α-clustering in Be isotopes

The Be chain of isotopes is investigated within the Sernimicroscopic Algebraic Cluster Model (SACM). For that the SACM is extended to odd-mass p-shell nuclei. We show that the main features of the Be isotopes can be well explained. Though for the neutron halo nucleus ¹¹Be some problems remain, the shell model still can describe the rough structures of these nuclei. In ¹¹Be a shell inversion takesplace reflecting the high deformation of the system. The quadrupole—quadrupole interaction plays a dominant role in p-shell nuclei.     

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.     

Multichannel neutron scattering on <Superscript>11</Superscript>Be nucleus

The effect of the Pauli exclusion principle on the relative motion of colliding light neutron-rich nuclei is investigated within a microscopic method for the examples of the ¹¹Be + n and ¹⁰Be + ² n reactions. The effective interaction of nuclei that is due to the change in the kinetic energy of their relative motion under the effect of the antisymmetrization operator is analyzed on the basis of a discrete representation of harmonic-oscillator states allowed by the Pauli exclusion principle. It is concluded that the bound state of the ¹²Be nucleus owes its origin to the impact of exchange effects on the operator of the kinetic energy of the relative motion of the neutron and the ¹¹Be nucleus. The structure of the ¹²Be ground state is discussed in the approximation of two coupled cluster configurations. The cross section for the inelastic-scattering reaction ¹¹Be(n, ² n)¹⁰Be is estimated.     

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     

The structure of11Be

More than twenty experimental level data of nuclei far from β-stability are selected to determine new effective parameters for the Modified Surface Delta Interaction and for the single particle energies. With these parameters used in the calculation for 1p-shell nuclei far from β-stability, the agreement between computed results and experimental data becomes fair, and the parity inversion for the 1/2⁺ ground state in¹¹Be is correctly reproduced. The structure of¹¹Be is discussed in some detail.     

β delayed emission of a proton by a one-neutron halo nucleus

Some one-neutron halo nuclei can emit a proton in a β 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 ¹¹Be, ¹⁹C and ³¹Ne one-neutron halo nuclei. It is very sensitive to the neutron separation energy.     

Effective nucleon-nucleon forces and interaction of light exotic nuclei with stable nuclei at low energies

The effect of the density dependence of effective nucleon-nucleon forces on the folded potential of the interactions of the light exotic nuclei ⁶He, ¹¹Li, ¹¹Be, and ⁸B with the stable nucleus ¹²C is studied, and the corresponding experimental data on the total reaction cross sections and on elastic scattering are analyzed. A semimicroscopic double-folding model featuring various density-dependent forces based on the M3Y interaction is used together with the nucleon densities as calculated within the density-functional method by using a unified set of parameters for all the above nuclei. It is shown that the angular distributions recently measured for elastic ⁶He scattering on ¹²C at an energy of 41.6 MeV per projectile nucleon and for elastic ¹¹Be scattering on ¹²C at an energy of 49.3 MeV per projectile nucleon can be described satisfactorily if the real part of the optical folded potential is supplemented with a surface term mimicking the contribution of the dynamical polarization potential.     

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.     

Time-dependent approaches for reaction and response in unstable nuclei

Time-dependent approaches for computation of quantum mechanical problems are presented for few-body models. Quantum tunneling in nuclear fusion is described using a time-dependent wave packet. Breakup and transfer reactions of ¹¹Be are visualized in the time-dependent manner. We also present a method to calculate strength functions using the time-dependent Schr?dinger equation. E1 strength distributions of halo nuclei, ¹¹Be and ⁶He, are presented.     

Forward-angle yields of 2≤Z≤11 isotopes in the reaction of 18O(35A MeV) with 9Be

A systematic investigation of the forward-angle inclusive yields of 2≤Z≤11 isotopes produced in collisions of ¹⁸O projectile nuclei with a ⁹Be target in the Fermi energy region (35A MeV) is performed. The measurements were based on the use of the COMBAS double achromatic kinematical separator in the spectrometry mode at the Flerov Laboratory of Nuclear Reactions at the Joint Institute for Nuclear Research, FLNR (JINR, Dubna). The velocity, isotopic, and element distributions are presented. There is no unique mechanism that would explain the total set of results obtained in this experiment. A dominant role of low-energy reaction mechanisms is observed. The intensity of secondary beams of halolike nuclei ¹¹Li, ¹²Be, and ¹⁴Be is determined.     

Structure of Exotic Three-Body Systems

The classification of large halos formed by two identical particles and a core is systematically addressed according to interparticle distances. The root-mean-square distances between the constituents are described by universal scaling functions obtained from a renormalized zero-range model. Applications for halo nuclei, ¹¹Li and ¹⁴Be, and for atomic ⁴He₃ are briefly discussed. The generalization to four-body systems is proposed.     

Core-breakup reactions of the halo nuclei 11Be and 11Li: momentum distributions and shadow effects

The halo nuclei ¹¹Be and ¹¹Li have been studied in core-breakup reactions where the halo neutrons are expected to be released without a major distortion due to the reaction. The widths of the halo-neutron momentum distributions have been extracted in coincidence with He fragments, Γ = 32 ± 4 MeV/c, and Li fragments, Γ = 42 ± 4 MeV/c for ¹¹Be and with He fragments, Γ = 42 ± 6 MeV/c for ¹¹Li. The ¹¹Be breakup gives a very low neutron multiplicity of 0.38±0.09 which is a manifestation of the shadowing of the neutron in the core-breakup reaction. This value can be understood from a simple theoretical calculation, which also accounts for the observed transverse momentum widths at small angles.     

Reactions with 9Be at subbarrier energies

The ⁹Be+⁹Be, ⁹Be+¹⁰B, ⁹Be+¹¹B and ⁹Be+¹³C reactions have been studied at subbarrier energies measuring the cross sections for the characteristic γ-rays emitted by the residual nuclei and comparing them with the statistical evaporation prediction. A substantial enhancement in the αn channel, which contains the the α-transfer reaction from ⁹Be, has been observed in all the systems studied. Evidence suggesting that the α-transfer reaction is not exclusively a direct transfer process is being presented.     

Investigation of neutron and proton distributions of He,Li, and Be isotopes using the new Skyrme-Force parameters

The proton and neutron densities, root-mean-square (rms) radii of proton density and neutron density, and neutron skin thickness of ^4–10He, ^6–11Li, and ^7–12Be isotopes are calculated using Skyrme-Hartree-Fock method with SLy4, SLy5, SLy6, and SLy7 force parameters. The evaluated results are compared with experimental data. Also, the results of halo nuclei (^6,8He, ¹¹Li, and ¹¹Be) are compared with the results of other isotopes for selected nuclei having the same neutron configuration.     

Structure of nuclei far from stability

The structure of neutron-rich unstable nuclei is discussed by focusing on three different subjects; (i) a superdeformed halo nucleus ¹¹Be studied by a deformed Woods-Saxon potential, (ii) retarded β decay due to neutron halo in ¹¹Li, and (iii) giant neutron excitations in nuclei with neutron skin.     

β-delayed neutron decay of drip line nuclei 11Li and 14Be

Experimental studies of β-decay measurements of the neutron drip line nuclei ¹¹Li and ¹⁴Be are presented. β- decay schemes of these nuclei are determined by measuring β-rays, delayed neutrons and γ-rays in triple coincidence. The decay schemes of both ¹¹Li and ¹⁴Be associated with single neutron emission are unambiguously determined. New levels in their daughter nuclei, ¹¹Be and ¹⁴B, are found. In addition, the deduced level scheme of 14B indicates the lowering of 2s _1/2 single neutron orbital with respect to 1p _1/2 orbital in the N=9 isotones. Such behavior is known to exist in N=7.     

Determination of microquantities of Be in samples using α-sensitive track etch detectors

A new technique of determining Be content in samples using 4.66 MeV γ-rays is proposed. This energy range is sufficient to knock out the neutron from the ⁹Be nucleaus and to excite the first 2.9 MeV level of the ⁸Be nuclei. 1.5 MeV alpha particles are registered by means of CR-39 or cellulose nitrate detectors. Alpha particles produced in the reaction of γ-rays with Li nuclei which are contained in samples may cause the background. The latter is excluded by heating of samples before irradiation for Li molecules to be evaporated. ¹¹B nuclei do not produce alpha particles at the energy range of γ-rays presented above.The results obtained in the experiments of determining Be content in natural beryl crystal samples are in good agreement with their known chemical composition. Microparticles containing Beryllium were found in soil samples from the Ust-Kamenogorsk are deposit region, which contains 10⁻³ − 10⁻⁴ g/g of Be. The sensitivity of the method is 10⁻⁶ g/g of Be in solids.     

中子滴线附近核异常大半径的解释

基于中子滴线附近核结合能的数据分析,¹¹Li,¹⁴Be和¹⁷B等可看作是核芯-中子-中子组成的三体系统。假定核芯-中子和中子-中子间作用势为弱吸引指数势,不足以形成核芯-中子和中子-中子束缚态。本文的研究表明,核芯-中子-中子三体系统可形成弱束缚态。⁶He,¹¹Li,¹⁴Be和¹⁷Be核的异常大核半径正是由于外层中子的弱束缚所致。 关键词：     

Binding energies of nuclei near the α-cluster nuclei in the brink model

The binding energies of the ⁹Be, ¹⁰Be, ¹⁰B, and ²⁵Mg and nuclei have been calculated with Volkov 2 nucleon-nucleon forces. Orbitals of the valence nucleons of the ⁹Be, ¹⁰Be, and ¹⁰B and nuclei are proposed, which are more optimal in comparison with those generally used in the α-cluster model. The clusterization is shown to decrease by adding two nucleons to the cluster core. An addition of one nucleon barely deforms the cluster core.     

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.