0}^{+}$ (92-keV) and ${2}^{+}$ (3.12-MeV) resonances. Simultaneous description of elastic scattering, transfer, and breakup cross sections have been made using CDCC plus CRC formalism.Conclusions: Production of $\ensuremath{\alpha}$ particles in $+1p$ transfer-triggered breakup is found to proceed mainly through three resonance (${0}^{+},\phantom{\rule{0.16em}{0ex}}{2}^{+}$, and ${4}^{+}$) states of $^{8}\mathrm{Be}$.

Role of cluster structure in the breakup of Li7

Direct and sequential breakups of the projectile in the $^{7}\mathrm{Li}+^{112}\mathrm{Sn}$ reaction have been measured at a beam energy of 30 MeV. Cross sections for sequential breakup of $^{7}\mathrm{Li}$ into $\ensuremath{\alpha}$ and $t$ cluster fragments via its second resonant state of $5/{2}^{\ensuremath{-}}$ (6.68 MeV) in the continuum have been measured for the first time along with the first resonant state ($7/{2}^{\ensuremath{-}}$, 4.63 MeV). Probabilities of sequential breakup proceeding through $\ensuremath{-}1n$ and $\ensuremath{-}2n$ transfer channels, i.e., ($^{7}\mathrm{Li},^{6}\mathrm{Li}$) and ($^{7}\mathrm{Li},^{5}\mathrm{Li}$) reactions followed by breakup, into $\ensuremath{\alpha}+d$ and $\ensuremath{\alpha}+p$, respectively, were found to dominate over $\ensuremath{\alpha}+t$ breakup. Measured cross sections for the above breakup channels and elastic scattering have been compared with coupled-channel calculations to understand the reaction mechanism involving the weakly bound projectile $^{7}\mathrm{Li}$. Significant cross section for direct breakup of $^{7}\mathrm{Li}\ensuremath{\rightarrow}^{6}\mathrm{He}+p$ has also been measured for the first time, indicating the importance of the new ($^{6}\mathrm{He}+p$) cluster configuration that may be necessary to understand the complete structure of $^{7}\mathrm{Li}$ and its energy levels.

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.

Elastic scattering and breakup reactions of the exotic nucleus 8B on nuclear targets

Microscopic calculations of the optical potentials (OPs) and elastic scattering cross sections of the proton-rich nucleus 8B on 12C, 58Ni and 208Pb targets are presented. The density distributions of 8B obtained within the variational Monte Carlo (VMC) model and the three-cluster model (3CM) are used to construct the optical potentials (OP). The real part of the hybrid OP (ReOP) is calculated using the folding model with the direct and exchange terms included, while the imaginary part (ImOP) is obtained on the base of the high energy approximation (HEA). In addition, the cluster model, in which 8B consists of a proton halo and a 7Be core is applied to calculate the breakup cross sections of 8B on 9Be, 12C and 197Au targets, as well as the momentum distributions of 7Be fragments. A comparison with the available experimental data is made and a good agreement is obtained.

Breakup and fusion cross sections of the 6Li nucleus with targets of mass A = 58, 144 and 208

We use the continuum discretized coupled channels method to investigate the effects of continuum–continuum coupling on the breakup and fusion cross sections of the weakly bound 6Li nucleus with the 58Ni, 144Sm and 208Pb nuclear targets. The cross sections were analyzed at incident energies Ecm below, close to and above the Coulomb barrier VB. We found that for the medium and heavy targets, the breakup cross sections are enhanced at energies below the Coulomb barrier (Ecm/VB ≤ 0.8) owing to these couplings. For the lighter target, relatively small enhancement of the breakup cross sections appear at energies well below the barrier (Ecm/VB ≤ 0.6). At energies Ecm/VB > 0.8 for medium and heavy targets, and Ecm/VB > 0.6 for the light target, the continuum–continuum couplings substantially suppress the breakup cross sections. On the other hand, the fusion cross sections are enhanced at energies Ecm/VB < 1.4, Ecm/VB < 1.2 and Ecm/VB < 0.8 for the light, medium and heavy target, respectively. The enhancement decreases as the target mass increases. Above the indicated respective energies, these couplings suppress the fusion cross sections. We also compared the breakup and fusion cross sections, and found that below the barrier, the breakup cross sections are more dominant regardless of whether continuum–continuum couplings are included.

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.