The production of $α$-particles in reactions using both the strongly and weakly bound projectiles at energies around the Coulomb barrier show several interesting features. To understand these, the role of various reaction mechanisms responsible for $α$-production, such as non-capture breakup, capture of only one of the fragments subsequent to projectile breakup and their contribution to reaction cross sections have been investigated. A systematic study of the $α$-particle production based on available data for various projectile target systems have been performed and a classification based on projectile type is obtained.
In this work we measured elastic and inelastic angular distributions of the weakly bound 9Be projectile on the 197Au target at several bombarding energies from 84% up to 140% of the Coulomb barrier. The elastic angular distributions were analyzed using a phenomenological Woods-Saxon potential and a double folding Sao Paulo potential and the energy dependence was extracted. Angular distributions from two inelastic peaks were compared with coupled channel calculations using reduced transition probabilities available in the literature. The energy dependence of the two interaction potential models…
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…
We study the behavior of the fusion, break-up, reaction and elastic scattering of different projectiles on $^{64}$Zn, at near and above barrier energies. We present fusion and elastic scattering data with the tightly bound $^{16}$O and the stable weakly bound $^{6}$Li, $^{7}$Li and $^{9}$Be projectiles. The data were analyzed by coupled channel calculations. The total fusion cross sections for these systems are not affected by the break-up process at energies above the barrier. The elastic (non-capture) break-up cross section is important at energies close and above the Coulomb barrier and inc…
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 …
A systematic analysis of the fusion cross sections around the Coulomb barrier energies with stable weakly bound ($^{6}$Li,$^{7}$Li,$^{9}$Be) and strongly bound $^{12}$C projectiles on various targets was performed by using neutron flow model and coupled channels approach. The analysis show that both the models are successful in explaining the near barrier fusion data. Further, it is also observed that the collective degrees of freedom as well as the neutron flow influence the near barrier fusion process involving weakly bound projectiles.
The virtual photon theory (VPT), which is based on first-order Coulomb dissociation restricted to the electric dipole ($E1$), has been successfully used to explain the breakup data for several cases. Our aim is to study the role of various higher-order processes that are ignored in the VPT, such as the nuclear breakup, interference between nuclear and Coulomb amplitudes, and multistep breakup processes mainly due to strong continuum-continuum couplings in the breakup of two-body projectiles on a heavy target at both intermediate and higher incident energies. For the purpose of numerical calcul…
The importance of the breakup channel in the vicinity of the Coulomb barrier (1<Ec.m./Vb<2) is investigated for the medium weight 6Li+59Co system. Three-body final-state analysis of light-particle coincident data was carried out to disentangle, for the first time, the breakup contributions from other competiting mechanisms. alpha-d angular correlations show incomplete fusion components as significant as that from breakup process. Their strong coupling to total fusion is discussed within a comparison with predictions of continuum discretized coupled-channel calculations.
The isospin effect and isoscaling behavior in projectile fragmentation have been systematically investigated by a modified statistical abrasion-ablation (SAA) model. The normalized peak differences and reduced isoscaling parameters are found to decrease with ($Z_{proj}-Z$)/$Z_{proj}$ or the excitation energy per nucleon and have no significant dependence on the size of reaction systems. Assuming a Fermi-gas behavior, the excitation energy dependence of the symmetry energy coefficients are tentatively extracted from $α$ and $β$ which looks consistent with the experimental data. It is pointed ou…
Probable projectile-target combinations for the synthesis of superheavy element $^{302}$120 have been studied taking Coulomb and proximity potential as the interaction barrier. The probabilities of compound nucleus formation, PCN for the projectile-target combinations found in the cold reaction valley of $^{302}$120 are estimated. At energies near and above the Coulomb barrier, we have calculated the capture, fusion and evaporation residue cross sections for the reactions of all the probable projectile-target combinations so as to predict the most promising projectile-target combinations for t…
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 discuss the role of deformation of the target nucleus in the fusion reaction of the $^{15}$C + $^{232}$Th system at energies around the Coulomb barrier, for which $^{15}$C is a well-known one-neutron halo nucleus. To this end, we construct the potential between $^{15}$C and $^{232}$Th with the double folding procedure, assuming that the projectile nucleus is composed of the core nucleus, $^{14}$C, and a valance neutron. By taking into account the halo nature of the projectile nucleus as well as the deformation of the target nucleus, we simultaneously reproduce the fusion cross sections for …
In many instances, single nucleon removal reactions from neutron-proton asymmetric projectile nuclei populate final states in the residual nuclei that are very weakly bound. Familiar examples include neutron removal reactions from neutron-rich $^{11}$Be and $^{12}$Be, the latter populating the well-known $1/2^+$ halo ground-state and $1/2^-$ excited-state of $^{11}$Be - both states less than 1 MeV from the first neutron-decay threshold. Numerous additional examples arise in reactions of asymmetric $p$- and $sd$-shell nuclei. The importance of this weak residue binding upon calculated single-nu…
The role of the breakup process and one neutron stripping on the near barrier fusion are investigated for the weakly bound projectile $^{9}$Be on $^{28}$Si, $^{89}$Y, $^{124}$Sn, $^{144}$Sm and $^{208}$Pb targets. Continuum-discretized coupled channels (CDCC) calculations for the breakup with a $^{8}$Be + n model of the $^{9}$Be nucleus and coupled reactions channels (CRC) calculations for the one neutron stripping to several single particle states in the target are performed for these systems. A good description of the experimental fusion cross sections above the Coulomb barrier is obtained f…
\item[Purpose] We suppose that the IYR(m) depends on the neutron-skin thickness ($δ_{np}$) of the projectile, and check the idea of whether the neutron-skin thickness effects can fully explain the systematic dependence of the IYR(m). \item[Methods] A modified statistical abrasion-ablation model is used to calculate the reactions induced by projectiles of three series. \item[Results] The IYR(m) shows a distribution of a linear part in the small-$x$ fragments, and a nonlinear part in the large-$x$ fragments. The linear part of IYR(m) is fitted. (1) In the calcium isotopic reactions, the IYR(m) d…
A large number of complete fusion excitation functions of reactions including the breakup channel were measured in recent decades, especially in the last few years. It allows us to investigate the systematic behavior of the breakup effects on the complete fusion cross sections. To this end, we perform a systematic study of the breakup effects on the complete fusion cross sections at energies above the Coulomb barrier. The reduced fusion functions F(x) are compared with the universal fusion functions which are used as a uniform standard reference. The complete fusion cross sections at energies …
Quasielastic excitation function measurement has been carried out for the $^{4}$He + $^{232}$Th system at $θ_{lab}$=160$^\circ$ with respect to the beam direction, to obtain a representation of the fusion barrier distribution. Using the present data along with previously measured barrier distribution results on $^{12}$C, $^{16}$O, and $^{19}$F + $^{232}$Th systems a systematic analysis has been carried out to investigate the role of target and/or projectile structures on fusion barrier distribution. It is observed that for $^{4}$He, $^{12}$C, and $^{16}$O + $^{232}$Th, reactions the couplings …
The fragment separator FRS has been for the first time used to measure the (n,p) and (p,n)-type isobaric charge-exchange cross sections of stable 112,124Sn isotopes accelerated at 1A GeV with an uncertainty of 3% and to separate quasi-elastic and inelastic components in the missing-energy spectra of the ejectiles. The inelastic contribution can be associated to the excitation of isobar Δ(1232) resonances and to the pion emission in s-wave, both in the target and projectile nuclei, while the quasi-elastic contribution is associated to the nuclear spin-isospin response of nucleon-hole excitation…
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 have measured production yields and longitudinal momentum distributions of projectile-like fragments in the reaction 129Xe + 27Al at an energy of Elab=790 AMeV. Production cross sections higher than expected from systematics were observed for nuclei in the neutron-deficient tails of the isotopic distributions. A comparison with previously measured data from the fragmentation of 136Xe ions shows that the production yields strongly depend on the neutron excess of the projectile with respect to the line of beta-stability. The momentum distributions exhibit a dependence on the fragment neutron-…
Hanbury Brown-Twiss (HBT) results of the neutron-proton correlation function have been systematically investigated for a series nuclear reactions with light projectiles with help of Isospin-Dependent Quantum Molecular Dynamics model. The relationship between the binding energy per nucleon of the projectiles and the strength of the neutron-proton HBT at small relative momentum has been obtained. Results show that neutron-proton HBT results are sensitive to the binding energy per nucleon.
Electromagnetic fission cross sections for the reactions U + (Be, C, Al, Cu, In, Au, U) at E/A = 0.6 and 1.0 GeV are compared to theoretical calculations using recently proposed quantum-mechanical equivalent-photon spectra. In contrast to semi-classical calculations, systematically lower cross sections are obtained that cannot reproduce the experimental results. Furthermore, we point out that the study of electromagnetic fission cross sections or electromagnetic 1-neutron removal cross sections alone cannot provide unambiguous information on the excitation of the double giant dipole resonance.
We use an improved version of the semiclassical method described in Refs. [1,2,3] to evaluate fusion cross sections in collisions of weakly bound nuclei. This version takes into account the static effects of the low breakup threshold, uses better bin states in the discretization of the continuum and avoids the excitation of closed channels. The population of these channels is a consequence of the violation of energy conservation, which is inherent in the semiclassical method. The method is employed to evaluate complete fusion and total fusion cross section in collisions of the weakly bound 6,7…
The aim of the present study is to make for the first time in the literature a systematic and quantitative assessment of the evaluation of the imaginary part of the optical potential calculated within the folding model and its consequences on the localization of surface reactions. Comparing theoretical and experimental reaction cross sections, for some light projectiles on a $^9$Be target, it has recently been shown that a single-folded s.f. (light-) nucleus-$^9$Be imaginary optical potential is more accurate than a double-folded d.f. optical potential. Within the eikonal formalism for the cro…
Background: Large $α$ yields have been reported over the years in reactions with $^{6}$Li and $^{7}$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 $α$ inclusive breakup cross sections, pointing toward the dominance of non-elastic breakup (NEB) mechanisms. Purpose: We aim to provide a systematic study of the $α$ inclusive cross sections observed in nuclear reactions induced by $^{6}$Li projectiles. In addition to estimatin…
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. …
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…
The elastic scattering of the radioactive halo nucleus 6He on 27Al target was measured at four energies close to the Coulomb barrier using the RIBRAS (Radioactive Ion Beams in Brazil) facility. The Sao Paulo Potential(SPP) was used and its diffuseness and imaginary strength were adjusted to fit the elastic scattering angular distributions. Reaction cross-sections were extracted from the optical model fits. The reduced reaction cross-sections of 6He on 27Al are similar to those for stable, weakly bound projectiles as {6,7}Li, 9Be and larger than stable, tightly bound projectile as 16O on 27Al.
There is a considerable interest in understanding the dependence of one-nucleon removal cross sections on the asymmetry of the neutron $S_n$ and proton $S_p$ separation energies, following a large amount of experimental data and theoretical analyses in a framework of sudden and eikonal approximations of the reaction dynamics. These theoretical calculations involve both the single-particle cross section and the shell-model description of the projectile initial state and final states of the reaction residues. The configuration mixing in shell-model description of nuclear states depends on the pr…
The total reaction cross section $σ_{\rm{reac}}$ is a valuable measure for the prediction of $α$-induced reaction cross sections within the statistical model and for the comparison of scattering of tightly bound projectiles to weakly bound and exotic projectiles. Here we provide the total reaction cross sections $σ_{\rm{reac}}$ derived from our previously published angular distributions of $α$-elastic scattering on $^{89}$Y, $^{92}$Mo, $^{112,124}$Sn, and $^{144}$Sm at energies around the Coulomb barrier.
Background: Models describing nuclear fragmentation and fragmentation-fission deliver important input for planning nuclear physics experiments and future radioactive ion beam facilities. These models are usually benchmarked against data from stable beam experiments. In the future, two-step fragmentation reactions with exotic nuclei as stepping stones are a promising tool to reach the most neutron-rich nuclei, creating a need for models to describe also these reactions. Purpose: We want to extend the presently available data on fragmentation reactions towards the light exotic region on the nucl…
With the recent availability of state-of-the-art radioactive ion beams, there has been a renew interest in the investigation of nuclear reactions with heavy ions near the Coulomb barrier. The role of inelastic and transfer channel couplings in fusion reactions induced by stable heavy ions can be revisited. Detailed Analysis of recent experimental fusion cross sections by using standard coupled-channel calculations is first discussed. Multi-neutron transfer effects are introduced in the fusion process below the Coulomb barrier by analyzing 32S+90,96Zr as benchmark reactions. The enhancement of …
Collective-flow signatures of bubble nuclei in intermediate-energy projectile fragmentation reactions
Henan Normal University（河南师范大学）；Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院）；Institute of Nuclear Science and Technology, Henan Academy of Sciences（河南省科学院核科学技术的研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（国家自然科学基金委与复旦大学理论物理上海研究中心）；Shanghai Institute of Applied Physics, Chinese Academy of Sciences（中国科学院上海应用物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
The influence on the fusion process of coupling to collective degrees of freedom has been explored. The significant enhancement of the fusion cross section at sub-barrier energies was compared to predictions of one-dimensional barrier penetration models. This was understood in terms of the dynamical processes arising from strong couplings to collective inelastic excitations of the target and projectile. However, in the case of reactions where at least one of the colliding nuclei has a sufficiently low binding energy, for breakup to become an important process, conflicting model predictions and…
There is now a large and increasing body of experimental data and theoretical analyses for reactions that remove a single nucleon from an intermediate-energy beam of neutron- or proton-rich nuclei. In each such measurement, one obtains the inclusive cross section for the population of all bound final states of the mass A-1 reaction residue. These data, from different regions of the nuclear chart, and that involve weakly- and strongly-bound nucleons, are compared with theoretical expectations. These calculations include an approximate treatment of the reaction dynamics and shell-model descripti…
A systematic study of isospin effects in the breakup of projectile spectators at relativistic energies has been performed with the ALADiN spectrometer at the GSI laboratory (Darmstadt). Four different projectiles 197Au, 124La, 124Sn and 107Sn, all with an incident energy of 600 AMeV, have been used, thus allowing a study of various combinations of masses and N/Z ratios in the entrance channel. The measurement of the momentum vector and of the charge of all projectile fragments with Z>1 entering the acceptance of the ALADiN magnet has been performed with the high efficiency and resolution achie…
We use the breakup absorption model to simultaneously describe the measured cross-sections of the Complete fusion (CF), Incomplete fusion (ICF), and Total fusion (TF) in nuclear reactions induced by weakly bound nuclei $^{6,7}$Li on $^{209}$Bi and $^{198}$Pt targets. The absorption cross-sections are calculated using the Continuum Discretized Coupled Channels (CDCC) method with different choices of short range imaginary potentials to get the ICF, CF and TF cross-sections. It is observed that the cross-sections for deuteron-ICF/deuteron-capture are of similar magnitude as the $α$-ICF/$α$-captur…
The body of experimental measurements of intermediate-energy reactions that remove a single nucleon from a secondary beam of neutron- or proton-rich nuclei continues to grow. These data have been analysed consistently using an approximate, eikonal-model treatment of the reaction dynamics combined with appropriate shell-model descriptions of the projectile initial state, the bound final states spectrum of the reaction residue and single-particle removal strengths computed from their wave-function overlaps. The systematics of the ratio $R_s$ of the measured inclusive cross-section to all bound f…
A systematic study of isotopic effects in the break-up of projectile spectators at relativistic energies has been performed at the GSI laboratory with the ALADiN spectrometer coupled to the LAND neutron detector. Besides a primary beam of 124Sn, also secondary beams of 124La and 107Sn produced at the FRS fragment separator have been used in order to extend the range of isotopic compositions. The gross properties of projectile fragmentation are very similar for all the studied systems but specific isotopic effects have been observed in both neutron and charged particle production. The breakup t…
The relative importance of neutron transfer and breakup process in reaction around Coulomb barrier energies have been studied for the $^{7}$Li+$^{124}$Sn system. Coupled channel calculations have been performed to understand the one neutron stripping and pickup cross sections along with the breakup in the $^{7}$Li+$^{124}$Sn system. The systematics of one and two neutron striping and pickup cross sections with $^7$Li projectile on several targets show an approximate universal behaviour that have been explained by a simple model. Complete reaction mechanism have been studied by comparing the re…
New experimental data from the scattering of 6He+208Pb at energies around and below the Coulomb barrier are presented. The yield of breakup products coming from projectile fragmentation is dominated by a strong group of $α$ particles. The energy and angular distributions of this group have been analyzed and compared with theoretical calculations. This analysis indicates that the $α$ particles emitted at backward angles in this reaction are mainly due to two-neutron transfer to weakly bound states of the final nucleus.
We investigate the isospin transport with 40,48 Ca+ 40,48 Ca reactions at 35 MeV/nucleon, measured with the coupling of the VAMOS high acceptance spectrometer and the INDRA charged particle multidetector. Using the quasi-projectile remnant measured with VAMOS and carefully selected light-charged-particles measured in coincidence with INDRA, a reconstruction method is applied to estimate the excited quasi-projectile (QP) on an event-by-event basis. The isospin diffusion is investigated using the isospin transport ratio with the asymmetry $δ$ = (N -- Z)/A of the projectile as an isospin-sensitiv…
Multi-fragment decays of 129Xe, 197Au, and 238U projectiles in collisions with Be, C, Al, Cu, In, Au, and U targets at energies between E/A = 400 MeV and 1000 MeV have been studied with the ALADIN forward-spectrometer at SIS. By adding an array of 84 Si-CsI(Tl) telescopes the solid-angle coverage of the setup was extended to θ_lab = 16 degree. This permitted the complete detection of fragments from the projectile-spectator source. The dominant feature of the systematic set of data is the Z_bound universality that is obeyed by the fragment multiplicities and correlations. These observables are …
The influence on the fusion process of coupling to collective degrees of freedom has been explored. The significant enhancement of he fusion cross setion at sub-barrier energies was understood in terms of the dynamical processes arising from strong couplings to collective inelastic excitations of the target and projectile. However, in the case of reactions where breakup becomes an important process, conflicing model predictions and experimental results have been reported in the literature. Excitation functions for sub- and near-barrier total (complete + incomplete) fusion cross sections have b…
Several investigations on the complete-incomplete fusion (CF-ICF) dynamics of $α$-cluster well-bound nuclei has been contemplated above the Coulomb barrier ($\sim$ 4-7 MeV/nucleon) in recent years. It is therefore expected to observe significant ICF over CF in the reactions induced by a weakly bound $α$-cluster nucleus at slightly above the barrier. In order to investigate CF-ICF in the loosely bound system, $^{\text{7}}$Li beam was bombarded on the $^{\text{nat}}$Mo foils, separated by the aluminium (Al) catcher foils alternatively, within $\sim$ 3-6.5 MeV/nucleon. Evaporation residues produc…
The reactions induced by the weakly bound 6Li projectile interacting with the intermediate mass target 59Co were investigated. Light charged particles singles and $α$-$d$ coincidence measurements were performed at the near barrier energies E_lab = 17.4, 21.5, 25.5 and 29.6 MeV. The main contributions of the different competing mechanisms are discussed. A statistical model analysis, Continuum-Discretized Coupled-Channels calculations and two-body kinematics were used as tools to provide information to disentangle the main components of these mechanisms. A significant contribution of the direct …
A systematic study of isotopic effects in the break-up of projectile spectators at relativistic energies has been performed with the ALADiN spectrometer at the GSI laboratory. Searching for signals of criticality in the fragment production we have applied the model independent universal fluctuations theory already proposed to track criticality signals in multifragmentation to our data. The fluctuation of the largest fragment charge and of the asymmetry of the two and three largest fragments and their bimodal distribution have also been analysed.
We show a systematic experimental study based on INDRA data of the stopping power in central symmetric nuclear reactions. Total mass of the systems goes from 80 to 400 nucleons while the incident energy range is from 12 AMeV to 100 AMeV. The role of isospin diffusion at 32 and 45 MeV/nucleon with 124,136Xe projectiles on 112,124Sn targets performed at GANIL is also discussed. Results suggest a strong memory of the entrance channel above 20 AMeV/A (nuclear transparency) and, as such, constitute valuable tests of the microscopic transport models.
