Manifestations of a dineutron cluster in elastic α 6He scattering

A consistent theoretical analysis of elastic α ⁶He scattering is performed with allowance for the correction associated with the exchange of a dineutron cluster. It is shown that the inclusion of the exchange mechanism, along with that of potential scattering, makes it possible to reproduce the measured cross section over the entire range of the ⁶He scattering angle. Concurrently, one can also obtain information about the spatial distribution of the dineutron cluster and the α particle in the ground state of the ⁶He nucleus.     

Mechanism of independent neutron transfer in elastic <Emphasis Type="Italic">α</Emphasis><Superscript>6</Superscript>He scattering and structure of the <Superscript>6</Superscript>He nuclear wave function

The presence of two topologically different configurations, a dineutron and a cigar-like one, in the spatial wave function for the neutron-rich nucleus ⁶He is predicted. In elastic α ⁶He scattering, the dineutron configuration leads to the appearance of backward maxima in the cross section for elastic α ⁶He scattering. The cigar-like configuration is responsible for the scattering mechanism involving independent sequential neutron transfer and the formation of the ⁵He-⁵He virtual system. In order to estimate the contribution of this mechanism, the matrix element for the two-step sequential particle transfer is calculated by a method that takes into account delay in the interaction and which is realized in the QUADRO code. Calculations performed on this basis make it possible to estimate the weight of the cigar-like component in the wave function for the ⁶He nucleus.     

Comparison of the noncoplanar 6Li(p,pd)4He reactions at 120 and 200 MeV

The ⁶Li(p, pd)⁴He reaction was studied at 200.2 MeV, at the quasi-free angle pair (θ_p, θ_d) = (54°, ?48.9°), for noncoplanarity angles φ from 0° to 28°. ⁶Li αd spectroscopic factors of 0.84 and 0.76 are deduced from our coplanar data at this energy and 120 MeV, respectively, for ground-state 2S Woods-Saxon wave functions. A recent microscopic three-body calculation predicts spectroscopic factors from 0.70 to 0.75; using the ground-state wave functions from this study, we deduce a factor of 0.76 from the 200 MeV data. DWIA calculations fit the measured integrated cross sections versus φ for spectator momenta P_α ? 100 MeV/c at both bombarding energies, but underpredict them for larger P_α. Momentum form factors were better reproduced with 1S αd cluster wave functions for a soft-core bound-state potential than with the 2S Woods-Saxon wave functions, but the former wave functions generate unphysically large (～1.25) spectroscopic factors.     

Breakup of exotic nuclei and correlations of halo neutrons

We show that cross sections for nuclear fragmentation and Coulomb dissociation depend essentially on the correlation between halo neutrons, and thus the experimental data for the given processes may serve as a source of information on this correlation. The recently obtained data on the Coulomb dissociation of ⁶He, when combined with the data on the proton elastic scattering, have allowed us to conclude that the motion of the halo neutrons in ⁶He is significantly correlated, the size of the dineutron cluster, in particular, being 2.0±0.5 fm.     

Detailed study of the cluster structure of light nuclei in a three-body model: (II). The spectrum of low-lying states of nuclei with A = 6

The three-body α + 2N model developed in our earlier works to describe the ground states of the A = 6 nuclei is generalized here to describe the spectrum of the low-lying states of these nuclei. The levels of the nuclei are shown to be differently sensitive to the various Nα interaction components, whence some conclusions concerning the true form of the Nα interaction are drawn. The geometric structure of the ⁶Li and ⁶He ground states is studied in detail. A significant contribution of the stretched cigar-shaped three-particle configuration NαN with an α-particle between two nucleons has been found. The wave functions of the ground and excited states of the A = 6 nuclei are tabulated. The wave functions found have been tested carefully using numerous experimental data.     

Theoretical Investigation into Production of Double-Λ Hypernuclei from Stopped Ξ − on 6Li

We have investigated theoretically a feasible nuclear reaction to produce light double-Λ hypernuclei by choosing a suitable target. In the reaction from stopped Ξ ^? on ⁶Li target light doubly-strange nuclei, ${^5_{\Lambda\Lambda}{\rm H}}$ and ${^6_{\Lambda\Lambda}{\rm He}}$ , are produced: we have calculated the formation ratio of ${^5_{\Lambda\Lambda}{\rm H}}$ to ${^6_{\Lambda\Lambda}{\rm He}}$ for Ξ ^? absorptions from 2S, 2P and 3D orbitals of Ξ ^?–⁶Li atom by assuming a d?α cluster model for ⁶Li. From this cluster model the d?α relative wave functions has a node due to Pauli exclusion among nucleons belonging to d and α clusters. Two kinds of d?α wave functions, namely 1s relative wave function with a phenomenological one-range Gaussian (ORG) potential and that of an orthogonality-condition model (OCM) are used. It is found that the probability of ${^5_{\Lambda\Lambda}{\rm H}}$ formation is larger than that of ${^6_{\Lambda\Lambda}{\rm He}}$ for all absorption orbitals: in the case of the major 3D absorption their ratio is 1.08 for ORG and 1.96 for OCM. The dominant low momentum component of the d?α relative wave function favors the ${^5_{\Lambda\Lambda}{\rm H}}$ formation with a low Q value compared to the ${^6_{\Lambda\Lambda}{\rm He}}$ formation with a high Q value. We have also calculated momentum distributions of emitted particles, d and n, displaying continuum spectra for single-Λ hypernuclei, ${^4_{\Lambda}{\rm H}}$ and ${^5_{\Lambda}{\rm He}}$ , and line spectra for the ${^5_{\Lambda\Lambda}{\rm H}}$ and ${^6_{\Lambda\Lambda}{\rm He}}$ nuclei. Thus, our present theoretical analysis would be a significant contribution to experiments in the strangeness ?2 sector of hypernuclear physics.     

Tests of the discretized-continuum method in three-body dipole strengths

We investigate the ⁶He dipole distribution in a three-body α+n+n model. Two approaches are used to describe the three-body ¹⁻ continuum: the discretized-continuum method, where the scattering wave functions are approximated by square-integrable functions, and the R-matrix formalism, where their asymptotic behaviour is taken into account. We show that some ambiguity exists in the pseudostate method, owing to the smoothing technique, necessary to derive continuous distributions. We show evidence for the important role of the halo structure in the E1 dipole strength. We also address the treatment of Pauli forbidden states in the three-body wave functions.     

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.     

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.     

Helium-cluster decay widths of molecular states in beryllium and carbon isotopes

⁴He (i.e., α particle) and ⁶He emissions from possible molecular states in beryllium and carbon isotopes have been investigated using a mean-field-type cluster potential. Calculations can reasonably describe the α-decay widths of studied states in beryllium and carbon isotopes, and also ²⁰Ne, compared with experiments. For the nucleus ¹⁰Be, we discussed α-decay widths with different shapes or different decay modes, in order to understand the very different decay widths of two excited states. The widths of ⁶He decays from ¹²Be and α decays from ^13,14C are predicted, which could be useful for future experiments.     

Compact and loosely bound structures in light nuclei

The role of various components in the wave function of loosely bound light nuclei is considered in terms of the cluster model by taking into account orbital polarization. We show that several structures corresponding to particular modes of nucleon motion can be concurrently important for such structures. Specific examples of simple and fairly flexible trial wave functions are given for the ⁸Be and ⁶He nuclei. Explicit expressions are derived for the microscopic wave functions of these nuclei and employed to calculate basic nuclear parameters for commonly used central exchange NN potentials.     

Structure of the <Superscript>6</Superscript>He nucleus in the three-particle model

The properties of the ⁶He nucleus were investigated in a three-particle approximation (a alpha-particle cluster plus two neutrons) on the basis of the variational approach by using a Gaussian basis. For nn and nα interactions, potentials that make it possible to describe S-wave phase shifts for elastic scattering and, simultaneously, to reproduce faithfully the energy and the size of the ⁶He nucleus were proposed. Characteristic structural features of this nucleus that are manifested in the density distributions, elastic form factor, pair correlation functions, and momentum distributions of particles constituting the ⁶He nucleus in the three-particle model were revealed.     

A radiochemical study on the existence of dineutron

A radiochemical study has been made to search for dineutron² n produced in the simultaneous two-neutron emission of the excited⁶He nuclei,⁶He^*, induced in the reaction of⁹Be+n→-⁶He^*+α with fast neutrons in a reactor. It was attempted to detect the radio-activity of²⁸Mg as a product of the reaction² n+²⁷Al→²⁸Mg+p. The²⁸Mg radioactivity observed in heterogeneous samples composed of the² n-producing target Be and the² n-detecting target Al separately was not found to be more than that of a side reaction,²⁷Al{(n, p)(n _th, γ)+(n _th, γ)(n, p)}²⁸Mg, whereas it clearly exceeded that of the side reaction in alloy samples made of Be and Al metals. The former experiment gives an upper limit of the production rate of the dineutron in the bound state 1×10^?7 per event of the simultaneous two-neutron emission. A tentative explanation for the excessive²⁸Mg radioactivity observed in the latter experiment is the following two-step process,⁹Be+n→⁶He+α and²⁷Al+⁶He→+²⁸Mg+α+p, rather than the process induced by the dineutron in a virtual state.     

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.     

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.     

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.     

Charge-exchange reaction on 12C with 217 MeV 3He particles

Differential cross sections for the (³He, t) charge-exchange reaction have been measured on a ¹²C target with 217 MeV ³He particles. High energy tritons were detected using a thick Ge(Li) crystal (43 mm) and a 4 mm Si(Li) detector in an E-ΔE telescope. Microscopic DWBA calculations have been carried out, using the rather well known wave functions of the ¹²C levels from Gillet and Vinh-Mau. The sensitivity of this reaction to the different terms of the two-body effective interaction is discussed. A comparison of the (³He, t) and (³He, ³He') reactions populating analog final states is also presented. The two-step mechanisms (³He,α)(α, t) and (³He, d)(d, t) are introduced for the first two levels 1⁺(g.s.) and 2⁺(0.969 MeV) and the results emphasize the importance of such processes at high energy.     

Structural properties of the 10Be and 10C four-cluster nuclei

The structure functions for the ¹⁰Be and ¹⁰C nuclei are studied in a four-particle approximation (two alpha-particle clusters plus two nucleons). New versions of the αα interaction potential are constructed. Together with the nα, pα, and NN potentials proposed previously, they make it possible to describe the binding energies and radii of the nuclei being considered, along with the S-wave twocluster phase shifts at low energies. General properties of four-particle wave functions are studied, and two basic configurations of the cross and tetrahedron types are revealed in the ¹⁰Be and ¹⁰C nuclei. A detailed analysis of the behavior of the structure functions is performed for these nuclei. The density distributions, form factors, and pair correlation functions are considered. The momentum distributions are obtained for the alpha particles and extra nucleons. The structure functions for the ¹⁰Be and ¹⁰C four-cluster nuclei are compared with those for the ⁶He three-cluster nucleus. The bound states of the nuclei are studied within a high-precision variational approach by using Gaussian bases.