We present a method for smoothing discrete breakup $S$-matrix elements calculated by the method of continuum-discretized coupled-channels (CDCC). This smoothing method makes it possible to apply CDCC to four-body breakup reactions. The reliability of the smoothing method is confirmed for two cases, $^{58}$Ni($d$, $p n$) at 80 MeV and the $E1$ transition of $^6$He. We apply CDCC with the smoothing method to $^6$He breakup reaction at 22.5 MeV. Multi-step breakup processes are found to be important.
We re-examine the deuteron elastic breakup cross sections on 12C and 10Be at low incident energies, for which a serious discrepancy between the continuum-discretized coupled-channels method (CDCC) and the Faddeev-Alt-Grassberger-Sandhas theory (FAGS) was pointed out. We show the closed-channels neglected in the preceding study affect significantly the breakup cross section calculated with CDCC, resulting in good agreement with the result of FAGS.
Background: In the continuum-discretized coupled-channel method, a breakup cross section (BUX) is obtained as an admixture of several components of different channels in multi-channel scattering. Purpose: Our goal is to propose an approximate way of decomposing the discretized BUX into components of each channel. This approximation is referred to as the "probability separation (P-separation)". Method: As an example, we consider $^{11}$Be scattering by using the three-body model with core excitation ($^{10}\mathrm{Be}+n+\mathrm{T}$, where T is a target). The structural part is constructed by th…
We apply the Lagrange-mesh method to discretize continuum states of weakly bound nuclei for continuum-discretized coupled-channel (CDCC) calculations of three-body breakup reactions. This discretization method is compared with the bin method, which is regarded as the standard continuum discretization method, for the $d$ and $^6$Li induced reactions. An improved Numerov algorithm is used to solve the coupled channels equations, which permits a fast integration of equations and a convenient treatment of the closed channels. A new CDCC model code named \emph{CDCC-R} is developed. In all cases, th…
A novel method to extract the $B(E1)$ strength of a weakly bound nucleus from experimental Coulomb dissociation data is proposed. The method makes use of continuum discretized coupled channels (CDCC) calculations, in which both nuclear and Coulomb forces are taken into account to all orders. This is a crucial advantage with respect to the standard procedure based on the Equivalent Photon Method (EPM) which does not properly take into account nuclear distortion, higher order coupling effects, or Coulomb-nuclear interference terms. The procedure is applied to the $^{11}$Be nucleus using two sets…
Breakup reactions are one of the favored probes to study loosely bound nuclei, particularly those in the limit of stability forming a halo. In order to interpret such breakup experiments, the continuum discretized coupled channel method is typically used. In this study, the first Bayesian analysis of a breakup reaction model is performed. We use a combination of statistical methods together with a three-body reaction model (the continuum discretized coupled channel method) to quantify the uncertainties on the breakup observables due to the parameters in the effective potential describing the l…
Three-body Coulomb breakup of 11Li in the complex scaling method
用复标度法研究了~（11）Li到~（9 Li +n+n）三体系统的库仑破碎强度。我们将跃迁强度分解为三体共振、两体"10 Li + n“和三体" 9 Li +n+ n”连续态的贡献。在计算结果中，我们没有发现11 Li中具有尖锐衰减宽度的偶极共振。两体和三体连续态都产生了低能量的破碎强度增强。三体连续态的增强与11 Li的晕结构有很强的联系。计算的破碎强度分布与MSU，RIKEN和GSI的实验数据进行了比较。
The Coulomb-breakup method to extract the cross section for neutron radiative capture at astrophysical energies is analyzed in detail. In particular, its sensitivity to the description of the neutron-core continuum is ascertained. We consider the case of 14C(n, $γ$)15C for which both the radiative capture at low energy and the Coulomb breakup of 15C into 14C+n on Pb at 68 MeV/nucleon have been measured with accuracy. We confirm the direct proportionality of the cross section for both reactions to the square of the asymptotic normalization constant of 15C observed by Summers and Nunes [Phys. Re…
We analyze the $^{16}{\rm C}+p$ and $^{16}{\rm C}+d$ reactions within the four- and five-body Continuum Discretized Coupled Channel (CDCC) method. The $^{16}$C nucleus is described by a $^{14}{\rm C}+n+n$ configuration in hyperspherical coordinates. This description reproduces fairly well several $^{16}$C low-lying states. First we analyze the $2^+\rightarrow 0^+$ $E2$ transition amplitude, which confirms that an effective charge must be introduced to reproduce the experimental value. Then, proton and deuteron elastic and inelastic scattering are investigated by including $^{16}$C pseudostates…
We investigate theoretically $Λ$ production spectra of $^3$He($π$, $K$) reactions at $p_π=$ 1.05--1.20 GeV/$c$ in the distorted-wave impulse approximation, using the continuum-discretized coupled-channel method. The production cross section of a $^3_Λ$H(1/2$^+$) ground state is also discussed.
The scattering of $^9$Be on $^{208}$Pb is addressed within a four-body Continuum-Discretized Coupled-Channels (CDCC) framework, considering a three-body $α+ α+ n$ projectile plus a structureless target. The projectile states are generated using the analytical Transformed Harmonic Oscillator (THO) basis in hyperspherical coordinates. Both the elastic and breakup channels are described on the same footing. We find a good agreement between our calculations and the experimental data at beam energies around and below the Coulomb barrier.
We investigate the elastic scattering of $^9$Be on $^{208}$Pb at beam energies above (50 MeV) and below (40 MeV) the Coulomb barrier. The reaction is described within a four-body framework using the Continuum-Discretized Coupled-Channels (CDCC) method. The $^9$Be projectile states are generated using the analytical Transformed Harmonic Oscillator (THO) basis in hyperspherical coordinates. Our calculations confirm the importance of continuum effects at low energies.
Four-body continuum-discretized coupled-channels calculations using a transformed harmonic oscillator basis
讨论了弱束缚三体系统与目标的散射问题。一个变换的谐振子基础是用来提供一个适当的离散和有限的基础处理的连续部分的频谱的弹丸。连续离散耦合通道框架用于散射计算。该方法适用于不同的反应，6 He +12 C在229.8 MeV，6 He +64 Zn在10和13.6 MeV，和6 He +208 Pb在22 MeV，由Borromean核6 He诱导。库仑和核与目标的相互作用都被考虑在内。
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.
The full quantum mechanical (QM) model of inclusive breakup of Ichimura-Austern-Vincent (IAV) is implemented in this paper to calculate breakup from heavy radioactive nuclei on a $^9$Be target at intermediate energies. So far it had been implemented and applied only to low energy reactions with light projectiles. The IAV model is successful in predicting absolute cross sections among other observables. In order to get insight on the content of the model in the case of the complicated heavy-ion reactions, results are compared with those of the semiclassical transfer to the continuum (TC) model.…
Breakup cross sections are determined for the Borromean nucleus 22C by using a four-body eikonal model, including Coulomb corrections. Bound and continuum states are constructed within a 20C + n + n three-body model in hyperspherical coordinates. We compute continuum states with the correct asymptotic behavior through the R-matrix method. For the n+ n potential, we use the Minnesota interaction. As there is no precise experimental information on 21C, we define different parameter sets for the 20C + n potentials. These parameter sets provide different scattering lengths, and resonance energies …
The Bardeen-Cooper-Schrieffer (BCS) formalism is extended by including the single-particle continuum in order to analyse the evolution of pairing in an isotopic chain from stability up to the drip line. We propose a continuum discretized generalized BCS based on single-particle pseudostates (PS). These PS are generated from the diagonalization of the single-particle Hamiltonian within a Transformed Harmonic Oscillator (THO) basis. The consistency of the results versus the size of the basis is studied. The method is applied to neutron rich Oxygen and Carbon isotopes and compared with similar pr…
The effect of core excitation in the elastic scattering and breakup of a two-body halo nucleus on a stable target nucleus is studied. The structure of the weakly-bound projectile is described in the weak-coupling limit, assuming a particle-rotor model. The eigenfunctions and the associated eigenvalues are obtained by diagonalizing this Hamiltonian in a square-integrable basis (pseudo-states). For the radial coordinate between the particle and the core, a transformed harmonic oscillator (THO) basis is used. For the reaction dynamics, an extension of the Continuum-Discretized Coupled-Channels (C…
Core-excitation effects in the scattering of two-body halo nuclei have been investigated in previous works. In particular, these effects have been found to affect in a significant way the breakup cross sections of neutron-halo nuclei with a deformed core. To account for these effects, appropriate extensions of the continuum-discretized coupled-channels (CDCC) method have been recently proposed. We aim to extend these studies to the case of breakup reactions measured under complete kinematics or semi-inclusive reactions in which only the angular or energy distribution of one of the outgoing fra…
