High-lying excited states in <Superscript>10</Superscript>Be from the <Superscript>9</Superscript>Be(<Superscript>9</Superscript>Be,<Superscript>10</Superscript>Be)<Superscript>8</Superscript>Be 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 + ⁷Li_g.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.     

Fragmentation channels of relativistic 7Be nuclei in peripheral interactions

At the JINR Nuclotron, ⁷Li nuclei are accelerated. The charge-exchange reaction involving these nuclei at an external target provides a secondary 1.23-A-GeV ⁷Be beam. This beam is used to irradiate emulsion chambers. The mean free path λ_inel(⁷Be) = 14.0 ± 0.8 cm for inelastic ⁷Be interactions in an emulsion coincides within the errors with those for ⁶Li and ⁷Li nuclei. More than 10% of the ⁷Be events are associated with the peripheral interactions in which the total charge of the relativistic fragments is equal to the charge of the ⁷Be nucleus and in which charged mesons are not produced. An unusual ratio of the helium isotopes is revealed in the composition of the doubly charged fragments of the ⁷Be nuclei: the number of the ³He fragments is twice as large as that of the ⁴He fragments. Each of 50% of peripheral interaction events includes two doubly charged fragments. The channels of the ⁷Be fragmentation into charged fragments are presented. In 50% of events, the ⁷Be fragmentation occurs only into charged fragments without the emission of neutrons. The ⁴He + ³He channel dominates, whereas each of the ⁴He + d + p and ⁶Li + p channels constitutes 10%. Two events without neutron emission are observed in the ³He + t + p and ³He + d + d three-body channels. The mean free path for the coherent dissociation of relativistic ⁷Be nuclei into ⁴He + ³He is equal to 7 ± 1 m. The main features of the fragmentation of relativistic ⁷Be nuclei in such peripheral interactions are explained by the ³He + ⁴He two-cluster structure of the ⁷Be nucleus.     

Solar neutrinos and a proposed level in Be

Arguments are given against the existence of a narrow 0⁺ level in ⁶Be just above the ³He+³He threshold, which has been postulated recently in order to explain the low observed flux of solar neutrinos.     

Clustering Features of the 7Be Nucleus in Relativistic Fragmentation

Charge topology of fragmentation of 1.2 A GeV ⁷Be nuclei in nuclear track emulsion is presented. The dissociation channels ⁴He + ³He, 2³He+ n, ⁴He + 2¹H are considered in detail. It is established that the events ⁶Be + n amount about to 27 % in the channel ⁴He + 2¹H.     

Interaction at the barrier in the systems 9, 10, 11Be + 209Bi: Well-established facts and open questions

The experimental data relative to the interaction for the systems ^{9, 10, 11}Be + ²⁰⁹Bi at the Coulomb barrier are critically discussed and compared also with present theories. The break-up (BU) of the two loosely bound projectiles, ^{9, 11}Be, seems to influence the fusion process by “hindering” the fusion cross-sections; but, contrary to expectations, the ¹¹Be halo structure has no influence, since no “enhancement” is evident from the existing data. Attempt to describe simultaneously all the ⁹Be + ²⁰⁹Bi system data: fusion, elastic scattering and BU, within a coupled-channel (CC) approach is only partly successful. It is important, from a theoretical viewpoint, to include in the CC formalism as well as possible the BU process both to continuum states as well as to unbound resonances. More accurate and well-focused experiments are also necessary to pin down this problem. Received: 1 May 2001 / Accepted: 4 December 2001     

Determination of the cluster spectroscopic factor of the 10.3 MeV state in 12Be

From an inelastic excitation and breakup experiment with a ¹²Be beam at 29 MeV/u, a large ⁴He+⁸He cluster decay width of 1.1(2) MeV is determined for a state at an excitation energy of 10.3 MeV and with a spin parity of 0+. By using the R-matrix analysis, a cluster spectroscopic factor of 0.53(10) is extracted from the cluster partial width, providing a strong support for the clustering structure in ¹²Be. A specially designed zero-degree telescope played an essential role in the present experiment and has been demonstrated to be a promising tool in future studies of the molecular-like resonances near the cluster separation threshold.     

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.     

Production of 6He and 9Be by radiative capture and four-body recombination

In this work we estimate the production rates for the three-body radiative capture processes α + n + n → ⁶He + γ and α + α + n → ⁹Be + γ, as well as the four-body recombination reactions α + α + n + n → ⁶He + α, ^α + n + n + n → ⁶He + n, α + α + n + n → ⁹Be + n and α + α + α + n → ^BeBe + α. These processes compete as a source of ⁶He and ⁹Be. The hyperspherical adiabatic expansion method is used. With this method no assumption is made about the capture mechanism. Both sequential and direct capture are included. The production rates for the radiative and the four-body recombination processes are found to be comparable for a mass density of about 10⁷g/cm³ ( ～ 10³⁰ neutrons/cm³) and temperatures of a few GK.     

Resonant structure observed in the 3He(τ, γ)6Be capture reaction

The ³He(τ,γ)⁶Be capture reaction has been studied for ³He bombarding energies from 12 to 27, MeV. Transitions to the first excited state in ⁶Be(T = 1, 2⁺) are readily seen. Transitions to the ground state in ⁶Be (T = 1, 0⁺) are very weak and their presence could not be ascertained. The 90° excitation function for these transitions shows a broad maximum centered at E_τ = 23 ±1 MeV. This is interpreted as a resonance in the compound nucleus ⁶Be at E_x = 23.0±0.5 MeV with a configuration other than ³He+³He. These results are compared with other experimental work as well as with theoretical predictions.     

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.     

Microscopic three-cluster study of the low-energy 9 Be photodisintegration

The ⁹Be and ⁹B nuclei are investigated in a microscopic three-cluster model involving α + α + n (or α + α + p) configurations. The ⁸Be (0 ⁺ , 2 ⁺ ) + n and ⁵He (3/2 ^- , 1/2 ^- ) + α (or mirror) channels are included by taking account of the unstable nature of ⁸Be and ⁵He. Spectroscopic properties of ⁹Be and ⁹B are analyzed. We show that the ⁵He + α configurations cannot be neglected to derive accurate results. The ⁹Be(γ,αα)n photodisintegration cross-section is shown to be mainly determined by ⁸Be + n channels at low energies, but ⁵He + α channels become important beyond E _γ≈ 4 MeV. Received: 7 September 2001 / Accepted: 19 November 2001     

Manifestation of the cluster structure of the <Superscript>9</Superscript>Be nucleus in direct nuclear reactions

Specific features of ⁴He interaction with light ⁹Be nuclei are studied. The potential of ⁴He–⁹Be interaction is calculated within the framework of the double folding model using the wave function of the ground state of the ⁹Be nucleus constructed in the three-cluster α + α + n approximation. The differential cross sections of elastic and inelastic ⁴He–⁹Be scattering and single-nucleon transfer in the intermediate range of energies are calculated. Comparative analysis of experimental and calculated results demonstrate their good agreement, indicating that the model assumptions on the cluster structure of ⁹Be nucleus are valid.     

Features of the 9Be → 2He fragmentation in an emulsion for an energy of 1.2 GeV per nucleon

The results of investigation of the fragmentation of relativistic nuclei ⁹Be in an emulsion, which is accompanied by the formation of two 1.2-A-GeV He fragments, are presented. The angular measurements of the ⁹Be → 2He events are analyzed. The ⁹Be → ⁸Be + n fragmentation channel with the decay of ⁸Be from the ground (0⁺) and first excited (2⁺) states into a pair of α particles appears to be dominant.     

Total reaction and transfer cross sections for 11B + 9Be and 13C + 9Be reactions at low energies

The total reaction cross sections for ¹¹B + ⁹Be and ¹³C + ⁹Be have been measured by the total γ-ray yield method over the energy intervals E_c.m. = 1.4–4.4 MeV and E_c.m. = 2.0–5.2 MeV, respectively. The cross sections for the neutron transfer reactions ¹¹B(⁹Be, ⁸Be)¹²B, leading to the ¹²B 0.953 and 1.674 MeV states, and ¹³C(⁹Be, ⁸Be)¹⁴C, leading to the ¹⁴C 6.094, 6.728 and 6.902 MeV states, have been obtained from the yields of the characteristic γ-rays. The α-transfer reaction ¹¹B(⁹Be, ⁵He)¹⁵N, leading to many unresolved ¹⁵N states, has been observed with large cross section. There is, however, no evidence for the ¹³C(⁹Be, ⁵He)¹⁷O transfer process in the ¹⁷O + nα channels. This different behaviour of the ¹¹B + ⁹Be and ¹³C + ⁹Be systems seems to indicate that the α-transfer reaction at sub-barrier energies is not a direct transfer process, and that it probably occurs via molecular state formation.     

Two-center molecular states in9B,9Be,10Be,and10B

The molecular states in the mass 9 and 10 nuclei, which consist of two α-particles plus one or two valence nucleons (protons or neutrons) are discussed. Arguments for the existence of two-center dimers as excited states in¹⁰Be and corresponding resonances (p+⁹Be) in¹⁰B are given. The latter states are observed as anomalous (non statistical) population in the final state interactions in thep+⁹Be channel in various heavy ion collisions. With the establishment of two-center states (dimers) based on the αα-potential and a localized binding via two nucleons in¹⁰Be, the existence of more extended structures (multimers) by adding (α2n) structures to¹⁰Be* is postulated. Generally clustering intoα-particles and nucleons in terms of molecular states is expected to occur at excitation energies close to the threshold for these substructures in analogy to the clustering rules of Ikeda forα-particle nuclei. Consequences to clustering properties of neutron rich nuclei are discussed.     

Use of supersymmetric isospectral formalism to realistic quantum many-body problems

We propose a novel mathematical approach for the calculation of resonances in weakly bound systems. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features can be generated. For systems having no bound ground state, an isospectral potential with a bound state in the continuum is possible. The quasi-bound state in the original shallow potential will be effectively trapped in the deep well of the isospectral family, facilitating more accurate calculation of resonance energy. Application to ⁶He, ⁶Li and ⁶Be yield excellent results. Another application is the calculation of Efimov states in weakly bound threebody system. We present the result of ⁴He trimer, where the first excited state is claimed to be an Efimov state.     

Trinucleon cluster structure at high-excitation energies in A=6 nuclei

Trinucleon molecular structures in ⁶He and ⁶Be were investigated by using the ⁶Li(⁷Li, ⁷Be)⁶He reaction at 455 MeV and ⁶Li(³He, t)⁶Be reaction at 450 MeV, respectively. Binary decays into t + t from a broad state at E _x =18.0±1.0 MeV in ⁶He and into ³He + ³He from one at E _x =18.0±1.2 MeV in ⁶Be, respectively, were observed by measuring trinucleon cluster decays in coincidence with reaction particles. The branching ratios for binary decay were estimated to be about 0.7 for ⁶He and ⁶Be. These large branching ratios show that a trinucleon cluster state exists as an isobaric partner around E _x =18 MeV in ⁶He and ⁶Be.     

Spectroscopic Measurement in 9He and 12Be

Spectroscopy for neutron-rich nuclei ⁹He and ¹²Be has been performed by means of heavy-ion double charge exchange (HIDCX) (¹⁸O, ¹⁸Ne) reaction on stable target nuclei ⁹Be and ¹²C, respectively. Several clear peaks in ¹²Be at low excitation energy region even above neutron separation energy have been observed in one-shot measurement, whereas no prominent signals of ⁹He have been observed owing to the small cross section. It is shown that the HIDCX reaction is a new powerful spectroscopic tool for study of unstable neutron-rich nuclei.     

Resonances in A=6 Nuclei: Use of Supersymmetric Quantum Mechanics

We propose a novel theoretical technique for the calculation of resonances at low excitation energies in weakly bound systems. Starting from an effective potential, supersymmetric quantum mechanics can be successfully used to generate families of isospectral potentials having desirable and adjustable properties. For resonance states, for which there is no bound ground state of the same spin-parity, one can construct an isospectral potential with a bound state in the continuum (BIC). The potential looks quite different but is strictly isospectral with the original one. The quasi-bound state in the original shallow potential will be effectively trapped in the deep well of the isospectral family facilitating an easier and more accurate calculation of the resonance energy. Application to ⁶He, ⁶Be, and ⁶Li systems yields quite accurate results. The beauty of our technique: We get both the bound ground state and the resonances by a single technique and using the same potential.     

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.