States In 12C Research Articles

Unbound states in 12C populated by $\gamma$ γ -decay of the $(J^{\pi},T) = (2^{+},1)$ ( J π , T ) = ( 2 + , 1 ) 16.11 MeV state

The reaction $^{11}\textrm{B}+p$ has been used to populate the $(J^\pi,T) = (2^+,1)$ state at an excitation energy of 16.11 MeV in $^{12}$C. $\gamma$-decay to unbound states in $^{12}$C are identified from analysis of the decay of the populated daughter states. Due to a new technique, $\gamma$-decay to the 10.8 MeV 1$^-$ state is observed for the first time, and transitions to the 9.64 MeV (3$^-$) and 12.71 MeV (1$^+$) are confirmed. Unresolved transitions to natural parity strength at 10 MeV and 11.5-13 MeV are also observed. For all transitions partial widths are deduced

Cluster decay of the high-lying excited states in 14C**Supported by the 973 Program of China (2013 CB834402) and National Natural Science Foundation of China (11275011, 11535004)

A cluster-transfer experiment of 9Be(9Be,14C → α+10Be)α at an incident energy of 45 MeV was carried out in order to investigate the molecular structure in high-lying resonant states in 14C. This reaction is of extremely large Q-value, making it an excellent case to select the reaction mechanism and the final states in outgoing nuclei. The high-lying resonances in 14C are reconstructed for three sets of well discriminated final states in 10Be. The results confirm the previous decay measurements with clearly improved decay-channel selections and also show a new state at 23.5(1) MeV. The resonant states at 22.4(3) and 24.0(3) MeV decay primarily into the typical molecular states at about 6 MeV in 10Be, indicating a well developed cluster structure in these high-lying states in 14C. Further measurements of more states of this kind are suggested.

Complete kinematical study of the 3 $\alpha$ breakup of the 16.11 MeV state in 12C

The reaction $^{11}B+p$ has been used to populate the $(J^{\pi},T)=(2^+,1)$ state at an excitation energy of 16.11 MeV in $^{12}$C, and the breakup of the state into three $\alpha$ particles has been studied in complete kinematics. A two-step breakup model which includes interference effects is found to provide the most accurate description of the experimental data. The branching ratio to the ground state of $^8$Be is determined to be 5.1(5)% in agreement with previous findings, but more precise by a factor of two, while the decay to the first-excited state in $^8$Be is found to be dominated by $d$-wave emission.

Monopole excitation of the Hoyle state and linear-chain state inC12

Background: Two new $J^\pi=0^+$ states are recently observed around a few MeV above the Hoyle state (the second $0^+$ state in 12C). The characters of them are only poorly discussed in theory and are still mysterious. Purpose: I give for the first time a comprehensive understanding of the structures of the $0^+$ states by analyzing their wave functions, and discuss relationship with the Hoyle state, similarities, and differences between the states. Method: I extend a microscopic $\alpha$-cluster model called Tohsaki-Horiuchi-Schuck-R\"opke (THSR) wave function so as to incorporate $2\alpha+\alpha$ asymmetric configuration explicitly. The so-called $r^2$-constraint method to effectively eliminate spurious continuum components is also used. Results: The $0_3^+$ state is shown to have a very large squared overlap with a single configuration of the extended THSR wave function in an orthogonal space to the Hoyle state as well as to the ground state. The $0_4^+$ state has a maximal squared overlap with a single extended THSR wave function with an extremely prolately-deformed shape. Conclusions: The $0_3^+$ state appears as a family of the Hoyle state to have a higher nodal structure in the internal motions of the $3\alpha$ clusters, due to the orthogonalization to the Hoyle state. The $0_4^+$ state dominantly has a linear-chain structure, where the $3\alpha$ clusters move freely in a non-localized way, like a one-dimensional gas of the $3\alpha$ clusters.

Nuclear states with anomalously large radius (size isomers)

Methods of determination of the nuclear excited state radii are discussed together with the recently obtained data on the states of some light nuclei having abnormally large radii (size isomers). It is shown that such states include excited neutron-halo states in 9Be, 11Be, and 13C and some alpha-cluster states in 12C, 11B, and 13C. Among the latter ones, there is the well-known Hoyle state in 12C—the structure of this state exhibit rudimentary features of alpha-particle states.

The cluster and single-particle states in 13C (α,α)13C reactions

The excitation functions of elastic scattering of 13C on alpha particle have been measured using the thick-target inverse kinematic method at the heavy ion DC-60 cyclotron. The helium gas was used as a target and also as a degrader to stop the beam. New data (including 180°degree) of the resonances close to the threshold in 17O have been obtained.

Rotational bands in 11B and identification of diluted states

Differential cross-sections of the 11B + α inelastic scattering at E(α) = 65 leading to the most of the known 11B states at the excitation energies up to 14 MeV were measured. The data analysis was done by DWBA and in some cases by the modified diffraction model allowing determining the radii of the excited states. The radii of the states with excitation energies less than ∼ 7 MeV with the accuracy not less than 0.1-0.15 fm coincide with the radius of the ground state. This result is consistent with the traditional view of the shell structure of the low-lying states in 11B. Most of the observed high-energy excited states are distributed among four rotational bands. The moments of inertia of band states are close to the moment of inertia of the Hoyle state of 12C. The calculated radii, related to these bands, are 0.7 - 1.0 fm larger than the radius of the ground state, and are close to the radius of the Hoyle state. These results are in agreement with existing predictions about various cluster structure of 11B at high excitation energies. The state with the excitation energy 12.56 MeV, Iπ = 1/2+, T = 1/2 and the root mean square radius R ∼ 6 fm predicted in the frame of the alpha condensate hypothesis was not found.

The 12C* Hoyle state in the inelastic 12C + 12C reaction and in 24Mg* decay

The reaction 12C + 12C at 95 MeV has been studied at the Legnaro Laboratories of INFN with the GARFIELD + RCo apparatus. Data have been analyzed in order to investigate the decay of the Hoyle state of 12C*. Two different data selections have been made. The first one corresponds to peripheral binary collisions where the quasi-projectile is excited to the Hoyle state and the target has been left in the ground state. The second selection allows for studying central events with the formation of a 24Mg* and the Hoyle state is obtained as a step of the decay chain. The characteristics of the Hoyle state decay are very similar in the two samples and point to a mainly sequential decay through the population of an intermediate 8Begs, with a small contribution (∼1.1%) from simultaneous three α-particle processes.

The Prototype Active-Target Time-Projection Chamber used with TwinSol radioactive-ion beams

The study of low-energy reactions with radioactive-ion beams has been greatly enhanced by the recent use of active-target detectors, which have high efficiency and low thresholds to detect low-energy charged-particle decays. Both of these features have been used in experiments with the Prototype Active-Target Time-Projection Chamber to study α-cluster structure in unstable nuclei and 3-body charged-particle decays after implantation. Predicted α-cluster structures in 14C were probed using resonant α scattering and the nature of the 3-α breakup of the 02+ Hoyle state in 12C after the beta decay of 12N and 12B was studied. These experiments used in-flight radioactive-ion beams that were produced using the dual superconducting solenoid magnets TwinSol at the University of Notre Dame. Preliminary results from these experiments as well as the development of future radioactive beams to be used in conjunction with the PAT-TPC are presented.

Analogues of the exotic Hoyle state in the 12C nucleus

Experimental data on inelastic scattering of alpha particles by the 11B, 12C, and 13C nuclei are analyzed using the modified diffraction model and the radii of these nuclei in some “abnormal” excited states are found. It is shown that the 0 2 + (7.65 MeV) Hoyle state in the 12C nucleus is the base state for a new 0 2 + –2 2 + –4 2 + rotational band (in addition to the ground-state band), in which the third member is the discovered 4 2 + (13.75 MeV) state. The radii of the 12C nucleus in the above-mentioned three states are 25–30% larger than its ground state radius. It is found that the radii of the 1/2– (8.86 MeV) state in the 13C nucleus and the 3/2– (8.56 MeV) state in the 11B nucleus are close to the radius of the Hoyle state in 12C and that a similar rotational band is based on the 8.56 MeV state. The above 13C and 11B states can be regarded as analogues of the Hoyle state. The prediction of the alpha-condensation model that a similar analogue in 11B is the 12.56 MeV state with a radius that is comparable with the nuclear radius of uranium was not confirmed.

Three-Body Calculation of 4He(αα,γ)12C Reaction at Stellar Energies**Supported by the University of Birjand.

The triple-alpha reaction is the key to our understanding about the nucleosynthesis and the observed abundance of 12C in stars. On the basis of our model, the triple-alpha radiative capture process is studied by using the three-body Faddeev approach as well as two- and three-body electromagnetic currents. The bound and resonance states of 12C are calculated via an inverse process: three-α photodisintegration of a 12C nucleus.

Cluster states and container picture in light nuclei, and triple-alpha reaction rate

The excited states in 12C are investigated by using an extended version of the so- called Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function, where both the 3α condensate and 8Be + α cluster asymptotic configurations are included. We focus on the structures of the “Hoyle band” states, 2+2, and 4+2 states, which are recently observed above the Hoyle state, and of the 0+3 and 0+4 states, which are also quite recently identified in experiment. We show that the Hoyle band is not simply considered to be the 8Be(0+) + α rotation as suggested by previous cluster model calculations, nor to be a rotation of a rigid-body triangle-shaped object composed of the 3α particles. We also discuss the rate of the triple-alpha radiative capture reaction, applyng the imaginary-time method. Results of the triple-alpha reaction rate are consistent with NACRE rate for both high (≈ 109K) and low (≈ 107 K) temperatures. We show that the rate of the imaginary-time calculation in coupled-channels approach has a large enhancement for low temperatures if we truncate the number of channels.

Emergent symmetries in atomic nuclei from first principles

An innovative symmetry-guided approach and its applications to light and intermediate-mass nuclei is discussed. This approach, with Sp(3, R) the underpinning group, is based on our recent remarkable finding, namely, we have identified the symplectic Sp(3,R) as an approximate symmetry for low-energy nuclear dynamics. This study presents the results of two complementary studies, one that utilizes realistic nucleon-nucleon interactions and unveils symmetries inherent to nuclear dynamics from first principles (or ab initio), and another study, which selects important components of the nuclear interaction to explain the primary physics responsible for emergent phenomena, such as enhanced collectivity and alpha clusters. In particular, within this symmetry-guided framework, ab initio applications of the theory to light nuclei reveal the emergence of a simple orderly pattern from first principles. This provides a strategy for determining the nature of bound states of nuclei in terms of a relatively small fraction of the complete shell-model space, which, in turn, can be used to explore ultra-large model spaces for a description of alpha-cluster and highly deformed structures together with associated rotations. We find that by using only a fraction of the model space extended far beyond current no-core shell-model limits and a long-range interaction that respects the symmetries in play, the outcome reproduces characteristic features of the low-lying 0+ states in 12C (including the elusive Hoyle state of importance to astrophysics) and agrees with ab initio results in smaller spaces. For these states, we offer a novel perspective emerging out of no-core shell-model considerations, including a discussion of associated nuclear deformation, matter radii, and density distribution. The framework we find is also extensible beyond 12C, namely, to the low-lying 0+ states of 8Be as well as the ground-state rotational band of Ne, Mg, and Si isotopes.

Triangular D3h Symmetry in the Rotation-Vibration Spectrum of 12C

Our recent measurements of new states in 12C including the second 2+ at 10 MeV and the high spin 5− state at 22.4 MeV allow us to study the Rotation-Vibration spectrum of 12C from which evidence for a new (D3h) geometrical symmetry emerges. The data fit very well to the predicted (ground state) rotational band of an oblate equilateral triangular spinning top with a D3h symmetry characterized by the sequence of states: 0+, 2+, 3−, 4±, 5− with almost degenerate 4+ and 4− (parity doublet) states. Such a D3h symmetry was observed in triatomic molecules, and it is observed in 12C for the first time in nuclear physics. The triatomic like structure in nuclei is reminiscent of the discovery of diatomic α+14C structure in 18O. We discuss a classification of other rotation-vibration bands in 12C such as the (0+) Hoyle band and the (1−) bending mode band and suggest measurements in search of the predicted ("missing") states that may shed new light on clustering in 12C and light nuclei. In particular, the observation (or non observation) of the predicted ("missing") states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.654 MeV in 12C.

HPC-enabled Nuclear Structure Studies – Description and Applications of the Symmetry-adapted No-Core Shell Model

By exploiting symmetries that enable the accounting of vital collective correlations in nuclei, we achieve significantly reduced dimensions for equivalent ultra-large model spaces, and hence resolve the scale explosion problem in nuclear structure calculations, i.e, the explosive growth in computational resource demands with increasing number of particles and size of the spaces in which they reside. As a result, we provide – with the help of High Performance Computing (HPC) resources – first solutions for selected benchmark calculations with remarkable findings of large-deformation and low-spin dominance in low-lying nuclear states. In the framework of a complementary symmetry-adapted study, one is able, facilitated by symmetry-preserving pieces of the inter-nucleon interaction, to accommodate unprecedented shell-model spaces critical to capture the physics governing the Hoyle state in 12C, thereby addressing a 60-year-old puzzle on the emergence of cluster substructures within a no-core shell model framework. All of these findings underline the key role of symmetries in nuclear structure studies.

Cluster features of stable and unstable nuclei in thep-shell region

Cluster aspects in light unstable nuclei as well as light stable nuclei are discussed. We focus on cluster structures of excited states in 12C, 9Li, and 10Be. The rotation of 3α cluster gas states in 12C and the 6He+t cluster resonances in 9Li are theoretically studied.

A solution to the old puzzle of 0+ resonances above the 0+2 Hoyle state in 12C — A new analysis with complex-scaled 3α OCM —

We have developed the complex-scaling method (CSM) by using the complex-range (or oscillating) Gaussian basis functions that are suited for describing highly oscillating few-body wave functions. The eigenvalue distribution of the complex scaled Hamiltonian becomes much more precise and the maximum scaling angle becomes drastically larger than those given by the use of real-range Gaussians. Owing to this advantage, we were able to isolate the S-matrix pole of the new broad 0+3 resonance from the 3α continuum. This confirms the Kurokawa-Kato's prediction (2005) of the new 0+3 resonance, which is considered to correspond to the newly observed 0+3 resonance (Ex = 9.04 MeV, Γ = 1.45 MeV) by Itoh et al. (2013). As a result the long-standing puzzle for the 0+ and 2+ resonances above the 0+ Hoyle state in 12C was solved. In this paper, the negative parity resonances with J = 1−, 2−, 3−, 4− and 5− are newly calculated.

The isoscalar transition strengths of the cluster states of 12C

An elaborate folding model + coupled channel analysis of the inelastic α+12C scattering has been done using the inelastic form factors based on the nuclear transition densities predicted by the antisymmetrized molecular dynamics. The form factors for the observed isoscalar states of 12C were fine-tuned against the measured (α, α') cross sections to estimate the corresponding Eλ transition strengths. A significant E2 transition strength has been allocated for the second 2+ state of 12C from our consistent coupled channel analysis of the (α, α') data measured at Eα = 240 and 386 MeV. The Eλ transition strengths of the 0+2, 3-1, 0+3, and 1-1 states were also carefully deduced from the same folding model + coupled channel analysis.

A newly observed state in 12C – characterisation and consequences

Measurements of the 12C(4He,4He)12C* reaction at 40 MeV were performed using a charged-particle detector array composed of four double-sided silicon strip detectors. Resonances in 12 C were reconstructed with the requirement that the a-decay proceeded first via the 8 Be ground state. Of primary significance was the population of the 13.3 and 22.4 MeV resonances, the latter, observed for the first time in this measurement. By using the angular correlation technique the spins of the resonances, have been established as Jπ 4+ and Jπ=5− respectively.

Emergence of cluster structures and collectivity within a no-core shell-model framework

An innovative symmetry-guided concept, which capitalizes on partial as well as exact symmetries that underpin the structure of nuclei, is discussed. Within this framework, ab initio applications of the theory to light nuclei reveal the origin of collective modes and the emergence a simple orderly pattern from first principles. This provides a strategy for determining the nature of bound states of nuclei in terms of a relatively small fraction of the complete shell-model space, which, in turn, can be used to explore ultra-large model spaces for a description of alpha-cluster and highly deformed structures together with the associated rotations. We find that by using only a fraction of the model space extended far beyond current no-core shell-model limits and a long-range interaction that respects the symmetries in play, the outcome reproduces characteristic features of the low-lying 0+ states in 12 C (including the elusive Hoyle state and its 2+ excitation) and agrees with ab initio results in smaller spaces. This is achieved by selecting those particle configurations and components of the interaction found to be foremost responsible for the primary physics governing clustering phenomena and large spatial deformation in the ground-state and Hoyle-state rotational bands of 12 C. For these states, we offer a novel perspective emerging out of no-core shell-model considerations, including a discussion of associated nuclear deformation, matter radii, and density distribution. The framework we find is also extensible to negative-parity states (e.g., the 3−1 state in 12C) and beyond, namely, to the low-lying 0+ states of 8Be as well as the ground-state rotational band of Ne, Mg, and Si isotopes. The findings inform key features of the nuclear interaction and point to a new insight into the formation of highly-organized simple patterns in nuclear dynamics.