Momentum Distribution of a Fragment and Nucleon Removal Cross Section in the Reaction of Halo Nuclei

Recently the research on the halo structure of drip-line nuclei has shown some interesting properties of the existence of one or more halo nucleons. In the framework of few-body Glauber model, the momentum distribution of a fragment and nucleon removal cross section in the reaction of halo nuclei is presented and extended to nuclei having more than one halo nucleons. The reaction mechanism is treated with and without taking account of the final-state interaction. The wave function of removal halo nucleons in the continuum state is modified by imposing an orthogonal condition to the bound state. An analytical expression of the longitudinal momentum distribution of the fragment is derived when the bound state wave function of halo nucleons is taken as a Gaussian-type function. This is useful in the further investigation on the structure of halo nuclei.     

复动量表象方法对奇特核中晕现象的研究

晕现象的研究使人们对核结构有了新的认识。连续谱,尤其是连续谱中的共振态在其中扮演着重要角色。复动量表象(CMR)方法不仅能够统一描述束缚态、共振态和连续谱,而且能够很好地描述窄共振和宽共振。本文介绍了CMR方法对原子核共振态的研究。给出了31Ne和19C等核的束缚态和共振态的单粒子能量随形变参数β₂的变化规律,分析了19C和31Ne中单中子晕形成的物理机制和在中子数N=20附近能级反转的原因,并预测了比37Mg重的核中的单中子晕现象,这一预测结果对在实验中寻找较重的晕核具有一定的参考价值。这些研究表明CMR 方法不仅适用于描述稳定核,也适用于描述具有弥散物质分布的奇特核。     

Bounds to the size of halo nuclei

Inspired by the Bertlmann-Martin inequality relating the rms radius of the ground state wave function to the lowest dipole transition energy, we have proposed a dimensional relationship to be used in weakly bound two-body systems. In the present work, it is applied to halo nuclei. Lower and upper bounds to the size of halo nuclei are compared to values obtained from reaction cross sections. The case of the deuteron is also presented. Received: 18 September 1998     

One-neutron knockout from individual single-particle states of 11Be

The structure of the halo nucleus 11Be has been studied using the reaction 9Be(11Be,10Be+gamma)X at 60 MeV/nucleon. The ground state structure of 11Be is determined by comparing the experimental cross sections to a calculation combining spectroscopic factors from the shell model with l-dependent single-particle cross sections obtained in an eikonal model. This experiment shows the dominant 1s single-particle character of the 11Be ground state and indicates a small contribution of 0d admixture in the wave function. After correction for the approximately 22% intensity to excited levels, a clean and precise distribution of parallel momentum for knockout from the 1s halo wave function is obtained for the first time.     

Nucleon-nucleon correlations with quark degrees of freedom

A dynamical equation of two nucleons in a nucleus is formulated in the nonrelativistic quark model including Pauli blocking due to the other nucleons. This equation is solved with a model wave function containing the possiblity of six-quark bags with different radii. It is shown that the Pauli blocking effect is emphasized by the non-nucleonic degrees of freedom represented by six-quark bags. The modification of the quark momentum distribution for correlated nucleons is calculated and probabilities of non-NN components in nuclei are estimated.     

Quark antisymmetrization and deep-inelastic scattering : I. Nuclear quark momentum distributions

We consider the effects of quark antisymmetrization for quark momentum distributions. The simple convolution of nucleon momentum distributions in a nucleus and quark momentum distribution in a nucleon in general does not satisfy the Pauli principle. Antisymmetrizing the product of wave functions in momentum space introduces additional contributions. This paper extends the results for s-wave nuclei to p-wave nuclei, showing that the effects of antisymmetrization in that case are very small. The extension beyond the simple s-wave nuclei is important for the discussion of the role of antisymmetrization in the ratio of deep-inelastic structure functions for nuclei and nucleons.     

Structure and reactions of halo nuclei: An entangled approach

Halo nuclei are characterised by their weak binding, large spatial extent and hence a quite pronounced, yet highly correlated, few-body structure. This is typically in terms of a well-defined core plus one or more valence nucleons. Over the past decade the properties of halo nuclei have been studied theoretically using a range of reaction models, many of which having served us well for half a century or more in the study of less exotic, “mean-field”, nuclei. However, it is now clear that for many reactions with halo nuclei, it is not appropriate to disentangle (factorise out) the structure information from the reaction information. That is, the few-body nature of these systems requires few-body reaction models in which the nuclear structure and reaction mechanisms are necessarily entangled. This talk will briefly review the physical assumptions made by various reaction models, and point to areas where progress is being made to extend their range of applicability in order to provide further insights into halo structure. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: j.al-khalili@surrey.ac.uk     

Nuclear dependence of structure functions in coordinate space

The momentum distributions of partons in bound nucleons are known to depend significantly on the size of the nucleus. The Fourier transform of the momentum (x _Bj) distribution measures the overlap between Fock components of the nucleon wave function which differ by a displacement of one parton along the light cone. The magnitude of the overlap thus determines the average range of mobility of the parton in the nucleon. By comparing the Fourier transforms of structure functions for several nuclei we study the dependence of quark mobility on nuclear size. We find a surprisingly small nuclear dependence (< 2% for He, C and Ca) for displacements t = z ? 2.5 fm, after which a nuclear suppression due to shadowing sets in. The nuclear effects observed in momentum space for x _Bj ? 0.4 can be understood as a reflection of only the large distance shadowing in coordinate space.     

On some approximations in the theory of halo nucleus reactions

The halo nucleus nucleon stripping reaction on a light target is studied using the diffraction theory of reactions with weakly bound nuclei. An improved version of the approximation of a small target’s radius (compared to the size of a halo nucleus) is formulated. Simple analytical expressions for the differential cross section and the longitudinal momentum distribution of observed particles that allow us to calculate them with good accuracy are obtained.     

Remarks on halo nuclei

On the ground of a relationship between the rms radius and the separation energy, we compare halo nuclei to diffuse diatomics. It underlines the essential difference between these two kinds of weakly bound systems: whereas the two-body approximation seems well justified in the case of diatomics, it becomes questionable in the nuclear case when the separation energy approaches zero. Because of this particular situation, we conjecture that the Efimov states have less chances to be observed in nuclear than in molecular cases. Discussing possibilities of measuring accurately the rms radius of halo wave function, we propose a strategy based on the parallel momentum distribution measured in dissociation experiments, together with the use of an Abel transform.     

Nuclear Structure in High Energy Scattering Processes

We suggest that in hard scattering processes the nuclear medium can be viewed as a background parton sea where the bound nucleons are "soaked". The quark and gluon distributions in nuclei are investigated under this assumption. The comparisons of this model with the experimental data of the structure function ratio from charged lepton deep inelastic scattering, the gluon momentum distribution ratio from inelastic J/Ψ production, and the dimuon yield ratio from Drell-Yan dimuon production are present.     

Experimental studies of the nuclear spatial structure of neutron-rich He and Li isotopes

Results of several experiments aimed at exploring the nuclear spatial structure of neutron-rich He and Li isotopes are presented and briefly discussed. The study of the density distributions in these nuclei by small-angle proton elastic scattering at intermediate energy is considered in more detail. The performed investigations allow one to obtain information on the total matter distributions, radii of the matter, neutron and proton distributions, effective and internal core sizes, halo sizes, and spatial correlations of the halo nucleons in the studied nuclei. The text was submitted by the authors in English.     

Non-relativistic bound states in a finite volume

We derive general results for the mass shift of bound states with angular momentum $?\ge 1$ in a periodic cubic box in two and three spatial dimensions. Our results have applications to lattice simulations of hadronic molecules, halo nuclei, and Feshbach molecules. The sign of the mass shift can be related to the symmetry properties of the state under consideration. We verify our analytical results with explicit numerical calculations. Moreover, we comment on the relations connecting the effective range parameter, the binding momentum of a given state and the asymptotic normalization coefficient of the corresponding wave function. We give explicit expressions for this relation in the shallow binding limit.     

晕核反应总截面和密度分布

利用考虑了量子修正、库仑修正、核子–核子碰撞同位旋效应和假定有效原子核密度分布后得到的改进的Glauber理论,计算了晕核与稳定核反应总截面,研究了晕核结构对反应总截面的影响.结果发现对于¹¹Be,¹⁴Be和¹¹Li等入射核,必须考虑它们的晕核结构和利用自由的核子–核子碰撞截面才能得到与实验符合的反应截面,并可依据反应总截面来确定晕核的密度分布和均方半径等信息.     

Relations between the differential cross sections for diffractive processes of nucleon stripping and halo-nucleus core stripping

A comparative analysis of the nucleon stripping and core stripping reactions induced by a halo nucleus is presented on the basis of certain models for diffractive processes. It follows from calculations for the halo nucleus 11Be that the transverse momentum distribution of nucleons for core stripping (as the longitudinal momentum distribution) is less distorted by absorption in a target than the distribution of core fragments for nucleon stripping. The obtained relations between the cross sections for the stripping reactions simplify interpretation of the calculation results.     

Structure functions of bound nucleons: From the EMC effect to nuclear shadowing

We describe the nuclear structure functions in the whole range of the Bjorken variablex, by combining various effects in a many-step procedure. First, we present a QCD motivated model of nucleons, treated, in the limit of vanishingQ ², as bound states of three relativistic constituent quarks. Gluons and sea quarks are generated radiatively from the input valence quarks. All parton distributions are described in terms of the confinement (or nucleon's) radius. The results for free nucleons are in agreement with the experimental determinations. The structure functions of bound nucleons are calculated by assuming that the main effect of nucleon binding is stretching of nucleons. The larger size of bound nucleons lowers the valence momentum and enhances the radiatively generated glue and sea densities. In the small-x region the competitive mechanism of nuclear shadowing takes place. It also depends on the size of the nucleons. By combining stretching, shadowing and Fermi motion effects (the latter confined to very largex), the structure function ratio is well reproduced. Results are also presented for theA-dependence of the momentum integral of charged partons, the nuclear gluon distribution and the hadron-nuclei cross sections.     

Momentum distributions in fragmentation reactions with relativistic heavy ions

The momentum distribution (or angular distribution) in inelastic heavy ion reactions is calculated by using a two-step model (“abrasion” and “ablation”). First, all nucleons in the volume element where projectile and target overlap spatially during the collision are sheared away. The remaining prefragment (the projectile minus the sheared off nucleons) has a recoil momentum proportional to the Fermi momentum. The prefragment is left in an excited state and emits nucleons, the recoil momentum given to the final fragment is proportional to the nuclear temperature. This two-step model reproduces the overall trend and the isotopic dependence for the widths of the experimental momentum distributions. Contrary to previous theoretical studies we find that surface and friction phenomena lead to an anisotropy: The momentum distributions in transverse direction are always broader than in the longitudinal direction by about 5 to 10%.     

The halo of the exotic nucleus 11Li: a single Cooper pair

If neutrons are progressively added to a normal nucleus, the Pauli principle forces them into states of higher momentum. When the core becomes neutron saturated, the nucleus expels most of the wave function of the last neutrons outside to form a halo, which, because of its large size, can have a lower momentum. It is an open question how nature stabilizes such a fragile system and provides the glue needed to bind the halo neutrons to the core. Here, we show that this problem is similar to that of the instability of the normal state of an electron system at zero temperature solved by Cooper, a solution which is at the basis of BCS theory of superconductivity. By mimicking this approach using, aside from the bare nucleon-nucleon interaction, the long wavelength vibrations of the nucleus ¹¹Li, the paradigm of halo nuclei, as tailored glues of the least bound neutrons, we are able to obtain a unified and quantitative picture of the observed properties of ¹¹Li. Received: 9 May 2001 / Accepted: 17 November 2001