We apply the Gamow shell model to study $^{25-31}$F isotopes. As both inter-nucleon correlations and continuum coupling are properly treated therein, the structure shape of $^{31}$F at large distance can be analyzed precisely. For this, one-nucleon densities, root-mean square radii and correlation densities are calculated in neutron-rich fluorine isotopes. It is then suggested that $^{31}$F exhibits a two-neutron halo structure, built from both continuum coupling and nucleon-nucleon correlations.
We discuss the difference between neutron halos and neutron skins matching to our usual thinking of a skin as being connected to a body whereas a halo is, in some sense, disconnected from the body. We emphasize that the existence of one or more neutrons behaving incoherently with respect to the rest of the nucleons in a nucleus can match the picture of a neutron halo.
Some one-neutron halo nuclei can emit a proton in a beta decay of the halo neutron. The branching ratio towards this rare decay mode is calculated within a two-body potential model of the initial core+neutron bound state and final core+proton scattering states. The decay probability per second is evaluated for the $^{11}$Be, $^{19}$C and $^{31}$Ne one-neutron halo nuclei. It is very sensitive to the neutron separation energy.
We set up a formalism to calculate the charge form factors of two-neutron halo nuclei with S-wave neutron-core interactions in the framework of the halo effective field theory. The method is applied to some known and suspected halo nuclei. In particular, we calculate the form factors and charge radii relative to the core to leading order in the halo EFT and compare to experiments where they are available. Moreover, we investigate the general dependence of the charge radius on the core mass and the one- and two-neutron separation energies.
We perform a detailed analysis for the structure of 31F, which is a candidate of the halo nucleus. We calculate the radius and reaction cross-section using a three-body model of 29F+n+n and discuss how the competition between the neutron-pairing and the single-particle energy induces structural changes of 31F. The present analysis further clarifies a new aspect of the anti-halo efect that suppresses the halo structure.
Using halo effective field theory (EFT), an expansion in $R_{core}/R_{halo}$, where $R_{core}$ is the radius of the core and $R_{halo}$ the radius of the halo nucleus, we calculate the charge and neutron form factors of the two-neutron halo nuclei $^{11}$Li, $^{14}$Be, and $^{22}$C to next-to-leading-order (NLO) by treating them as an effective three-body system. From the form factors we extract the point charge and point matter radii, inter-neutron distance, and neutron opening angle. Agreement is found with existing experimental extractions. Results are given for the point charge and point m…
The nucleon density distributions and the thickness of pure neutron matter in Ca isotopes were systematically studied using the Skyrme-Hartree-Fock model (SHF) from the $β$-stability line to the neutron drip-line. The pure neutron matter, related with the neutron skin or halo, was shown to depend not only on the Fermi levels of the neutrons but also on the orbital angular momentum of the valence neutrons. New definitions for the thickness of pure neutron matter are proposed.
The electromagnetic form factors for single neutron halo nuclei Be-11, C-15 and C-19 are calculated. The calculations are performed in halo effective field theory (EFT) where the halo nuclei are approximated as made of a single neutron and a core. The form factors depend on the single neutron separation energy, the s-wave neutron-core scattering effective range and a two-body current. The EFT expressions are presented to leading order for C-15 and next-to-leading order for Be-11 and C-19.
The connection between the neutron halo observed in light neutron rich nuclei and the neutron radiative capture process is outlined. We show how nuclear structure information such as spectroscopic factors and external components of the radial wave function of loosely bound states can be derived from the neutron capture cross section. The link between the direct radiative capture and the Coulomb dissociation process is elucidated.
Although the neutron (n) does not carry a total electric charge, its charge and magnetization distributions represented in momentum space by the electromagnetic form factors, $F_1^{(n)} (q^2)$ and $F_2^{(n)} (q^2)$, lead to an electromagnetic potential of the neutron. Using this fact, we calculate the electromagnetic corrections to the binding energy, $B_d$, of the deuteron and a one neutron halo nucleus (11Be), by evaluating the neutron-proton and the neutron-charged core (10Be) potential, respectively. The correction to $B_d$ (~9 keV) is comparable to that arising due to the inclusion of the…
The even-Z odd-N neutron-halo nuclei, which are the possible lightest neutron-halo nuclei heavier than $^{37}$Mg, are explored by studying the shell-structure unique in weakly-bound neutrons for spherical or deformed shape. It is pointed out that due to the narrowed N=50 spherical energy-gap and a few resulting close-lying neutron one-particle levels, 1g$_{9/2}$, 3s$_{1/2}$, and 2d$_{5/2}$, for spherical shape, nuclei with some weakly-bound neutrons filling in those levels may be deformed and have a good chance to show deformed s-wave halo. Promising candidates are $^{71}_{24}$Cr$_{47}$, $^{73…
Fusion reactions of neutron-halo nuclei are investigated theoretically with a three-body model. The time-dependent wave-packet method is used to solve the three-body Schrodinger equation. The halo neutron behaves as a spectator during the Coulomb dissociation process of the projectile. The fusion cross sections of 11Be-209Bi and 6He-238U are calculated and are compared with measurements. Our calculation indicates that the fusion cross section is slightly hindered by the presence of weakly bound neutrons.
The proton and neutron density distributions, one- and two-neutron separation energies and radii of nuclei for which neutron halos are experimentally observed, are calculated using the self-consistent Hartree-Fock-Bogoliubov method with the effective interaction of Gogny. Halo factors are evaluated assuming hydrogen-like antiproton wave functions. The factors agree well with experimental data. They are close to those obtained with Skyrme forces and with the relativistic mean field approach.
Giant neutron halos in medium-heavy nuclei are studied in the framework of the Hartree-Fock-Bogoliubov (HFB) approach with Skyrme interactions. The appearance of such structures depends sensitively on the effective interaction adopted. This is illustrated by comparing the predictions of SLy4 and SkI4 in the Ca and Zr isotopic chains. The former force gives no halo effect, the latter predicts a neutron halo in the Zr chain with A>122 due to the weakly bound orbitals 3p1/2 and 3p3/2. The structure of the halo is analyzed in terms of the occupation probabilities of these orbitals and their partia…
We consider the Parity Nonconserving (PNC) mixing in the ground state of exotic (halo) nuclei caused by the PNC weak interaction between outer neutron and nucleons within nuclear interior. For the nucleus $^{11}Be$ as an example of typical nucleus with neutron halo, we use analytical model for the external neutron wave functions to estimate the scale of the PNC mixing. The amplitude of the PNC mixing in halo state is found to be an order of magnitude bigger than that of typical PNC mixing between the ``normal'' nuclear states in nearby nuclei. The enhanced PNC mixing in halo cloud is proportio…
Relativistic Hartree-Bogoliubov (RHB) theory in coordinate space is used to describe the chain of even-even Zirconium isotopes reaching from Zr116 to the drip line nucleus Zr140. Pairing correlations are taken into account by a density dependent force of zero range. For neutron numbers larger than the magic number N=82 a giant neutron halo outside the core of Zr122 is observed. It is formed by up to six neutrons.
We exploit the separation of scales in weakly-bound nuclei to compute E2 transitions and electric form factors in a Halo EFT framework. The relevant degrees of freedom are the core and the halo neutron. The EFT expansion is carried out in powers of $R_{core}/R_{halo}$, where $R_{core}$ and $R_{halo}$ denote the length scales of the core and halo, respectively. We include the strong $s$-wave and $d$-wave interactions by introducing dimer fields. The dimer propagators are regulated by employing the power divergence subtraction scheme and matched to the effective range expansion in the respective…
A dripline nucleus $^{22}$C is studied in a Borromean three-body model of $^{20}$C+$n$+$n$. The valence neutrons, interacting via a realistic potential, are constrained to be orthogonal to the occupied orbits in $^{20}$C. We obtain ample results supporting that $^{22}$C is an ideal $S$-wave two-neutron halo nucleus: The ground state is bound by 390-570 keV, the root mean square neutron and proton radii are 4.0 and 2.4 fm, and the two neutrons are predominantly in $(s_{1/2})^2$ orbits. The binding mechanism of $^{22}$C is discussed. One- and two-body density distributions elucidate the halo cha…
The formalism to describe electron scattering reactions on two-neutron halo nuclei is developed. The halo nucleus is described as a three-body system (core+n+n), and the wave function is obtained by solving the Faddeev equations in coordinate space. We discuss elastic and quasielastic scattering using the impulse approximation to describe the reaction mechanism. We apply the method to investigate the case of electron scattering on $^6$He. Spectral functions, response functions, and differential cross sections are calculated for both neutron knockout and $α$ knockout by the electron.
We describe a reaction mechanism which is consistent with all available experimental information of high energy three-body breakup processes. The dominating channels are removal of one of the three halo particles leaving the other two either undisturbed or absorbed. We compare with the commonly used deceptive assumption of a decay through two-body resonance states. Our predictions can be tested by measuring neutron-neutron invariant mass spectra.
The neutron skin and halo distributions in medium and heavy nuclei are calculated within the extended Thomas-Fermi approximation. Calculations are carried out for the effective Skyrme-like forces using the direct variational method. The analytical expression for the isovector shift of the rms radii $Δr_{np}$ as a sum of skin- and halo-like terms is obtained. The contribution of halo and skin terms to $Δr_{np}$ are found to be approximately equal.
We investigate the role of higher multipole excitations in the electromagnetic dissociation of one-neutron halo nuclei within two different theoretical models -- a finite range distorted wave Born approximation and another in a more analytical method with a finite range potential. We also show, within a simple picture, how the presence of a weakly bound state affects the breakup cross section.
The Relativistic Hartree Bogoliubov (RHB) model is applied in the self-consistent mean-field approximation to the description of the neutron halo in the mass region above the s-d shell. Pairing correlations and the coupling to particle continuum states are described by finite range two-body forces. Finite element methods are used in the coordinate space discretization of the coupled system of Dirac-Hartree-Bogoliubov integro-differential eigenvalue equations, and Klein-Gordon equations for the meson fields. Calculations are performed for the isotopic chains of Ne and C nuclei. We find evidence…
The two--neutron separation energy of $^6$He has been reproduced for the first time in a realistic parameter--free microscopic multicluster model comprising the $α+n+n$ and $t+t$ clusterizations, with $α$ cluster breathing excitations included. The contribution of the $t+t$ channel is substantial. A very thick (0.85 fm) neutron halo has been found in full agreement with the results of the latest phenomenological analysis.
The halo effect in the final states of astrophysically relevant direct neutron--capture reactions by neutron--rich nuclei is discussed. As an example, we calculate the cross sections for $^{18}$O(n,$γ$)$^{19}$O at thermonuclear and thermal energies.
Instituto Tecnológico de Aeronáutica（巴西航空研究院）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎萨克雷大学，法国国家科学研究中心/法国国家核子与粒子物理研究所，IJCLab）；Instituto de Física Teórica, Universidade Estadual Paulista（圣保罗州立大学理论物理研究所）
We have investigated the halo formation in the neutron rich $\rm{Ca}$ isotopes within the framework of recently proposed relativistic mean-field plus BCS (RMF+BCS) approach wherein the single particle continuum corresponding to the RMF is replaced by a set of discrete positive energy states for the calculation of pairing energy. For the neutron rich $\rm{Ca}$ isotopes in the vicinity of neutron drip-line, it is found that further addition of neutrons causes a rapid increase in the neutron rms radius with a very small increase in the binding energy, indicating thereby the occurrence of halos. T…
Direct reaction experiments provide a powerful tool to probe the structure of neutron-rich nuclei like beryllium-11. We use halo effective field theory to calculate the cross section of the deuteron-induced neutron transfer reaction ${}^{10}\text{Be}(\text{d},\,\text{p}){}^{11}\text{Be}$. The effective theory contains dynamical fields for the beryllium-10 core, the neutron, and the proton. In contrast, the deuteron and the beryllium-11 halo nucleus are generated dynamically from contact interactions using experimental and ab initio input. The reaction amplitude is constructed up to next-to-lea…
The present contribution summarizes the content and slightly updates the discussion of a recently proposed theoretical analysis of the halo phenomenon in many-fermion systems. We focus here on applications to potential neutron halos in mid-mass nuclei.
The range corrections to the universal properties and structure of two-neutron halo nuclei are investigated within an effective quantum mechanics framework. Treating the nucleus as an effective three-body system, we make a systematic improvement upon previous calculations by calculating the linear range corrections at next-to-leading order. Since the effective ranges for the neutron-core interactions are not known, we estimate the effective range to be set by the inverse of the pion mass. We investigate the possibility of excited Efimov states in two-neutron halo nuclei and calculate their mea…
Experimental data on Coulomb breakup and neutron removal indicate that 31Ne is one of the heaviest halo nuclei discovered so far. The possible ground state of 31Ne is either 3/2- coming from p-wave halo or 1/2+ from s-wave halo. In this work, we develop a treatable model to include deformed wave functions and a dynamical knockout formalism which includes the dependence on the nuclear orientation to study the neutron removal from 31Ne projectiles at energies around E=200 MeV/nucleon. A detailed account of the effects of deformation on cross sections and longitudinal momentum distributions is ma…
The radii of nucleon distribution and neutron skin in nuclei beyond the β-stability line are studied within the extended Thomas-Fermi approximation. We show that the growth of neutron skin in unstable nuclei does not obey the saturation condition because of the neutron coat. The neutron coat indicates the possibility of giant neutron halo which is growing with moving away from the beta stability line. We demonstrate the presence of strong shell oscillations in the charge radius R_C and the relation of R_C to the isospin shift of neutron-proton chemical potentials Δλ=λ_n-λ_p for nuclei beyond t…
Recently, the energy spectrum of $^{10}$Li was measured upto 4.6 MeV, via one-neutron transfer reaction d($^{9}$Li, p)$^{10}$Li. Considering the ambiguities on the $^{10}$Li continuum spectrum with reference to new data, we report the configuration mixing in the ground state of the two-neutron halo nucleus $^{11}$Li for two different choices of the $^{9}$Li$+$n potential. For the present study, we employ a three-body (core$+$n$+$n) structure model developed for describing the two-neutron halo system by explicit coupling of unbound continuum states of the subsystem (core$+$n), and discuss the t…
Nuclei with large neutron-to-proton ratios have neutron skins, which manifest themselves in an excess of neutrons at distances greater than the radius of the proton distribution. In addition, some drip-line nuclei develop very extended halo structures. The neutron halo is a threshold effect; it appears when the valence neutrons occupy weakly bound orbits. In this study, nuclear skins and halos are analyzed within the self-consistent Skyrme-Hartree-Fock-Bogoliubov and relativistic Hartree-Bogoliubov theories for spherical shapes. It is demonstrated that skins, halos, and surface thickness can b…
A theoretical model able to describe fragmentation reactions of three--body halo nuclei on different targets, from light to heavy, is used to compute neutron and core momentum distributions. Both Coulomb and nuclear interactions are simultaneously included. We specify the different reaction mechanisms related to various processes. The method is applied to fragmentation of $^6$He and $^{11}$Li on C and Pb. We find good agreement with the available experimental results.
The phenomena of giant halo and halo of neutron-rich even-Ca isotopes are investigated and compared in the framework of the relativistic continuum Hartree-Bogoliubov (RCHB) and non-relativistic Skyrme Hartree-Fock-Bogoliubov (HFB) calculations. With two parameter sets for each of the RCHB and the Skyrme HFB calculations, it is found that although halo phenomena exist for Ca isotopes near neutron drip line in both calculations, the halo of the Skyrme HFB calculations starts at a more neutron-rich nucleus than that of the RCHB calculations, and the RCHB calculations have larger neutron root-mean…
We study the two-neutron correlations in the ground state of the weakly-bound two-neutron halo nucleus $^{22}$C sitting at the edge of the neutron-drip line and also in the unbound nucleus $^{26}$O sitting beyond the neutron dripline. For the present study, we employ a three-body (core$+n+n$) structure model designed for describing the two-neutron halo system by explicit inclusion of unbound continuum states of the subsystem (core$+n$). We use either a density-independent or a density-dependent contact-delta interaction to describe the neutron-neutron interaction and its strength is varied to …
We explore the evolution of the structure of the ground state of a nucleus with two valence nucleons as the system approaches the two particle threshold. We use a three-body model of $core+n+n$ where the core is deformed and allowed to excite. We find that both NN correlations and correlations due to deformation/excitation of the core inhibit the formation of halos. Our results suggest that it is unlikely to find halo nuclei on the dripline of deformed nuclei.
The giant halos predicted in neutron-rich Zr isotopes with $A=124-138$ are investigated by using the self-consistent continuum Skyrme Hartree-Fock-Bogoliubov approach, in which the asymptotic behavior of continuum quasiparticle states is properly treated by the Green's function method. We study in detail the neutron pair correlation involved in the giant halo by analyzing the asymptotic exponential tail of the neutron pair condensate (pair density) in addition to that of the neutron particle density. The neutron quasiparticle spectra associated with these giant halo nuclei are examined. It is …
An analytical model, recently developed to study the electromagnetic dissociation (EMD) energy spectra of two-neutron halo nuclei, is applied to 11-Li and 14-Be. We find that a reliable set of experimental data on EMD could help to resolve the problem concerning the structure of the 11-Li ground state. For 14-Be we find a mutual inconsistency between the existing experimental data on the binding energy, radius and EMD energy spectrum. We also conclude that the structure of 14-Be is essentially more complicated than the structure of other Borromean two--neutron halo nuclei.
A systematic study of the root-mean-square distance between the constituents of weakly-bound nuclei consisting of two halo neutrons and a core is performed using a renormalized zero-range model. The radii are obtained from a universal scaling function that depends on the mass ratio of the neutron and the core, as well as on the nature of the subsystems, bound or virtual. Our calculations are qualitatively consistent with recent data for the neutron-neutron root-mean-square distance in the halo of $^{11}$Li and $^{14}$Be nuclei.
An analytical model is developed to study the spectra of electromagnetic dissociation of two-neutron halo nuclei without precise knowledge about initial and final states. Phenomenological three-cluster bound state wave functions, reproducing the most relevant features of these nuclei, are used along with no interaction final states. The 6-He nucleus is considered as a test case, and a good agreement with experimental data concerning the shape of the spectrum and the magnitude of the strength function is found.
Halo phenomena in deformed nuclei are investigated within a deformed relativistic Hartree Bogoliubov (DRHB) theory. These weakly bound quantum systems present interesting examples for the study of the interdependence between the deformation of the core and the particles in the halo. Contributions of the halo, deformation effects, and large spatial extensions of these systems are described in a fully self-consistent way by the DRHB equations in a spherical Woods-Saxon basis with the proper asymptotic behavior at large distance from the nuclear center. Magnesium and neon isotopes are studied and…
We take a new look at $^{6}\textrm{He}$ halo nucleus and set up a halo effective field theory at low energies to calculate the charge form factor of ${}^{6}\textrm{He}$ system with resonant P-wave interaction. P-wave Lagrangian has been introduced and the charge form factor of ${}^{6}\textrm{He}$ halo nucleus has been obtained at Leading-Order. In this study, the mean-square charge radius of ${}^{6}\textrm{He}$ nucleus relative to ${}^{4}\textrm{He}$ core and the root-mean-square (r.m.s) charge radius of ${}^{6}\textrm{He}$ nucleus have been estimated as $\langle r_{E}^{2}\rangle=1.408\; \text…
Assuming a~simple spherical relativistic mean field model of the nucleus, we estimate the width of the antiproton--neutron annihilation ($Γ_n$) and the width of antiproton--proton ($Γ_p$) annihilation, in an antiprotonic atom system. This allows us to determine the halo factor $f$, which is then discussed in the context of experimental data obtained in measurements recently done on LEAR utility at CERN. Another quantity which characterizes the deviation of the average nuclear densities ratio from the corresponding ratio of the homogeneous densities is introduced too. It was shown that it is al…
We formulate a method to compute breakup processes of three-body halo systems reacting with a target. The reaction between one of the particles and the target as well as the corresponding pairwise final state interactions are carefully treated. Both absorption and diffraction processes are included. Detailed differential and total cross sections are calculated for two-neutron (2n) removal from 6He by fragmentation on 12C. Effects due to the core shadowing are taken into account. Good agreement with available experimental data is obtained.
The scaled harmonic oscillator basis (SHO) is derived by a local scaling-point transformation of the spherical harmonic oscillator radial wave functions. The unitary scaling transformation produces a basis with improved asymptotic properties. The SHO basis is employed in the solution of the relativistic Hartree-Bogoliubov (RHB) equations in configurational space. The model is applied in the self-consistent mean-field approximation to the description of the neutron halo in Ne isotopes. It is shown that an expansion of nucleon spinors and mean-field potentials in the SHO basis reproduces the asy…
Renormalizing Two-Neutron Halo Nuclei Without Neutron-Core Interaction
Technische Universität Darmstadt（达姆施塔特工业大学）；Nuclear Physics Institute, Czech Academy of Sciences（捷克科学院核物理研究所）；Istituto Nazionale di Fisica Nucleare, Sezione di Pisa（意大利国家核物理研究所比萨分部）；Helmholtz Forschungsakademie Hessen für FAIR (HFHF) and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH（黑森FAIR亥姆霍兹研究院及极端物质研究所EMMI，GSI重离子研究中心有限公司）
A fully antisymmetrized microscopic model is developed for light two-neutron halo nuclei using a hyper-spherical basis to describe halo regions. The many-body wavefunction is optimized variationally. The model is applied to 6He bound by semi realistic Minnesota nucleon-nucleon forces. The two-neutron separation energy and the radius of the halo are reproduced in agreement with experiment. Antisymmetrization effects between 4He and halo neutrons are found to be crucial for binding of 6He. We also properly extract two-neutron overlap functions and find that there is a significant increase of 30%…
The strong dependence of Coulomb energies on nuclear radii makes it possible to extract the latter from calculations of the former. The resulting estimates of neutron skins indicate that two mechanisms are involved. The first one---isovector monopole polarizability---amounts to noting that when a particle is added to a system it drives the radii of neutrons and protons in different directions, tending to equalize the radii of both fluids independently of the neutron excess. This mechanism is well understood and the Duflo-Zuker (small) neutron skin values derived 14 years ago are consistent wit…
The analysis of the core recoil momentum distribution of neutron-rich isotopes of light exotic nuclei is performed within a model of the halo nuclei described by a core and two neutrons dominated by the $s-$wave channel. We adopt the renormalized three-body model with a zero-range force, that accounts for the universal Efimov physics. This model is applicable to nuclei with large two-neutron halos compared to the core size, and a neutron-core scattering length larger than the interaction range. The halo wave function in momentum space is obtained by using as inputs the two-neutron separation e…
Using the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB) model, we explore the mechanism behind the parity inversion and halo occurrence in $^{11}$Be, which are well reproduced by the RHF Lagrangian PKA1. It is illustrated that evidently enhanced deformation effects by the $π$-pseudo-vector and $ρ$-tensor couplings in PKA1 are crucial for correctly describing both even-parity ground state (GS) and neutron halo of $^{11}$Be. Coupling with the deformation, the intrude $1d_{5/2}$ component largely enhances the couplings between the even-parity orbit $1/2_2^+$ and the nuclear core …
In this paper we study the energy spectra and related parallel momentum distributions of the neutrons from the breakup of 11Be. Earlier papers on transfer to the continuum reactions have shown that the breakup amplitude reduces to a simple eikonal approximation in the limit of weakly bound projectiles. The aim is to establish a reliable method to obtain information on the structure of the halo from the experimental results which depend on the reaction mechanism. Theoretical results for the widths of the parallel momentum distributions and for the total breakup cross section are compared to rec…
We have investigated the implications of the neutron halo configuration, observed in the ground-state of some neutron-rich light nuclei, on neutron radiative transition processes. In particular, we have studied the influence of the neutron halo on the direct radiative capture (DRC) process. The energy dependence as well as the strength of E1 emission due to incident p-wave neutrons is strongly influenced by the halo configuration of the residual nucleus capturing state. We have compared the calculated 10Be(n,gamma)11Be DRC cross section with that derived from the experiment in the inverse kine…
The interaction cross sections for $^A Na + ^{12}C$ reaction are calculated using Glauber model. The continuum Hartree-Bogoliubov theory has been generalized to treat the odd particle system and take the continuum into account. The theory reproduces the experimental result quite well. The matter distributions from the proton drip line to the neutron drip line in Na isotopes have been systematically studied and presented. The relation between the shell effects and the halos has been examined. The tail of the matter distribution shows a strong dependence on the shell structure. The neutron N=28 …
The mechanism of the Coulomb breakup reactions of the nuclei with neutron-halo structure is investigated in detail. A time-dependent Schrödinger equation for the halo neutron is numerically solved by treating the Coulomb field of a target as an external field. The momentum distribution and the post-acceleration effect of the final fragments are discussed in a fully quantum mechanical way to clarify the limitation of the intuitive picture based on the classical mechanics. The theory is applied to the Coulomb breakup reaction of $^{11}$Be + $^{208}$Pb. The breakup mechanism is found to be differ…
