States Of 8Be Research Articles

The Algebraic Cluster Model (8Be, 12C) and the Cluster Shell Model (13C, 7Be, 19F, 8Be)

Bijker and Iachello’s algebraic cluster model (ACM) and its extension to the cluster shell model (CSM), provides a new theoretical platform for the study of alpha-clustering in light nuclei. It led to the discovery of the D3h symmetry in 12C and 20Ne, with the discovery in 12C of a new g.s. rotational band with the spin sequence of, 0+, 2+, 3-, 4+/4- and 5-, including the predicted 4+ and 4- parity doublet. Applications of the CSM shell model to particle molecular orbits in 9Be and 13C (C2’ and D3h’ particle symmetries, respectively), lead us to conjecture molecular hole states in 7Be and 19F. We observe in these nuclei the predicted phenomenological structure. And we further consider conjectured p-h states in 8Be with the predicted phenomenological p-h structure of rotational band at high excitations of approximately 20 MeV. A search for these rotational band in 8Be was performed at ISOLDE.

Searching for particle-hole cluster bands in 8Be using the ISOLDE Solenoidal Spectrometer

The 7Be(d, p)8Be∗ reaction was measured in inverse kinematics at a beam energy of 11 MeV/u using the ISOLDE Solenoidal Spectrometer, in order to identify and characterise high-excitation states in 8Be. The spin-parities of many of the states in the 16−20 MeV region can be explained as being particle-hole excitations within a two-centre shell model. The present experiment aims to elucidate the spin parities of higher excited states, > 20 MeV, to assess their candidacy as rotational excitations of the aforementioned particlehole states. The beam intensity in this experiment was measured using a downstream Micron S1 double-sided silicon strip detector to pick up elastically scattered deuterons. The focus of this paper is to present methods for calculating the beam intensity, which is key for extracting the spectroscopic factors of the measured states. Preliminary excitation spectra are also presented.

Conjectured Hole States (7Be, 19F) and p-h states (8Be) of the CSM

The remarkable success of the Algebraic Cluster Model (ACM) to describe the N=Z even-even light nuclei, 8Be, 12C, 16O and 20Ne, and the neighbouring nuclei with one particle added, 9Be, 9B, 13C, 21Ne and 21Na, using the Cluster Shell Model (CSM), lead us to consider the phenomenology of data on conjectured hole states of the CSM in 7Be and 19F, and conjectured high lying particle-hole states (p-h) in 8Be.We propose the first application of the Cluster Shell Model (CSM) of Della Rocca and Iachello to conjectured p-h states in 8Be. We demonstrate a few essential phenomenological features of the CSM in 8Be: 1) All predicted conjectured p-h states of the CSM, and only the predicted p-h states, are observed near thresholds and up to 19.5 MeV in 8Be. 2) The states are observed in the predicted order, with positive parity states below negative parity states. 3) Some of the conjectured p-h states are already known to have the predicted rotational structure of the deformed p-h states. 4) The rotational structures observed at high excitations in the conjectured p-h bands in 8Be, resemble the ground state bands of 8Be, 9Be and 9B, with similar moment of inertia.Based on these observations we contemplate new measurements of the spectroscopy of 8Be at energies above 19.5 MeV, where our knowledge of states in 8Be is incomplete. We examine the observed B(M1)s and B(E2)s in these nuclei and contemplate a measurement of the B(E2) of the iso-baric Analog transition in 8Li.

Angular correlations in the e+e− decay of excited states in Be8

Motivated by the recent observation of anomalous electron-positron angular correlations in the decay of the 18.15 MeV 1+ excited states in 8Be, we reexamine in detail the Standard Model expectations for these angular correlations. The 18.15 MeV state is above particle threshold, and several multipoles can contribute to its $e^+e^-$ decay. We present the general theoretical expressions for $e^+e^-$ angular distributions for nuclear decay by C0, C1, C2 M1, E1, and E2 multipoles, and we examine their relative contribution to the $e^+e^-$ decay of 8Be at 18.15 MeV. We find that this resonance is dominated by M1 and E1 decay, and that the ratio of M1 to E1 strength is a strong function of energy. This is in contract to the original analysis of the $e^+e^-$ angular distributions, where the M1/E1 ratio was assumed to be a constant over the energy region Ep = 0:8-1:2 MeV. We find that the existence of a `bump' in the measured angular distribution is strongly dependent on the assumed M1/E1 ratio, with the present analysis finding the measured large-angle contributions to the $e^+e^-$ angular distribution to be lower than expectation. Thus, in the current analysis we find no evidence for axion decay in the 18.15 MeV resonance region of 8Be.

Towards modeling cluster structure of 8Be with chiral interaction

Abstract How the nuclear force behaves in cluster states, in particular those consisting of the α clusters, has been investigated so far, but not yet elucidated. Today the chiral effective field theory (EFT) is established and it would shed new light on the microscopic understanding of the cluster states. We aim to address a possible source of the attraction in the cluster states of 8Be in view of the pion exchange. Namely, we investigate whether the two-pion-exchange interaction acts as a dominant attraction in the α + α system as predicted by a previous work. We describe theoretically the cluster structure of 8Be by the Brink model, for which the effective interaction is designed from the realistic nuclear force derived through the chiral EFT. The two-body matrix elements of the chiral interaction with the local-Gaussian bases are formulated within the approximation of the spin–isospin saturation forming an α particle. Introducing a global prefactor to the chiral interaction phenomenologically, the ground and low-lying excited states of 8Be, the scattering phase shift of the α–α system as well, are satisfactorily depicted. The attraction in the cluster states is found to be stemming from the two-pion-exchange contributions dominantly, along with nonnegligible short-range terms. The present work can be the foundation towards constructing realistic cluster models, by which the cluster states will be revealed microscopically in the next step.

Exclusive decay study of the 16.62 MeV (2−, T = 1) resonance in 12C

The 3α decay of the 16.62 MeV (2−, T=1) resonance in 12C has been studied for nearly a century starting with one of the first nuclear reaction studies at the Cavendish Laboratory in the 1930s. In the hitherto latest study published a decade ago a model based on earlier work from the 1960s was found to give a good account of a set of inclusive data. This model describes the decay as an l=3 α-particle populating the 2+ state of 8Be. Here we provide new exclusive data on the 3α decay of the 16.62 MeV resonance, and demonstrate that the decay is best described by a model with predominantly l=1 emission with an admixture of l=3.

The experiments to determine the electron capture and β-decay of 8B into the highly excited states of 8Be

The main goal of this work is to study the structure of the highest energy states in 8Be populated following the β+-decay and the electron capture (EC) of 8B. With this aim, two experiments were performed at ISOLDE-CERN in 2017 and 2018. The first experiment had the aim to resolve the 2+ doublet at 16.6 and 16.9 MeV, in order to study their isospin mixing. The second experiment aimed to determine a value or give an experimental upper limit to the branching ratio of the exotic EC-p decay.In this paper, we present the experimental setups and we discuss the analysis and present the preliminary results obtained so far.

A new anomaly observed in 4He supporting the existence of the hypothetical X17 particle

Recently, we observed an anomalous peak-like excess of internal e+e− pairs at around 140° for the M1 transition depopulating the 18.15 MeV isoscalar 1+ state in 8Be. The deviation from the theoretical prediction can be described by GEANT simulations assuming the creation and subsequent decay of a new, light boson with a mass of 16.7 MeV/c2. In order to reduce the possible systematic errors from the experimenntal data, we re-investigated the 8Be anomaly with an improved setup and confirmed the anomaly within the statistical uncertainties. We also studied the angular correlation of the electron-positron pairs created in the M0 transition depopulating the 21.01 MeV 0− state in 4He, and observed an anomalous excess of e+e− pairs at a significantly smaller angle of 115°. Since the transition energy was higher in this case, the observed anomaly could be described by assuming the creation and subsequent decay of the same light particle in the simulations.

Fifth force and hyperfine splitting in bound systems

Two recent experimental observations at the ATOMKI Institute of the Hungarian Academy of Sciences (regarding the angular emission pattern of electron-positron pairs from nuclear transitions from excited states in 8Be and 4He) indicate the possible existence of a particle of a rest mass energy of roughly 17 MeV. The so-called X17 particle constitutes a virtual state in the process, preceding the emission of the electron-positron pair. Based on the symmetry of the nuclear transitions ($1^+$ to $0^+$ and $0^-$ to $0^+$), the X17 could either be a vector, or a pseudoscalar particle. Here, we calculate the effective potentials generated by the X17, for hyperfine interactions in simple atomic systems, for both the pseudoscalar as well as the vector X17 hypotheses. The effective Hamiltonians are obtained in a general form which is applicable to both electronic as well as muonic bound systems. The effect of virtual annihilation and its contribution to the hyperfine splitting also is considered. Because of the short range of the X17-generated potentials, the most promising pathway for the observation of the X17-mediated effects in bound systems concerns hyperfine interactions, which, for $S$ states, are given by modifications of short-range (Dirac-delta) potentials in coordinate space. For the pseudoscalar hypothesis, the exchange of one virtual X17 quantum between the bound lepton and the nucleus exclusively leads to hyperfine effects, but does not affect the Lamb shift. Effects due to the X17 are shown to be drastically enhanced for muonic bound systems. Prospects for the detection of hyperfine effects mediated by X17 exchange are analyzed for muonic deuterium, muonic hydrogen, muonium, true muonium ($\mu^+\mu^-$ bound system), and positronium.

Simulation of the Inelastic Alpha-Particle Scattering Reaction for Investigating the Cluster Structure of Excited States of 9Be

It is proposed to investigate inelastic scattering of alpha particles on the clusters of the $$^{9}{\text{Be}}$$ nucleus for determining the contribution from the cluster configurations ( $$^{8}{\text{Be}} + n$$ , $$\alpha + \alpha + n$$ , $$^{5}{\text{He}} + \alpha $$ ) to the $$^{9}{\text{Be}}$$ structure. The kinematic simulation of the $$^{9}{\text{Be}}(\alpha ,\alpha {\kern 1pt} 'n)X$$ and $$^{9}{\text{Be}}(\alpha ,\alpha {\kern 1pt} '\alpha )X$$ reactions shows that detection of the scattered alpha particle in coincidence with the particle from the breakup of a certain excited state of $$^{9}{\text{Be}}$$ allows determining the contribution from different cluster configurations to the structure of those states.

The first excited 1/2+ state in 9Be and 9B

Nuclear states observed around threshold energies provide us with interesting problems associated withthe nuclear cluster structure [1, 2, 3, 4]. The first excited Jπ = 1/2+ state of 9Be [5], which is an α+ α + nBorromean nucleus, is one of the typical examples in light nuclei. This state of 9Be has been observed as asharp peak above the 8Be + n threshold energy in the photo-disintegration cross section of γ+9Be→ α + α+ n [6, 7]. The strength of the peak has a strong influence on the reaction rate of the 9Be synthesis. Weperformed the calculations using an α + α + n three-body model [8, 9] and the complex scaling method(CSM), which well reproduces the observed photo-disintegration cross section. However, the resultindicates that the 1/2+ state shows the s-wave virtual-state character of 8Be+n. In addition to this problem,we discuss a mirror state problem of the first excite 1/2+ state in 9B.

Particle-Hole Cluster Shell Model States in 8Be, a Challenge for Ab-Intio Nuclear Theories

We propose the first application of the Cluster Shell Model (CSM) of Della Rocca and Iachello to particle-hole (p-h) states in 8Be. We demonstrate a few essential features of the CSM in 8Be: 1) All predicted p-h states of the CSM, and only the predicted p-h states, are observed near thresholds and up to 19.5 MeV in 8Be. 2) The states are observed in the predicted order, with positive parity states below negative parity states. 3) Some of the p-h states are already known to have the rotational structure predicted for the deformed p-h states. 4) The rotational structures observed at high excitations in the p-h bands in 8Be, resemble the ground state bands of 8Be, 9Be and 9B, with similar moment of inertia. Based on these observations we contemplate new measurements of the spectroscopy of 8Be at energies above 19.5 MeV, where our knowledge of states in 8Be is scarce. We examine the observed B(M1)s and B(E2)s in these nuclei and contemplate a measurement of the B(E2) of the isobaric Analog transition in 8B. We discuss the observed rotational structure in 8Be as a challenge to ab-initio calculations that searched for “emerging rotational structures at high excitations" in beryllium nuclei, and reveal rotational structure at high excitations in 10Be and 12Be but not in 8Be.

On three-cluster disintegration of 9Be

We study a process of the photodisintegration of some Borromean light nuclei into three clusters. Thisstudy is performed within a three-cluster microscopic model. In Reference [1] this model was applied toobtain parameters of resonance states in 9Be and 9B and to establish their nature. Main aim of the presentinvestigations is to describe the dipole transition probability from the ground state of 9Be to the states ofthree-cluster α+α+n continuum by using the same model. That model exploits the hypersphericalharmonics basis (HHB) and thus reduces many-channel Schrödinger equation to the algebraic matrix(AM) form. The dipole transitions from the ground 3/2- state to the 1/2+ states of three-cluster continuumwere studied in detail. The role of resonance states in three-cluster continuum to this process isinvestigated in detail. The dominant channels with the maximal dipole strength due to the couplingbetween the ground and scattering states are discovered

A New Measurement of 11Be(p,d) Transfer Reaction**Supported by the National Key Research and Development Program of China under Grant No 2018YFA0404403, and the National Natural Science Foundation of China under Grant Nos 11775004 and 11775036.

A new 11Be(p,d) transfer reaction experiment is performed in inverse kinematics with a radioactive 11Be beam at 26.9A MeV. Three low-lying states, namely the 0+ ground state, the 2+ state at Ex = 3.37 MeV, and the multiplet at around 6 MeV in 10Be, are populated by this one-neutron transfer reaction. These three states in 10Be are clearly discriminated from the Q-value spectrum, which is rebuilt from energies and angles of the recoil deuterons in coincidence with 10Be. A spectroscopic factor for each state is extracted by comparing the experimental differential cross sections to the theoretical calculation results using the finite range adiabatic distorted wave approximation method with different global nucleon-nucleus potentials. It is found that the newly extracted spectroscopic factors for the 0+ and 2+ states are consistent with the previous ones, but the factor for the multiplet is smaller than the value in the reference, and the possible reason is discussed.

New results on the 8Be anomaly

Recently, we observed anomalous internal pair creation for the M1 transition depopulating the 18.15 MeV isoscalar 1+ state in 8Be. We observed a significant (σ = 7.37) peak-like deviation from the predicted angular correlation of the e+ e pairs at θ = 140°. To the best of our knowledge no nuclear physics related description of such deviation can be made. However, the deviation can be described by assuming the creation and subsequent decay of a boson with mass of ≈17 MeV. In order to clarify the interpretation, we re-investigated the 8Be anomaly with an improved, and independent setup. We have confirmed the signal of the assumed X(17) particle and constrained its mass (m0c2 = 17.01(16) MeV) and branching ratio compared to the γ-decay (Bx = 6(1) × 10−6).

A new measurement of the intruder configuration in 12Be

A new 11Be(d,p)12Be transfer reaction experiment was carried out in inverse kinematics at 26.9A MeV, with special efforts devoted to the determination of the deuteron target thickness and of the required optical potentials from the present elastic scattering data. In addition a direct measurement of the cross section for the 02+ state was realized by applying an isomer-tagging technique. The s-wave spectroscopic factors of 0.20−0.04+0.03 and 0.41−0.11+0.11 were extracted for the 01+ and 02+ states, respectively, in 12Be. Using the ratio of these spectroscopic factors, together with the previously reported results for the p-wave components, the single-particle component intensities in the bound 0+ states of 12Be were deduced, allowing a direct comparison with the theoretical predictions. It is evidenced that the ground-state configuration of 12Be is dominated by the d-wave intruder, exhibiting a dramatic evolution of the intruding mechanism from 11Be to 12Be, with a persistence of the N=8 magic number broken.

7Li(15N, 14C)8Be reaction at 81 MeV and 14C + 8Be interaction versus that of 13C + 8Be

Angular distributions of the 7Li(15N, 14C)8Be reaction were measured at the energy Elab(15N) = 81 MeV. Data for transfer to the ground and first two excited states in 8Be were acquired as well as to the 14C ground and excited states. The reaction data were analyzed within the coupled-reaction-channels (CRC) method. The required 15N + 7Li entrance channel potential was taken from the 15N + 7Li elastic scattering. The 14C + 8Be potential was found by fitting Woods–Saxon form potentials to those generated by double folded real and imaginary potentials in the region of interaction. These generated potentials were then used in the CRC calculations. Proton transfer dominants this reaction, including to the excited states of 8Be. The reaction dependence on the exit channel potential was examined by using the 13C + 8Be potential previously deduced from the 9Be(12C, 13C)8Be reaction and 14C + 8Be from the 13C(9Be, 8Be)14C reaction.

The α-decay of the Hoyle state in 12C: a new high-precision investigation

The αdecay path of the Hoyle state in 12C (Ex = 7:654MeV) represents one ofthe most challenging questions of modern nuclear physics. Its knowledge can help in theunderstanding of cluster configurations in light nuclei and the possible existence of Bose-Einstein condensates in nuclei. In stars, it is involved in the so-called 3αprocess, wherethe 12C nucleosynthesis occurs. We studied the 14N(d; α2)12C(7:654) reaction at 10:5MeVincident energy to probe its direct decay component. We found, with a precision higherof a factor 5 than any other previous experiment, an almost total absence of direct decaysby-passing the ground state of 8Be. From our analysis, a new upper limit of such decayis found at 0:043% (95% C.L.). Astrophysical 3α process reaction rate calculations haveto be accordingly revised.

High-lying excited states in 10Be from the 9Be(9Be,10Be)8Be reaction

A transfer-reaction experiment of 9Be(9Be, 10Be)8Be was performed at a beam energy of 45 MeV. Excited states in 10Be up to 18.80 MeV are produced using missing mass and invariant mass methods. Most of the observed high-lying resonant states, reconstructed from the α + 6He and t + 7Li decay channels, agree with the previously reported results. In addition, two new resonances at 15.6 and 18.8 MeV are identified from the present measurement. The 18.55 MeV state is found to decay into both the t + 7Lig.s. and t + 7Li* (0.478 MeV) channels, with a relative branching ratio of 0.93 ± 0.33. Further theoretical investigations are encouraged to interpret this new information on cluster structure in neutron-rich light nuclei.

Study of bound states in 10Be by one neutron removal reactions of 11Be

The bound states of 10Be have been studied by removing single neutrons from 11Be nuclei. A 2.8 MeV u–1 beam of 11Be was produced at ISOLDE, CERN and directed on to both proton and deuteron targets inducing one-neutron removal reactions. Charged particles were detected to identify the two reaction channels (d, t) and (p, d), and the individual states in 10Be were identified by gamma detection. All bound states but one were populated and identified in the (d, t) reaction. The combination of REX-ISOLDE and MINIBALL allowed for a clean separation of the high-lying states in 10Be. This is the first time these states have been separated in a reaction experiment. Differential cross sections have been calculated for all the reaction channels and compared to DWBA calculations. Spectroscopic factors are derived and compared to values from the litterature. While the overall agreement between the spectrocopic factors is poor, the ratio between the ground state and the first excited state is in agreement with the previous measured ones. Furthermore, a significant population of the state is observed, which which may indicate the presence of multi-step processes at our beam energy.