The eikonal description of breakup reactions diverges because of the Coulomb interaction between the projectile and the target. This divergence is due to the adiabatic, or sudden, approximation usually made, which is incompatible with the infinite range of the Coulomb interaction. A correction for this divergence is analysed by comparison with the Dynamical Eikonal Approximation, which is derived without the adiabatic approximation. The correction consists in replacing the first-order term of the eikonal Coulomb phase by the first-order of the perturbation theory. This allows taking into account both nuclear and Coulomb interactions on the same footing within the computationally efficient eikonal model. Excellent results are found for the dissociation of 11Be on lead at 69 MeV/nucleon. This Coulomb Corrected Eikonal approximation provides a competitive alternative to more elaborate reaction models for investigating breakup of three-body projectiles at intermediate and high energies.
We construct a microscopic optical potential including breakup effects for elastic scattering of weakly-binding projectiles within the Glauber model, in which a nucleon-nucleus potential is derived by the $g$-matrix folding model. The derived microscopic optical potential is referred to as the eikonal potential. For $d$ scattering, the calculation with the eikonal potential reasonably reproduces the result with an exact calculation estimated by the continuum-discretized coupled-channels method. As the properties of the eikonal potential, the inaccuracy of the eikonal approximation used in the …
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 …
Background: Breakup reactions are often used to probe the nuclear structure of halo nuclei. The eikonal model diverges for Coulomb breakup since it relies on the adiabatic approximation. To correct this weakness, a Coulomb-corrected eikonal method (CCE) using the Coulomb first-order-perturbation approximation was developed. Purpose: Since the CCE mixes two reaction models and treats the Coulomb and nuclear interactions on different footings, we study here an alternative approach. We develop a simplification to the dynamical eikonal approximation (S-DEA) which has a similar numerical cost as th…
In this paper we discuss the evolution of breakup models from fully quantum mechanical, such as the Ichimura-Austern-Vincent model to semiclassical, to eikonal approximations following the insight on the mechanism first proposed by Hussein and McVoy (HM) for the presently called stripping term. In particular we concentrate on, and stress that, the correct implementation of a quantum mechanical model of breakup requires the use of energy dependent interactions and the energy averaging procedure is a key point to understand the difference among models. On the other hand using fixed energy potent…
We analyze the breakup of the one-neutron halo nucleus $^{11}$Be measured at 520 MeV/nucleon at GSI on Pb and C targets within an eikonal description of the reaction including a proper treatment of special relativity. The Coulomb term of the projectile-target interaction is corrected at first order, while its nuclear part is described at the optical limit approximation. Excellent agreement with the data is obtained using a description of $^{11}$Be, which fits the breakup data of RIKEN. This solves the apparent discrepancy between the $dB({\rm E1})/dE$ estimations from GSI and RIKEN for this nu…
A new method for calculating the Coulomb breakup of unstable neutron-rich isotopes at high energies is presented. The calculations employ the eikonal approximation and use a new Coulomb dynamical polarization potential (CDPP), calculated by solving the Schrödinger equation for the entire motion of the exotic projectile as a two-body cluster structure using the adiabatic approximation and incorporating excitations to the continuum. Calculations for some exotic isotopes are compared with Coulomb dissociation cross section data and found to be in good agreement.
In 1985, Hussein and McVoy [Nuc. Phys. A445 (1985) 124] elucidated a formula for the evaluation of the nonelastic breakup ("stripping") contribution in inclusive breakup reactions. The formula, based on the spectator core model, acquires a particularly simple and appealing form in the eikonal limit, to the extent that it has become the standard procedure to analyze single-nucleon knockout reactions at intermediate energies. In this contribution, a critical assessment of this formula is presented and its connection with other, noneikonal expressions discussed. Some calculations comparing the di…
破裂截面的Borromean核22 C确定通过使用四体程函模型，包括库仑修正。在超球坐标系下，在20 C + n + n三体模型中构造了束缚态和连续态。我们通过R-矩阵方法计算具有正确渐近行为的连续态。对于n+ n势，我们使用明尼苏达相互作用。由于21 C没有精确的实验数据，我们对20 C + n势定义了不同的参数集。这些参数组提供不同的散射长度，和预期的3/2+激发态的共振能量。然后我们分析了22 C基态能量和均方根半径，以及E1强度分布和破裂截面。E1强度分布在低能量下呈现增强。它的振幅与低结合能有关，而不是与三体共振有关。我们发现，在低能量的截面的形状是敏感的基态性质。此外，我们建议存在一个低能量的2+共振，这应该是可观察到的分裂实验。
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 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…
Aside from being a one-neutron halo nucleus, $^{15}$C is interesting because it is involved in reactions of relevance for several nucleosynthesis scenarios. The aim of this work is to analyze various reactions involving $^{15}$C, using a single structure model based on Halo EFT. To develop a Halo-EFT model of $^{15}$C at NLO, we first extract the ANC of its ground state by analyzing $^{14}$C(d,p)$^{15}$C transfer data at low energy. Using this Halo-EFT description, we study the $^{15}$C Coulomb breakup at high (605AMeV) and intermediate (68AMeV) energies using eikonal models with a consistent …
Light ion (A<5) breakup cross sections are important for studies of cosmic ray interactions in the inter-stellar medium or radiation protection considerations of energy deposition in tissue. Nucleon abrasion cross sections for heavy ion reactions are often calculated using the Glauber model in the large mass limit or with the Eikonal form of the optical potential model. Here we formulate an abrasion model for 4He nuclei fragmentation on hydrogen targets with a classical model for final state interactions. Comparisons to the heavy ion abrasion model are made. Calculations of energy dependent to…
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-r…
We present a description of the break-up of halo nuclei in peripheral nuclear reactions by coupling a model of the projectile motivated by Halo Effective Field Theory with a fully dynamical treatment of the reaction using the Dynamical Eikonal Approximation. Our description of the halo system reproduces its long-range properties, i.e., binding energy and asymptotic normalization coefficients of bound states and phase shifts of continuum states. As an application we consider the break-up of 11Be in collisions on Pb and C targets. Taking the input for our Halo-EFT-inspired description of 11Be fr…
Background: One-nucleon knockout reactions provide insightful information on the single-particle structure of nuclei. When applied to one-neutron halo nuclei, they are purely peripheral, suggesting that they could be properly modeled by describing the projectile within a Halo Effective Field Theory (Halo-EFT). Purpose: We reanalyze the one-neutron knockout measurements of $^{11}$Be and $^{15}$C-both one-neutron halo nuclei-on beryllium at about 60MeV/nucleon. We consider Halo-EFT descriptions of these nuclei which already provide excellent agreement with breakup and transfer data. Method: We i…
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 effe…
