Spatial periphery of lithium and beryllium isotopes

The spatial structure of the periphery of lithium and beryllium isotopes is studied by means of charge-exchange reactions and the (t, p) and (d, p) reactions on their nuclei. It is shown that the 0⁺ isobaric-analog state of ⁶Li at 3.56 MeV has a halo structure formed by a proton and a neutron, that there is virtually no manifestation of a neutron halo in the ground state of the ⁹Li nucleus, and that the ¹¹Li nucleus has a Borromean halo structure that two neutrons form with respect to the ⁹Li core and which manifests itself in cigar and dineutron configurations. The ¹⁰Be nucleus has a substantial two-neutron periphery in either configuration both in the ground and in the 2⁺ excited state at 3.37MeV.     

Studying of the neutron halo structure in quasi-free proton scattering from 6He Halo nucleus

An experimental method based on an analysis of the neutron-neutron correlations in reactions induced by halo nuclei in nuclear photoemulsion is proposed for studying the two-neutron halo structure. Photoemulsion stacks were exposed to a beam of radioactive ⁶He nuclei. Preliminary data on interaction of the ⁶He halo nucleus to hydrogen are compared with the results of the kinematic calculation for the reaction of quasi-free proton scattering from clusters making up the ⁶He halo nucleus. A fraction of quasi-free scattering events with “survival” of the dineutron is evaluated for scattering of protons by the dineutron configuration of the ⁶He nucleus.     

Neutron periphery in light nuclei

A spatial configuration of light nuclei that involves two excess neutrons (⁶He, ¹⁰Be, and ¹²B) is studied by analyzing cross sections for various reactions on these nuclei: ⁶He(α, α)⁶He, ⁹Be(d, p)¹⁰Be, and ¹⁰B(t, p)¹²B. Pole dineutron-transfer mechanisms (dineutron configuration of the neutron periphery) and second-order mechanisms involving sequential neutron transfer (cigar-like configuration of the neutron periphery) are taken into account in the calculations. It is shown that the neutron periphery is drastically different in the nuclei in question: in ⁶He, there is a halo receiving a contribution from both configurations; in ¹⁰Be, there is an only slightly noticeable halo featuring a contribution of practically one neutron from the cigar-like configuration; and, in ¹²B, there is a neutron skin.     

Spatial periphery of lithium isotopes

The spatial structure of lithium isotopes is studied with the aid of the charge-exchange and (t, p) reactions on lithium nuclei. It is shown that an excited isobaric-analog state of ⁶Li (0⁺, 3.56MeV) has a halo structure formed by a proton and a neutron, that, in the ⁹Li nucleus, there is virtually no neutron halo, and that ¹¹Li is a Borromean nucleus formed by a ⁹Li core and a two-neutron halo manifesting itself in cigar-like and dineutron configurations.     

Very neutron-rich exotic nuclei

A brief summary is done of the various types of experiment used in studies of the very neutron rich nuclei. Some highlights are given for the two-neutron halo and¹¹Li nucleus and for the one-neutron halo and¹¹Be nucleus.     

The role of various mechanisms in the formation of the 12B nucleus in the 10B(t, p)12B reaction

The angular distribution of protons from the ¹⁰B(t, p)¹²B reaction is analyzed within the framework of three mechanisms: dineutron cluster stripping, heavy ⁹Be cluster stripping, and successive time-delay neutron transfer. The dineutron cluster stripping and successive neutron transfer mechanisms are shown to be of considerable importance. Wave functions of the relative motion of the ¹⁰B and dineutron, as well as of the ¹⁰B and both neutrons, in the ¹²B ground state are reconstructed, which revealed that the neutron halo in the ¹²B nucleus practically does not manifest itself in the ¹⁰B(t, p)¹²B reaction.     

Universal properties and structure of halo nuclei

The universal properties and structure of halo nuclei composed of two neutrons (2n) and a core are investigated within an effective quantum mechanics framework. We construct an effective interaction potential that exploits the separation of scales in halo nuclei and treat the nucleus as an effective three-body system. The uncertainty from higher orders in the expansion is quantified through theoretical error bands. First, we investigate the possibility to observe excited Efimov states in 2n halo nuclei. Based on the experimental data, ²⁰C is the only halo nucleus candidate to possibly have an Efimov excited state, with an energy less than 7 keV below the scattering threshold. Second, we study the structure of ²⁰C and other 2n halo nuclei. In particular, we calculate their matter form factors, radii, and two-neutron opening angles.     

Excess neutron nucleus <Superscript>11</Superscript>Be as a product of reaction (<Emphasis Type="Italic">t</Emphasis>, <Emphasis Type="Italic">p</Emphasis>)

The (t, p) reaction on the ⁹Be nucleus is analyzed using the mechanisms of dineutron stripping and ⁸Li heavy cluster stripping. It is shown that in the shell model, the wave function of the ¹¹Be(1/2⁺) nucleus formed by adding two neutrons to the 9Be nucleus is constructed from a ¹⁰Be(0⁺) core and a 2s-neutron. This concept of the ¹¹Be(1/2⁺) structure allows us to calculate the reduced width of tritium and a dineutron with a relative orbital angular momentum equal to 1. The differential cross section of the (t, p) reaction is calculated with allowance for the contribution from both mechanisms. The agreement between the theoretical and experimental cross sections of dineutron stripping at narrow angles θ_p confirms the shell model can be used to describe the states of nuclei with complex structure and mixed configurations of different shells.     

Dynamic deformation of light nuclei in excited states

An important property—the dynamic deformation of B* light aligned nuclei—is investigated for the nuclear reactions A(x, y)B* → γ + B ₀ by measuring the y-γ correlations. Dynamic deformation is determined from the orientation tensors of multipolar moments. Normalization constants of the contributions from even-rank orientation tensors are determined from the condition of coincidence between dynamic and static deformations of the B* nucleus for θ _y = 0°. Experimental dynamic deformations of ¹²C(2⁺) nuclei caused by the inelastic scattering of α particles and deuterons are determined, along with the ¹⁰Be(2⁺) nuclei formed in reaction ⁹Be(d, p)¹⁰Be(2⁺). It is shown that the dynamic deformation of the aligned nuclei depends on how they are formed and their structure, and evolves substantially when the angle θ _y is varied.     

Structure of the spatial periphery of the <Superscript>11</Superscript>Li and <Superscript>11</Superscript>Be isobars

On the basis of the shell model with an extended basis, the structure of ⁹Li-⁹Be to ¹¹Li-¹¹Be nuclei is examined with allowance for the competition of ^jj coupling and Majorana exchange forces via considering the sequential addition of neutrons, and the respective wave functions are determined. A formalism for calculating the spectroscopic factor for a dineutron and for individual neutrons in nuclei whose wave functions incorporate the mixing of shell configurations is developed. The reactions ⁹Li(t, p)¹¹Li and ⁹Be(t, p)¹¹Be treated with allowance for the mechanisms of dineutron stripping and a sequential transfer of two neutrons are considered as an indicator of the proposed structure of lithium and berylliumisotopes. The parameters of the optical potentials, the wave functions for the bound states of transferred particles, and the interaction potentials corresponding to them are determined from a comparison of the theoretical angular distribution of protons from the reaction ⁹Be(t, p)¹¹Be with its experimental counterpart. It is shown that a dineutron periphery of size about 6.4 fm is present in the ¹¹Li nucleus and that a single-neutron periphery of size about 8 fm is present in the ¹¹Be nucleus.     

First observation of ground state dineutron decay: 16Be

We report on the first observation of dineutron emission in the decay of 16Be. A single-proton knockout reaction from a 53 MeV/u 17B beam was used to populate the ground state of 16Be. 16Be is bound with respect to the emission of one neutron and unbound to two-neutron emission. The dineutron character of the decay is evidenced by a small emission angle between the two neutrons. The two-neutron separation energy of 16Be was measured to be 1.35(10) MeV, in good agreement with shell model calculations, using standard interactions for this mass region.     

Isospin in halo nuclei: Borromean halo,tango halo,and halo isomers

It is shown that the wave functions for isobaric analog, double isobaric analog, configuration, and double configuration states may simultaneously have components corresponding to nn, np, and pp halos. The difference in the halo structure between the ground and excited states of a nucleus may lead to the formation of halo isomers. A halo structure of both Borromean and tango types can be observed for np configurations. The structure of ground and excited states with various isospins in halo-like nuclei is discussed. The reduced probabilities B(Mλ) and B(Eλ) for gamma transitions in ^6?8Li, ^8?10Be, ^8,10,11B, ^10?14C, ^13?17N, ^15?17,19O, and ¹⁷F nuclei are analyzed. Particular attention is given to the cases where the ground state of a nucleus does not have a halo structure, but where its excited state may have it.     

The role of configurations of neutron halo in the formation of the model vertex function for description of the two-neutron transfer reaction

The nuclear vertex functions for virtual decay of halo nuclei ⁶He → α + n + n (¹¹Li-⁹Li + n + n) for dineutron and cigarlike configurations of the neutron halo have been analytically investigated using the diagram method of direct nuclear reactions. These vertex functions describe the one-step process of two-neutron transfer. It is shown that the angular and energy distributions of the reaction products (α particles, ⁹Li, etc.) in different ranges of variables correspond to different structural elements of the halo. The vertex function describing the two-step process of halo neutron transfer has also been analyzed.     

Universal Aspects of Neutron Halos in Light Exotic Nuclei

The theoretical few-body aspects associated with universal properties of weakly-bound neutron-rich light nuclei close to the drip line will be reviewed briefly, considering recent theoretical and experimental works. We will address low-energy properties of the one- and two-neutron halo of light exotic nuclei, which are dominated by s-wave short-range two-body interactions. In view of recent experiments with light neutron-rich nuclei, we will discuss properties of exotic nuclei as ¹¹Li, ¹⁴Be, ²⁰C and ²²C, within a three-bodyneutron–neutron-core model. Particular emphasis will be given to model independent properties associated to halo neutrons, which obey universal scaling laws. We discuss how the scaling laws for the s-wave observables of two-neutron halo will be identified with limit-cycles and Thomas–Efimov effect in a zero-range three-body model.     

Break-up of neutron-halo nuclei by diffraction dissociation and shakeoff

The interplay of diffraction dissociation and nuclear shakeoff is considered in a schematic but still realistic model for the case of the break-up of halo nuclei on light targets. We demonstrate that the shakeoff effect, arising from the momentum imparted by the core diffraction, is small but still identifiable in the experimental data for the dissociation of the one- and two-neutron halo nuclei ¹¹Be and ¹¹Li. Received: 29 October 1999 / Revised version: 15 January 2000     

A Systematic Study on 1neutron and 2neutron Halo Nuclei Using Coulomb and Nuclear Proximity Potential

The halo-structure of a nucleus is analyzed on the basis of potential energy consideration and separation energy calculations and thereby characterized a nucleus as a halo nucleus. The separation energy analysis showed that ¹¹Be, ¹⁴B, ^{15, 17, 19}C, ²²N, ²³O, ^{24, 26}F, and ²⁹Ne are 1n-halo nuclei since the 1n separation energy S(n) is the lowest and ^{6, 8}He, ¹¹Li, ¹⁴Be, ¹⁷B, ²²C, and ²⁹F are 2n-halo candidates as 2n separation energy S(2n) is the lowest. The potential energy calculations are consistent with the predictions based on separation energy calculations except for ¹²Be, ¹⁹B, and ²⁷F which can be considered as 2n-halo candidates by potential energy consideration. Also, a discrepancy is noticed in the case of the proposed 2n-halo ⁸He and ¹⁷B nuclei. Further, the possibility of emitting halo nucleus via heavy particle decay of heavy nuclei, within the range 82?≤?Z?≤?102, has been studied using the Coulomb and proximity potential model (CPPM). It is observed that the probability of emission of a halo nucleus is lower than that of a normal cluster Nevertheless, there is a finite chance of emission of a halo nucleus in the decay of a heavy nucleus.     

Quasifree proton scattering on halo nuclei as a tool for studying the neutron-halo structure

An experimental method is proposed for investigating the structure of the two-neutron halo in quasifree proton scattering on clusters of halo nuclei. This scattering process is studied in inverse kinematics by using a ⁶He beam incident to a stack of track emulsions. Preliminary data on the reaction ⁶He + p → ⁴He + p + X are compared with the results of simple kinematical calculations for quasifree proton scattering on the clusters forming the halo of the ⁶He nucleus.     

Dineutron configurations in neutron-excess nuclei from the viewpoint of the diffraction model

Cross sections measured for the interactions of incident neutron-excess nuclei ⁶He and ¹¹Li with other nuclei are analyzed in terms of expressions obtained for relevant integrated cross sections within the diffraction approximation. The results of this analysis suggest that there exists a dineutron configuration in the ⁶He nucleus and that there is no such configuration in the ¹¹Li nucleus. On the basis of calculations performed for various observables, some new specific experiments are proposed for discovering dineutrons more reliably in nuclei having a neutron halo.     

Two-body and three-body halo nuclei

We have extracted the nuclear asymptotic normalization coefficients (ANC) for the virtual transitions B→A+N via some transfer reactions and the radioactive nuclear beam experiments. With these coefficients, root-mean-square (rms) radii for the valence particle in some possible halo nuclei have been calculated. The values of rms radii extracted with ANC approach are nearly model-independent, hence are a good quantity for the investigation of nuclear halo. In addition, we have also calculated the rms radii for the two valence neutrons in some three-body systems in terms of the relationship between the radii of valence particle, core nucleus and nuclear matter. With two conditions for nuclear halo formation, we have examined these extracted rms radii. The results show that 11Be(1/2+, g.s), 12B(1-, 2.621 MeV), 13C(1/2+, 3.089 MeV), 14C(0-, 6.903 MeV), 14C(1-, 6.094 MeV), 15C(1/2+, g.s) and 19C(1/2+, g.s) with the valence particle in the 2s ground or excited state are the neutron halo nuclei, whereas 17F(1/2+, 0.495 MeV) and 21Na(1/2+, 2.423 MeV) are the proton halo nuclei in the excited state. For three-body systems, except the well-established two-neutron halo nuclei 6He and 11Li, 14Be and 17B might be the two-neutron halo nuclei as well.     

Structure of the neutron periphery of isotopes 9,11Li

The spatial periphery structure of lithium isotopes with A = 9 and 11 is investigated using the (t, p) reaction for ^7,9Li nuclei. It is shown that the neutron halo is almost absent in the ⁹Li nucleus, while the ¹¹Li nucleus has the Borromean halo structure formed by two neutrons relative to the ⁹Li core, which manifests itself in both the cigar and the dineutron configurations.