Hoyle State Research Articles

The Hoyle State in the Relativistic Dissociation of Light Nuclei

In the context of the search for triples of relativistic $\alpha$-particles in the Hoyle state, the analysis of available data on the dissociation of the nuclei ${}^{12}$C, ${}^{16}$O and ${}^{22}$Ne in the nuclear emulsion was carried out. The Hoyle state is identified by the invariant mass calculated from pair angles of expansion in $\alpha$-triples in the approximation of the conservation of the momentum per nucleon of the parent nucleus. The contribution of the Hoyle state to the dissociation of ${}^{12}$C $\to$ 3$\alpha$ is 11\%. In the case of the coherent dissociation of ${}^{16}$O $\to$ 4$\alpha$ it reaches 22\% when the portion of the channel ${}^{16}$O $\to$ 2${}^{8}$Be is equal to 5\%.

Four α-particle decay of the excited 16O* quasi-projectile in the 16O + 12C reaction at 130 MeV

The four α-particle decay of the excited 16O* quasi-projectile (QP) produced in peripheral 16O + 12C reactions at 130 MeV is studied in detail. The different decay channels leading to the four α-particle final state are reconstructed from an event-by-event analysis of α correlations through the population of intermediate 8Be and 12C resonant states. A small but non-negligible contribution of 8Begs evaporation is observed. The branching ratios of the different evaporation channels are compared to the prediction of an Hauser-Feshbach code (once characteristics of the QP source are extracted from the experimental data), which very accurately reproduces all the inclusive observables of the reaction. However, significative deviations are observed. In particular, the experimental population of the Hoyle state is significantly lower than the predictions of the statistical model, suggesting possible structure effects in the Coulomb barrier and/or in the transmission coefficients.

Experimental investigation of α condensation in light nuclei

Method: To examine signatures of this alpha-condensation, a compound nucleus reaction using 160, 280, and 400 MeV 16O beams impinging on a carbon target was used to investigate the 12C(16O,7a) reaction. This permits a search for near-threshold states in the alpha-conjugate nuclei up to 24Mg. Results: Events up to an alpha-particle multiplicity of 7 were measured and the results were compared to both an Extended Hauser-Feshbach calculation and the Fermi break-up model. The measured multiplicity distribution exceeded that predicted from a sequential decay mechanism and had a better agreement with the multi-particle Fermi break-up model. Examination of how these 7 alpha final states could be reconstructed to form 8Be and 12C(0_2+) showed a quantitative difference in which decay modes were dominant compared to the Fermi break-up model. No new states were observed in 16O, 20Ne, and 24Mg due to the effect of the N-alpha penetrability suppressing the total alpha-particle dissociation decay mode. Conclusion: The reaction mechanism for a high energy compound nucleus reaction can only be described by a hybrid of sequential decay and multi-particle breakup. Highly alpha-clustered states were seen which did not originate from simple binary reaction processes. Direct investigations of near-threshold states in N-alpha systems are inherently impeded by the Coulomb barrier prohibiting the observation of states in the N-alpha decay channel. No evidence of a highly clustered 15.1 MeV state in 16O was observed from (28Si*,12C(0_2+))16O(0_6+) when reconstructing the Hoyle state from 3 alpha-particles. Therefore, no experimental signatures for alpha-condensation were observed.

Nonlocalized clustering and evolution of cluster structure in nuclei

We explain various facets of the THSR (Tohsaki-Horiuchi-Schuck-R\"opke) wave function. We first discuss the THSR wave function as a wave function of cluster-gas state, since the THSR wave function was originally introduced to elucidate the 3$\alpha$-condensate-like character of the Hoyle state ($0_2^+$ state) of $^{12}$C. We briefly review the cluster-model studies of the Hoyle state in 1970's in order to explain how there emerged the idea to assign the $\alpha$ condensate character to the Hoyle state. We then explain that the THSR wave function can describe very well also non-gaslike ordinary cluster states with spatial localization of clusters. This fact means that the dynamical motion of clusters is of nonlocalized nature just as in gas-like states of clusters and the localization of clusters is due to the inter-cluster Pauli principle which is against the close approach of two clusters. The nonlocalized cluster dynamics is formulated by the container model of cluster dynamics. The container model describes gas-like state and non-gaslike states as the solutions of the Hill-Wheeler equation with respect to the size parameter of THSR wave function which is just the size parameter of the container. When we notice that fact that the THSR wave function with the smallest value of size parameter is equivalent to the shell-model wave function, we see that the container model describes the evolution of cluster structure from the ground state with shell-model structure up to the gas-like cluster state via ordinary non-gaslike cluster states. For the description of various cluster structure, more generation of THSR wave function have been introduced and we review some typical examples with their actual applications.

Theoretical approaches to the 3α break-up of 12C

Two recent experiments have indicated that the break-up of the 12C Hoyle state is dominated by the sequential 8Be(g.s.) + α decay channel. The rare direct 3α decay was found to contribute with a branching ratio of less than 0.047% (95% C.L.). However, the ability of experimentalists to successfully disentangle these two competing decay channels relies on accurate theoretical predictions of how they each manifest in phase space distribution of the three break-up α-particles. The following paper reviews the current theoretical approaches to calculating the break-up of the Hoyle state and introduces a semi-classical WKB approach, which adequately reproduces the results of more sophisticated calculations. It is proposed that a more accurate upper limit on this branching ratio may be obtained if these new theoretical results are taken into account when analysing experimental data.

New high precision study on the decay width of the Hoyle state in 12C

Precise estimation of the rare direct 3α decay of the Hoyle state of 12C has been made to unveil its unusual α-cluster configurations ranging from linear 3α chain structure to diffuse Bose gas as well as Bose Einstein condensate. The present new high precision, nearly zero background experimental study with 1.6×105 Hoyle events has converged on the upper limit for direct decay at ∼0.019% with 95% confidence limit, which is more than a factor of 2 lower than the limit obtained in the previous studies.

Strongly resonating bosons in hot nuclei

When two heavy ions near the Fermi energy collide, a warm and low-density region can form in which fragments appear. This region is mainly dominated by proton (p) and alpha particles. In such an environment, the alphas interact with each other, and especially through strong resonances, form complex systems such as 8Be and 12C. Our experiments show that in the reactions 70(64)Zn(64Ni)+70(64)Zn(64Ni) at E/A=35 MeV/nucleon levels of 8Be appear around relative energies Eij=0.092 MeV, 3.03 MeV as well as above 10 MeV and 100 MeV. For the 3 alpha systems, multi resonance processes give rise to excited levels of 12C. In particular, the Hoyle state at 7.654 MeV excitation energy shows a decay component through the ground state of 8Be and also shows components where two different alpha couples are at relative energies consistent with the ground state of 8Be at the same time. A component where the three alpha relative energies are consistent with the ground state of 8Be (i.e., E12=E13=E23=0.092 MeV) is also observed at the 7.458 MeV excitation energy, which was suggested as an Efimov state.

Cluster structures in C12 from global energy density functionals

Spectroscopic properties of low-lying states and cluster structures in $^{12}$C are analyzed in a "beyond mean-field framework" based on global energy density functionals (EDFs). To build symmetry-conserving collective states, axially-symmetric and reflection-asymmetric solutions of the relativistic Hartree-Bogoliubov equations are first projected onto good values of angular momentum, particle number, and parity. Configuration mixing is implemented using the generator coordinate method formalism. It is shown that such a global microscopic approach, based on a relativistic EDF, can account for the main spectroscopic features of $^{12}$C, including the ground-state and linear-chain bands as well as, to a certain approximation, the excitation energy of the Hoyle state. The calculated form factors reproduce reasonably well the available experimental values, and display an accuracy comparable to that of dedicated microscopic cluster models.

Four α-particles as a final state of 16O* Quasi Projectile decay

Four α-particles as a final state of 16O* quasi-projectile decayproduced in peripheral 16O+12C reactions at 130 MeV is thoroughly studied. The differentdecay channels leading to the four α-particles final state are reconstructed by carrying out an event-by-event analysis of α correlations in the population of intermediate 8Be and 12C. Although small, a non negligible contribution due to 8Begs evaporation is found.A comparison between predictions of an accurate Hauser-Feshbach decay code and branching ratios of the different decay channels is performed. Significant deviations are observed, among these the Hoyle state population which is considerably lower than the one predicted according to the statistical model, thus suggesting possible structure effects in the Coulomb barrier and/or in the transmission coefficients.

Three-body description of 12C: From the hyperspherical formulation to the algebraic cluster model and its application to α + 12C inelasticscattering

Form factors for α+12C inelastic scattering are obtained within two theoretical (α+α+α) approaches:The hyperspherical framework for three identical bosons, and the algebraic cluster model assuming the D3h symmetry of an equilateral triangle subject to rotations and vibrations. Results show a good agreement, with form factors involving the Hoyle state having a slightly larger extension within the hyperspherical approach. Coupled-channel calculations using these form factors are ongoing.

Application of Nuclear Track Emulsion in Search for the Hoyle State in Dissociation of Relativistic 12C Nuclei

In dissociation in nuclear track emulsion of 4.5 and 1 A GeV/c12C nuclei, the formation of triplets of α particles in the Hoyle state (the second excited state 0+) is observed. This state is identified by the invariant mass, calculated from pair angles in the α triples in approximation of conservation of momentum per nucleon of the parent nucleus. An estimate of the contribution of the Hoyle state to the dissociation of 12C→ 3α is 10–15%.

Nuclear track emulsion in search for the Hoyle-state in dissociation of relativistic 12C nuclei

• Nuclear track emulsion is applied to identify the Hoyle’s state in dissociation of relativistic 12 C nuclei. • The Hoyle's state events are identified by invariant mass values calculated on a basis of most prices measurements of α-particle emission angles in approximation of conservation of momentum per nucleon of the parent nucleus. • An estimate of the Hoyle's state contribution to the relativistic dissociation 12 C → 3α is 10–15%.

Explicit inclusion of the spin-orbit contribution in the Tohsaki-Horiuchi-Schuck-Röpke wave function

The Tohsaki-Horiuchi-Schuck-Roepke (THSR) wave function has been successfully used for the studies of gas-like nature of alpha clusters in various nuclei including the so-called Hoyle state of 12C and four alpha states of 16O. In standard alpha cluster models, however, each alpha cluster wave function has spin zero because of its spatial symmetry and antisymmetrization effect. Thus the non-central interactions do not contribute, and this situation is the same in the THSR wave function. In this work, the spin-orbit contribution, which is found to be quite important at short alpha-alpha distances, is taken into account in the THSR wave function by combing it with antisymmetrized quasi cluster model (AQCM). The application to 12C is presented. The multi-integration in the original THSR wave function is carried out by using Monte Carlo technique, which is called Monte Carlo THSR wave function. For the nucleon-nucleon interaction, the Tohsaki interaction, which contains finite-range three-body terms and simultaneously reproduces the saturation properties of nuclear systems, the alpha-alpha scattering phase shift, and the size and binding energy of 4He, is adopted.

Bose-Einstein condensation of α clusters and new soft mode in C12 – Fe52 4N nuclei in a field-theoretical superfluid cluster model

Bose-Einstein condensation of alpha clusters in light and medium-heavy nuclei is studied in the frame of the field theoretical superfluid cluster model. The order parameter of the phase transition from the Wigner phase to the Nambu-Goldstone phase is a superfluid amplitude, square of the moduli of which is the superfluid density distribution. The zero mode operators due to the spontaneous symmetry breaking of the global phase in the finite number of alpha clusters are rigorously treated. The theory is systematically applied to N alpha nuclei from12C-52Fe at various condensation rates. In 12C it is found that the energy levels of the gas-like well-developed alpha cluster states above the Hoyle state are reproduced well in agreement with experiment for realistic condensation rates of alpha clusters. The electric E2 and E0 transitions are calculated and found to be sensitive to the condensation rates. The profound raison d'etre of the alpha cluster gas-like states above the Hoyle state, whose structure has been interpreted geometrically in the nuclear models without the order parameter such as the cluster models or ab initio calculations, is revealed. It is found that in addition to the Bogoliubov-de Gennes vibrational mode states collective states of the zero mode operators appear systematically at low excitation energies from the N alpha threshold energy. These collective states, new-type soft modes in nuclei due to the Bose-Einstein condensation of the alpha clusters, emerge systematically in light and medium-heavy mass regions and are also located at high excitation energies from the ground state in contrast to the traditional concept of soft mode in the low excitation energy region.

Searching for states analogous to the C12 Hoyle state in heavier nuclei using the thick target inverse kinematics technique

Identification of alpha cluster states analogous to the 12C Hoyle state in heavier alpha- conjugate nuclei can provide tests of the existence of alpha condensates in nuclei. Such states are predicted for 16O, 20Ne, 24Mg, 28Si etc. at excitation energies slightly above the multi-alpha particle decay threshold, but have not yet been experimentally identified. The Thick Target Inverse Kinematics (TTIK) technique can be used to study the breakup of excited self-conjugate nuclei into many alpha particles. The reaction 20Ne+{\alpha} was studied using a 20Ne beam at 12 MeV/nucleon from the K150 cyclotron at Texas A&M University. The TTIK method was used to study both single {\alpha}-particle emission and multiple {\alpha}-particle decays. Events with alpha multiplicity up to four were analyzed. The analysis of the three {\alpha} - particle emission data allowed the identification of the Hoyle state and other 12C excited states decaying into three alpha particles. The results are shown and compared with other data available in the literature. Although the statistics for events with alpha multiplicity four is low, the data show a structure at about 15.2 MeV that could indicate the existence in 16O of a state analogous to the 12C Hoyle state. This structure is confirmed by the re-analysis of alpha multiplicity four events from a previous experiment performed at 9.7 MeV/nucleon with a similar setup but lower granularity. Moreover, the reconstructed excitation energy of 24Mg for these events peaks at around 34 MeV, very close to the predicted excitation energy for an excited state analogous to the 12C Hoyle state in 24Mg.

Search for the Hoyle State in Dissociation of Relativistic 12C Nuclei

Search for the Hoyle State in Dissociation of Relativistic 12C Nuclei

Nuclear Track Emulsion in Search for the Hoyle’s State in Dissociation of Relativistic 12C Nuclei

Study of production of ensembles of alpha-particle triples associated with the Hoyle state (the second excited state 0+ 2 of the 12 C nucleus) in peripheral dissociation of relativistic 12C nuclei is started. Stacks of pellicles of nuclear track emulsion exposed to 12C of energy from hundreds MeV to few GeV per nucleon serve as the material of the study. The Hoyle state decays are reconstructed via measurements of emission angles of α-particles with accuracy that allows one to identify the unstable 8Be nucleus. A role in the Hoyle state of alpha-particle bonds corresponding to 8Be is determined.

12C within the Semimicroscopic Algebraic Cluster Model

The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 12C as a system of three alpha- clusters. The microscopic model space, which observes the Pauli-Exclusion-Principle (PEP), is constructed. It is shown that the 12C nucleus can effectively be treated as a two-cluster system 8Be+alpha. The experimental spectrum is well reproduced. The geometrical mapping is discussed and it is shown that the ground state must correspond to a triangular structure, which is in agreement with other microscopic calculations. The non-zero B(E2; 0_2+ --> 2_1+) transition requires a mixing of SU(3) irreducible representations (irreps) whose consequences are discussed. The Hoyle state turns out to contain large shell excitations. The results are compared to another phenomenological model, which assumes a triangular structure and, using simple symmetry arguments, can reproduce the states observed at low energy. This model does not observe the PEP and one objective of our contribution is to verify the extend of importance of the PEP.

Investigation of exotic states of 13C at low energy

The differential cross-sections of the elastic and inelastic [Formula: see text]C scattering have been measured at E[Formula: see text][Formula: see text]MeV. The radii of the exited states: 3.09 [Formula: see text] and 8.86 [Formula: see text] MeV were determined using the Modified Diffraction Model. The radii of these excited states are larger than that of the ground state of [Formula: see text]C, confirming the suggestion that the 8.86 [Formula: see text] MeV state could be an analog of the Hoyle state in [Formula: see text]C and the 3.09 [Formula: see text] MeV state has a neutron halo. The possibility of coexistence of various exotic states in the structure of the [Formula: see text]C nucleus is shown.

Decay modes of the Hoyle state in [formula omitted

Recent experimental results give an upper limit less than 0.043% (95% C.L.) to the direct decay of the Hoyle state into 3α respect to the sequential decay into Be8+α. We performed one and two-dimensional tunneling calculations to estimate such a ratio and found it to be more than one order of magnitude smaller than experiment depending on the range of the nuclear force. This is within high statistics experimental capabilities. Our results can also be tested by measuring the decay modes of high excitation energy states of 12C where the ratio of direct to sequential decay might reach 10% at E⁎(12C)=10.3 MeV. The link between a Bose Einstein Condensate (BEC) and the direct decay of the Hoyle state is also addressed. We discuss a hypothetical ‘Efimov state’ at E⁎(12C)=7.458 MeV, which would mainly sequentially decay with 3α of equal energies: a counterintuitive result of tunneling. Such a state, if it would exist, is at least 8 orders of magnitude less probable than the Hoyle's, thus below the sensitivity of recent and past experiments.