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.     

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.     

Analyzing the p(<Superscript>6</Superscript>He,n gamma)<Superscript>6</Superscript>Li reaction

The differential cross section of the charge-exchange reaction p(⁶He, n)⁶Li(0⁺, 3.56 MeV) is calculated within the context of direct mechanisms: the stripping of a heavy ⁵He cluster, replacing a virtual neutron with a proton in the 5He cluster field, and the mechanism of consecutive transfer of a neutron and an α particle. The spatial structure of initial and final nucleus is determined from the dependence of various direct mechanisms contributions from spatial configurations.     

Role of various mechanisms in the formation of a <Superscript>12</Superscript>C nucleus in the reaction <Superscript>13</Superscript>C(<Superscript>3</Superscript>He, <Emphasis Type="Italic">α</Emphasis>)<Superscript>12</Superscript>C

The contributions of various mechanisms to the production of the final nucleus ¹²C in the reaction ¹³C(³He, α)¹²C are estimated. These are neutron stripping and the transfer of the heavy cluster ⁹Be in the pole approximation or via a sequential transfer of virtual ⁸Be and a neutron. It is shown that the sequential mechanism of heavy-cluster transfer must be taken into account in order to describe correctly experimental data over the whole angular range.     

Investigation of the mechanism of the reaction 10B(d, pγ)11B at E d = 15.3 MeV by the method of angular pγ correlations

The results are presented that were obtained by measuring the differential cross sections for the reaction ¹⁰B(d, p)¹¹B occurring at E _d = 15.3 MeV and leading to the production of a ¹¹B nucleus in the ground state (3/2^?) and in the lowest two excited states (the 1/2^? state at 2.125 MeV and the 5/2^? state at 4.445 MeV). The energy dependence of the differential cross section for this reaction was measured for several proton emission angles in the energy range E _d = 12–15.3 MeV. The double-differential cross sections for the reaction ¹⁰B(d, pγ)¹¹B were measured for the 5/2^? state of the ¹¹B nucleus at 4.445 MeV, and the angular dependences of the even spin-tensor components of the density matrix were reconstructed on the basis of these data. The angular dependences of the populations of magnetic sublevels are also given. The experimental results in question are compared with their theoretical counterparts obtained under the assumption of various reaction mechanisms (neutron stripping, heavy-particle stripping, and a two-step mechanism that takes into account the delay of interaction). On the basis of this comparison, the deformation parameters of the boron nuclei were found to be β ₂(¹⁰B) = ?0.55 and β ₂(¹¹B) = 0.4.     

Isospin mixing in 12C

Gamma-ray decays of the 12.71 and 16.11 MeV states of ¹²C are investigated in a coincidence study of the ¹⁰B(τ, pγ) reaction, and using the 163 keV ¹¹B(p, γ) resonance. This information together with existing data on M1 transitions and stripping and pickup spectroscopic factors is used to determine the isospin mixing between the 12.71 and 15.11 MeV levels. A charge dependent mixing matrix element of 110 ± 30 keV is deduced.     

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.     

Coupled-channels analysis of energy-dependent isospin violation in the 12C(d, α)10B(1.74 MeV,T = 1) reaction

We have studied the isospin non-conserving ¹²C(d, α)¹⁰B(1.74 MeV, 0⁺, T= 1) reaction at several incident energies of 9 ≦ E_d ≦ 16 MeV in terms of a coupled-channels method. The reaction processes involved in the present analysis are the successive single-nucleon pick-up processes as well as the inelastic scattering of deuterons from ¹²C. It is assumed that the isospin violation should occur in the intermediate mirror cluster states of ³He + ¹¹B and t + ¹¹C, due to the Coulomb interaction. The calculation reproduces fairly well the observed features of the reaction, i.e. the decreasing cross section with increasing incident energy, and the variation of the angular distribution. We also note that the calculation shows the energy-dependent localization of isospin violation in the angular momentum space, i.e. a specifically narrow localization at the lower incident energies studied and its broadening at the higher energies. This fact is associated with the variation of the angular distribution from a forward-backward symmetry at the lower incident energies to a forward peak at the higher energies.     

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.     

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.     

Mathematical simulation of few-nucleon experiments with three or more particles in the final state

A computer program for the kinematic simulation of nuclear reactions with three or more particles in the final state is described. Simulation results for the d + ²H → (nn)^S + (pp)^S → p + p + n + n reaction, which proceeds through the formation of a singlet dineutron and diproton in the intermediate state, are presented as an example. It is shown that the kinematic parameters of breakup particles depend on the parameters of the intermediate state. The results from simulating secondary neutron spectra are compared to an experimental neutron time-of-flight spectrum obtained in a kinematically complete experiment at a deuteron energy of 15 MeV. As a result of the comparison, the energy of the quasi-bound singlet ¹S₀ state of the ²n-system is determined.     

Two site occupation by 12B implanted in copper above T=300 K

Polarized ¹²B is produced in the reaction ¹¹B (d,p) ¹²B and recoil implanted in single crystal copper. Above room temperature two depolarization peaks are observed. They are identified as arising from ¹²B occupying the octahedral interstitial site and also the substitutional site.     

Nuclear field theory predictions for 11Li and 12Be: Shedding light on the origin of pairing in nuclei

Recent data resulting from studies of two-nucleon transfer reaction on ¹¹Li, analyzed through a unified nuclear-structure-direct-reaction theory have provided strong direct as well as indirect confirmation, through the population of the first excited state of ⁹Li and of the observation of a strongly quenched ground state transition, of the prediction that phonon-mediated pairing interaction is the main mechanism binding the neutron halo of the 8.5-ms-lived ¹¹Li nucleus. In other words, the ground state of ¹¹Li can be viewed as a neutron Cooper pair bound to the ⁹Li core, mainly through the exchange of collective vibration of the core and of the pigmy resonance arizing from the sloshing back and forth of the neutron halo against the protons of the core, the mean field leading to unbound two-particle states, a situation essentially not altered by the bare nucleon-nucleon interaction acting between the halo neutrons. Two-neutron pick-up data, together with (t, p) data on ⁷Li, suggest the existence of a pairing vibrational band based on ⁹Li, whose members can be excited with the help of inverse kinematic experiments as was done in the case of ¹¹Li(p, t)⁹Li reaction. The deviation from harmonicity can provide insight into the workings of medium polarization effects on Cooper-pair nuclear pairing, let alone specific information concering the “rigidity” of the N = 6 shell closure. Further information concerning these questions is provided by the predicted absolute differential cross sections σ _abs associated with the reactions ¹²Be(p, t)¹⁰Be(g.s.) and ¹²Be(p, t)¹⁰Be(pv) (≈¹⁰Be(p, t)⁸Be(g.s.)). In particular, concerning this last reaction, predictions of σ _abs can change by an order of magnitude depending on whether the halo properties associated with the d _5/2 orbital are treated selfconsistently in calculating the ground state correlations of the (pair removal) mode, or not.     

Fusion cross sections for 10,11B+12C at sub-Coulomb energies

Total fusion cross sections for the ¹⁰B + ¹²C and ¹¹B + ¹²C reactions have been determined over a 5 MeV (c.m.) energy range extending to ≈ 3 MeV below the Coulomb barrier. Absolute γ-ray yields for specific transitions in the de-excitation of the heavy products following compound nucleus decay were measured using a Ge(Li) detector. Statistical model calculations of the decay modes of the compound nucleus have been used to deduce, from the γ-ray data, cross sections for single proton, neutron and α-particle emission, and to determine total cross sections for compound nucleus formation. No evidence has been found for sub-Coulomb resonances in either reaction. The total reaction cross sections are compared with optical model calculations using different parameter sets and the observed trend in the very low energy cross sections is discussed relative to other reactions in the same mass region.     

The Novel Cluster States in 10Be

We have investigated the cluster structures in ¹⁰Be by using ⁶He+α cluster wave functions and dineutron condensate wave functions. We suggested two kinds of exotic cluster states which have not been confirmed experimentally yet. One of them has a gas-like structure of two alphas and one dineutron, and another has ⁶He and an extremely developed α.     

Hyperfine interactions of12B in BN (hexagonal)

Hyperfine interactions of¹²B(I =1⁺,T _1/2=21 ms) implanted in the substitutional site of B in BN (hexagonal) was studied by detecting -NMR. In order to measure the quadrupole coupling constant efficiently, we employed a newly developed quadrupole resonance technique (NNQR). The quadrupole moment of¹²B was determined to be |Q(¹²B)|=13.21±0.26 mb.     

First study of the (14C, 12C) reaction: Selectivity of the reaction and the energy levels of 28Mg and 30Si

The first measurements are reported for (¹⁴C, ¹²C) two-neutron stripping reactions. Energy spectra up to an excitation energy of 12 MeV have been measured at 69 MeV for the ²⁶Mg(¹⁴C, ¹²C) and ²⁸Si(¹⁴C, ¹²C) reactions. A strong selectivity of this reaction is observed. Using this selectivity, the comparison of the spectra suggests J^π assignments for several ³⁰Si and ²⁸Mg states. The results from the other two-neutron stripping reactions, (t, p) and (¹⁸O, ¹⁶O) are compared with those of the (¹⁴C, ¹²C) reaction.     

Measurement of the 11B(11B, 10Be)12C proton transfer reaction at low energies

Differential cross sections for the ¹¹B(¹¹B,¹⁰Be)¹²C proton transfer reaction leading to the ¹⁰Be(g.sO+¹²C(4.43 MeV) $\text{(Q = 0.289}\text{MeV}\text{)}\text{and}{}^{10}\text{(3.37}\text{MeV}\text{) +}{}^{12}\text{C}\text{(g.s.) (Q = 1.36}\text{Me V}\text{)}$ final channels have been measured at E_c.m. = 5.5 MeV by coincident detection of the ¹⁰Be and ¹²C nuclei. The integrated cross sections for the ¹⁰Be + ¹²C(4.43 MeV) channel have been obtained for incident energies between E_c.m. = 2.66 and 3.64 MeV from the yields of the 4.43 MeV γ-ray emitted in the ¹²C 4.43 MeV → g.s. transition. The cross-section magnitudes compare well with the DWBA calculations. The sub-barrier transfer cross sections exhibit an unusual energy dependence: their ratio to the total reaction cross section is decreasing with decreasing incident energy.