F. A . Souza, C. Beck, N. Carlin, N. Keeley, R. Liguori Neto, M. M. de Moura, M. G. Munhoz, M. G. Del Santo, A. A. P. Suaide, E. M. Szanto, A. Szanto de Toledo
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 breakup was observed through the difference between the experimental sequential breakup cross section and the CDCC prediction for the non-capture breakup cross section.
Differential cross sections for deuteron breakup $^{1}H(d, pp)n$ reaction were measured for a large set of 243 geometrical configurations at the beam energy of 80 MeV/nucleon. The cross section data are normalized by the luminosity factor obtained on the basis of simultaneous measurement of elastic scattering channel and the existing cross section data for this process. The results are compared to the theoretical calculations modeling nuclear interaction with and without taking into account the three-nucleon force (3NF) and Coulomb interaction. In the validated region of the phase space both t…
In this work, we reexamine the extension of the CDCC formalism to include target excitation and apply it to a variety of reactions to study the effect of breakup on inelastic cross sections. We use a transformed oscillator basis to discretize the continuum of the projectiles in the different reactions and use the extended CDCC method developed in this work to solve the resulting coupled differential equations. A new code has been developed to perform the calculations. Reactions 58Ni(d, d) 58Ni*, 24Mg(d, d) 24Mg* , 144Sm( 6Li, 6Li) 144Sm* and 9Be( 6Li, 6Li) 9Be* are studied. Satisfactory agreem…
New experimental results for the elastic scattering of 6He on 64Zn at incident energies of 15.0 and 18.0 MeV and 4He at 17.5 MeV along with results already published at 10.0 and 13.6 MeV, are presented. Elastic and alpha experimental cross sections are compared with coupled-reaction-channel, continuum-discretized coupledchannel, and DWBA inclusive-breakup models. The large yield of alpha particles observed at all measured energies can be explained by considering a nonelastic breakup mechanism.
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 + 208…
Previous studies of $(d,p)$ reactions in three-body (proton, neutron, nuclear core) systems revealed a nontrivial effect of the core excitation: the transfer cross section cannot be factorized into the spectroscopic factor and the single-particle cross section obtained neglecting the core excitation. This observable, up to a kinematic factor, is the angular distribution of the core nucleus in the $(p,d)$ reaction. The study of the core excitation effect for the most closely related observable in the $(p,pn)$ three-body breakup, i.e., the core angular distribution, is aimed in the present work.…
$^{1}S_{0}$ \textit{nn}-scattering length has been measured in the \textit{nd}-breakup reaction at 60 MeV. The experiment was performed in the final state interaction geometry with registration of all three secondary particles. The scattering length $a_{nn} = -16.3 \pm 0.5$~fm was obtained from a comparison of the experimental dependence of the \textit{nd}-breakup yield on the relative energy of \textit{nn}-pair with the simulation results. An analysis of this value of scattering length together with the data obtained in other experiments on \textit{nd}- and \textit{dd}-breakup confirms the hy…
The 9Be(28Mg,27Na) one-proton removal reaction with a large proton separation energy of Sp(28Mg)=16.79 MeV is studied at intermediate beam energy. Coincidences of the bound 27Na residues with protons and other light charged particles are measured. These data are analyzed to determine the percentage contributions to the proton removal cross section from the elastic and inelastic nucleon removal mechanisms. These deduced contributions are compared with the eikonal reaction model predictions and with the previously measured data for reactions involving the re- moval of more weakly-bound protons f…
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…
Exact four-body equations of Alt, Grassberger and Sandhas are solved for neutron-${}^3\mathrm{He}$ and proton-${}^3\mathrm{H}$ scattering in the energy regime above the four-nucleon breakup threshold. Cross sections and spin observables for elastic, transfer, charge-exchange, and breakup reactions are calculated using realistic nucleon-nucleon interaction models, including the one with effective many-nucleon forces due to explicit $Δ$-isobar excitation. The experimental data are described reasonably well with only few exceptions such as vector analyzing powers.
Nucleon transfer reactions in deuteron-deuteron collisions at energies above the three- and four-body breakup threshold are described using exact four-body equations for transition operators that are solved in the momentum-space framework. Differential cross sections, analyzing powers, polarizations, and spin transfer coefficients are obtained using realistic two-nucleon potentials and including the Coulomb repulsion between protons. Overall good agreement between predictions and experimental data is found. Most remarkable discrepancies are seen around the minima of the differential cross sect…
The astrophysical factor of $^8$B($p$,$γ$)$^9$C at zero energy, $S_{18}(0)$, is determined by a three-body coupled-channels analysis of the transfer reaction $^{8}$B($d$,$n$)$^{9}$C at 14.4 MeV/nucleon. Effects of the breakup channels of $d$ and $^9$C are investigated with the continuum-discretized coupled-channels method. It is found that, in the initial and final channels, respectively, the transfer process through the breakup states of $d$ and $^9$C, its interference with that through their ground states in particular, gives a large increase in the transfer cross section. The finite-range e…
Complete fusion cross sections in collisions of light, weakly bound nuclei and high Z targets show above-barrier suppression of complete fusion. This has been interpreted as resulting from breakup of the weakly bound nucleus prior to reaching the fusion barrier, reducing the probability of complete fusion. This paper investigates how these conclusions are affected by lifetimes of the resonant states that are populated prior to breakup. If the mean life of a populated resonance is much longer than the fusion timescale, then its breakup cannot suppress complete fusion. For short-lived resonances…
We extend our previous calculation of the breakup of 11Be using Halo Effective Field Theory and the Dynamical Eikonal Approximation to include an effective 10Be-n-target force. The force is constructed to account for the virtual excitation of 10Be to its low-lying 2+ excited state. In the case of breakup on a 12C target this improves the description of the neutron-energy and angular spectra, especially in the vicinity of the 11Be 5/2+ state. By fine-tuning the range parameters of the three-body force, a reasonable description of data in the region of the 3/2+ 11Be state can also be obtained. T…
The $^9$C nucleus and related capture reaction, ${^8\mathrm{B}}(p,γ){^9\mathrm{C}}$, have been intensively studied with an astrophysical interest. Due to the weakly-bound nature of $^9$C, its structure is likely to be described as the three-body (${^7\mathrm{Be}}+p+p$). Its continuum structure is also important to describe reaction processes of $^9$C, with which the reaction rate of the ${^8\mathrm{B}}(p,γ){^9\mathrm{C}}$ process have been extracted indirectly. We perform three-body calculations on $^9$C and discuss properties of its ground and low-lying states via breakup reactions. We employ…
The two-body core+$2n$ cluster structure was implemented to describe the two-neutron halo nucleus $^{\mathrm{14}}\mathrm{Be}$, where the core$^{\mathrm{12}}\mathrm{Be}$ was assumed inert and at ground state and the dineutron was assumed at pure $2S_0$ state. Based on such a structure the three-body continuum-discretized coupled-channel (CDCC) calculation was successfully used to deal with the $^{\mathrm{14}}\mathrm{Be}$ breakup reactions of $^{\mathrm{14}}\mathrm{Be}+^{\mathrm{12}}\mathrm{C}$ at 68~MeV/nucleon and $^{\mathrm{14}}\mathrm{Be}+ $Pb at 35~MeV/nucleon.Consequently, we modeled the k…
A kinematically complete measurement of the four-body breakup reaction d+2H-->2ps+2ns --> p +p +n +n has been performed at 15 MeV deuteron beam of the SINP MSU. The two protons and neutron were detected at angles close to those of emission of 2ps and 2ns systems. The energy of singlet dineutron state was determined by comparing experimental TOF spectrum of breakup neutrons with simulated spectra depending on this energy. A low value Enn = 0.076 +/- 0.006 keV obtained by fitting procedure apparently indicates an effective enhancement of nn-interaction in the intermediate state of studied reacti…
Transfer/Breakup Channel Couplings in Sub-barrier Fusion Reactions
近年来，随着放射性离子束的出现，人们对库仑势垒附近重离子核反应的研究又重新引起了人们的兴趣。非弹性和传输通道耦合在稳定重离子引起的聚变反应中的作用可以重新考虑。本文首先讨论了用标准耦合道计算方法对最近的实验熔合截面的详细分析。以32 S +90，96 Zr为基准反应，分析了库仑位垒下聚变过程中的多中子转移效应。通过NTFus程序计算，包括中子转移通道的耦合，根据Zagrebaev半经典模型，32 S +96 Zr的熔合截面的增强在亚势垒能量下被很好地再现。对40 Ca +90 Zr和40 Ca +96 Zr的熔合激发函数也发现了类似的效应，同时还发现，在弹性散射和弱束缚稳定射弹引起的熔合过程中，破碎耦合也是关键的.在这项工作的第二部分中，全耦合通道计算的聚变激发函数进行分裂耦合的中子更丰富的反应和更弱的约束射弹。我们清楚地证明了连续离散耦合道计算能够再现来自6Li+59 Co中的分裂耦合的聚变增强。
The formation of continuum neutron distribution in $^7$Li(p,n) has been identified as due to the coupling of the $^7$Be breakup levels to the final state of the reaction. The continuum neutron spectra produced by $^7$Li(p,n) reaction has been estimated by measuring the double differential cross sections for continuum and resonant breakup of $^7$Be, through $^7$Li(p,n)$^7$Be$^*$ reaction at 21 MeV of proton energy. The breakup contributions from continuum and $5/2^-$, $7/2^-$ states of $^7$Be have been identified. The measured double differential cross sections have been reproduced through CDCC…
The study of exotic nuclear structures, such as halo nuclei, is usually performed through nuclear reactions. An accurate reaction model coupled to a realistic description of the projectile is needed to correctly interpret experimental data. In this contribution, we briefly summarise the assumptions made within the modelling of reactions involving halo nuclei. We describe briefly the Continuum-Discretised Coupled Channel method (CDCC) and the Dynamical Eikonal Approximation (DEA) in particular and present a comparison between them for the breakup of 15C on Pb at 68AMeV. We show the problem face…
The momentum distribution of $^{11}$Be fragments produced by the breakup of $^{12}$Be interacting with a proton target at 700.5 MeV/$u$ energy has been measured at GSI Darmstadt. To obtain the structure information on the anomaly of the $N=8$ neutron shell, the momentum distribution of $^{11}$Be fragments from the one-neutron knockout $^{12}$Be(p,pn) reaction, measured in inverse kinematics, has been analysed in the distorted wave impulse approximation (DWIA) based on a quasi-free scattering scenario. The DWIA analysis shows a surprisingly strong contribution of the neutron $0d_{5/2}$ orbital …
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…
We present an account of the current status of the theoretical treatment of inclusive $(d,p)$ reactions in the breakup-fusion formalism, pointing to some applications and making the connection with current experimental capabilities. Three independent implementations of the reaction formalism have been recently developed, making use of different numerical strategies. The codes also originally relied on two different but equivalent representations, namely the prior (Udagawa-Tamura, UT) and the post (Ichimura-Austern-Vincent, IAV) representations. The different implementations have been benchmark…
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 …
The effect of core excitations in transfer reactions of the form A(d, p)B has been found to affect significantly the calculated cross sections and to depend strongly and non-linearly on the incident deuteron energy in Faddeev/AGS calculations. Our goal is to investigate these effects within a coupled-channels formulation of the scattering problem which, in addition of being computationally less demanding than the Faddeev counterpart, may help shed some light into the physical interpretation of the cited effects. We use an extended version of the continuum-discretized coupled-channels (CDCC) me…
We develop a model to treat the inclusive non-elastic break up reactions involving weakly bound three-cluster nuclei. Borromean, two-nucleon, halo nuclei are candidates of unstable three-fragments projectiles. The model is based on the theory of inclusive breakup reactions commonly employed in the treatment of incomplete fusion and surrogate method. The theory was developed in the 80's by Ichimura, Autern and Vincent (IAV) [Phys. Rev. C 32, 431 (1985)] \cite{IAV1985}, Udagawa and Tamura (UT)[Phys. Rev. C 24, 1348 (1981)], \cite{UT1981} and Hussein and McVoy (HM)[Nucl. Phys. A 445, 124 (1985)],…
Background: Nuclear transfer reactions are a useful tool to study the structure of a nucleus. For reactions involving weekly bound nuclei, breakup effects can play significant role and theoretical calculations can be computational expensive in such cases. Purpose: To utilize the Lagrange-mesh and R-matrix methods for nuclear transfer reactions. Methods: We use the adiabatic distorted wave approximation (ADWA) method which can approximately treats the breakup effects in a simpler manner. In our approach, we apply the R-matrix method combining it with the Lagrange-mesh method, which is known to …
