12C Nuclei Research Articles

On the symmetries of the 12C nucleus

The consequences of some symmetries of the three-alpha system are discussed. In particular, the recent description of the low-energy spectrum of the [Formula: see text]C nucleus in terms of the algebraic cluster model (ACM) is compared to that of the multichannel dynamical symmetry (MUSY), which is the intersection of the shell and cluster models. The previous one applies interactions of a [Formula: see text] geometric symmetry [D. J. Marin-Lambarri et al., Phys. Rev. Lett. 113 (2014) 012502], while the latter one has a U(3) dynamical symmetry. The available data is in line with both descriptions.

Production of 11C and 18F Isotopes. Getting the “Glucose, 11C “ Radiopharmaceutical

The results of the photonuclear production of 11C and 18F isotopes in various target-matrices are summarized. The studies were performed using linear electron accelerators of the R&DE "Accelerator" NSC KIPT NAS of Ukraine in the energy range 10 -40 MeV to determine the possibilities of obtaining the maximum achievable activity levels of 11C isotopes, and 18F with a view to planning further developments on the creation of radiopharmaceutical for these nuclear isotopes. In the framework of the above approach, we measured the activity levels of the 18F which is transferred to the surrounding aquatic environment during irradiation of targets-matrices of fluoroplastic (C2F4) with bremsstrahlung flux. The release of the 18F isotope into the aquatic environment under the most favorable conditions (in terms of energy and average beam current) was 3.6% of the target-matrices activity - 40 MBq/g, which is a very low figure. Despite the encouraging value of the specific activity of 18F isotope in lithium fluoride (LiF) -77 MBq/g target–matrices and hydrofluoric acid (HF) - close to 100 MBq/g, the process of extracting 18F from C2F4, LiF and HF as basis of the radiopharmaceutical is not sufficiently effective and brings into question the feasibility of such a methodology for producing 18F isotope for further use. More efficient was the production of the 11C isotope in the irradiated target-matrix of the standard therapeutic form "glucose monohydrate" (glucose). It was shown that, as a result of irradiation of glucose with a gamma-quanta beam, it is possible to “label” glucose with the 11C isotope, which is formed as a result of the photonuclear reaction 12C(γ, n)11C at the 12C nucleus, which is part of the glucose molecule C6H12O6 ×H2O. Irradiated sample of glucose dissolved in a given volume of solvent (distilled water) will be ready for use radiopharmaceutical "Glucose, 11C". It has been shown that the “photonuclear method” provides for obtaining the “Glucose, 11C” radiopharmaceutical complex with total activity necessary for performing PET diagnostics. The radiopharmaceutical "Glucose, 11C" by the time of its use has 100% radionuclide purity. “Glucose, 11C” obtained in this way was produced for the first time. The choice of the optimal design of a water-cooled target station, providing a moderate (in terms of heat loads) mode of irradiation of a capsule filled with glucose tablets, is discussed. Using the program “SolidWorks FlowSimulation 2011”, the quantitative characteristics of the flow rates of water flowing around the glucose capsule and the converter are calculated.

Rotational excitation of the Hoyle state in 12C

12C is synthesised in stars by fusion of three α particles. This process occurs through a resonance in the 12C nucleus, famously known as the Hoyle state. In this state, the 12C nucleus exists as a cluster of α particles. The state is the band-head for a rotational band with the 2+ rotational excitation predicted in the energy region 9 - 11 MeV. This rotational excitation can affect the triple-α process reaction rate by more than an order of magnitude at high temperatures (109 K). Depending on the energy of the resonance, the knowledge of the state can also help determine the structure of the Hoyle state. In the work presented here, the state of interest is populated by beta decay of radioactive 12N ion beam delivered by the IGISOL facility at JYFL, Jyväskylä.

MANIFESTATION OF NUCLEAR CLUSTERIZATION IN COULOMB SUMS

The new experimental Coulomb sums values of 6Li and 7Li nuclei have been obtained at momentum transfers range q = 0.750¸ 1.000 fm-1 and q = 0.750¸ 1.125 fm-1, respectively, extending significantly the earlier reported momentum transfers range of Coulomb sums for these nuclei. The dependence of the 6Li and 7Li Coulomb sums on the momentum transferred is shown to differ substantially from same dependences for all the other investigated nuclei. It is suggested that the observed feature of the 6Li and 7Li Coulomb sums is related to a strong clusterization of these nuclei. The parameter qp corresponding to the value of the momentum transferred, at which the Coulomb sum ceases to grow and remains constant for larger momentum transfers, is introduced. The values of the parameter qp for the lithium isotopes nuclei were obtained (qp(7Li) = 1.20 ± 0.10fm-1 and qp(7Li) = 1.35 ± 0.10 fm-1), which are much lower than qp of 4He, 12C, 40Ca, 48Ca and 56Fe nuclei (qp » 2 fm-1). The graph represented the qp values of the nuclei as a function of the isolation parameter x, which characterizing the degree of nuclear clusterization, is constructed. The obtained graph shows the explicit proportionality of the qp dependence from the parameter x and predicts the qp value for the Coulomb sum of the 9Be nucleus not yet measured.

Container evolution and dynamics of cluster formation

We introduce the so-called Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function to describe various nuclear cluster states. Its importance, applicability, and usefulness are extensively discussed in this report. It is demonstrated that the THSR wave function provides a “container” picture for cluster structures and even an evolution of the container, for a couple of typical examples, such as 20Ne, 12C, and 16O nuclei.

Isoscalar and isovector spin responses in p-shell and sd-shell nuclei

We study the spin magnetic dipole transitions in sd-shell even-even nuclei with N=Z and a p-shell nucleus 12C by modern shell model calculations. The shell model wave functions take into account enhanced isoscalar (IS) spin-triplet pairing as well as the effective spin operators. We point out that the IS pairing and the effective spin operators give a large quenching effect on the isovector (IV) spin transitions to be consistent with observed data by (p, p′) experiments. On the other hand, the observed IS spin strengths do not show large quenching effect suggested by the calculated investigation. The IS pairing gives a substantial quenching effect on the spin magnetic dipole transitions, especially on the IV ones.

A new treatment of nonlocality in scattering process

Nonlocality in the scattering potential leads to an integro-differential equation. In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schrödinger equation is usually handled by approximating r,-dependence of the nonlocal kernel. The present work proposes a novel method to solve the integro-differential equation. The method, using the mean value theorem of integral calculus, converts the nonhomogeneous term to a homogeneous term. The effective local potential in this equation turns out to be energy independent, but has relative angular momentum dependence. This method is accurate and valid for any form of nonlocality. As illustrative examples, the total and differential cross sections for neutron scattering off 12C, 56Fe and 100Mo nuclei are calculated with this method in the low energy region (up to 10 MeV) and are found to be in reasonable accord with the experiments.

Study of the Involvement of 8Be and 9B Nuclei in the Dissociation of Relativistic 10C, 10B, and 12C Nuclei

The results obtained by estimating the contribution of 8Be and 9B nuclei to the coherent dissociation of 10C, 10B, and 12C relativistic nuclei in nuclear track emulsions (“white” stars) are presented. The selection of white stars accompanied by 9B leads to a distinct peak appearing in the distribution of the excitation energy of 2α2p ensembles and having a maximum at 4.1 ± 0.3 MeV. A 8Be nucleus manifests itself in the coherent-dissociation reaction 10B → 2He + H with a probability of (25 ± 5)%, (14 ± 3)% of it being due to 9B decays. The ratio of the branching fractions of the 9B + n and 9Be + p mirror channels is estimated at 6 ± 1. An analysis of the relativistic dissociation of 12C nuclei in a nuclear track emulsion revealed nine 3α events corresponding to the Hoyle state.

Optical potentials derived from nucleon-nucleon chiral potentials at N4LO

Background: Elastic scattering is probably the main event in the interactions of nucleons with nuclei. Even if this process has been extensively studied in the last years, a consistent description, i.e., starting from microscopic two- and many-body forces connected by the same symmetries and principles, is still under development. Purpose: In a previous paper we derived a theoretical optical potential from NN chiral potentials at fourth order (N3LO). In the present work we use NN chiral potentials at fifth order (N4LO), with the purpose to check the convergence and to assess the theoretical errors associated with the truncation of the chiral expansion in the construction of an optical potential. Methods: The optical potential is derived as the first-order term within the spectator expansion of the nonrelativistic multiple scattering theory and adopting the impulse approximation and the optimum factorization approximation. Results: The pp and np Wolfenstein amplitudes and the cross section, analyzing power, and spin rotation of elastic proton scattering from 16O, 12C, and 40Ca nuclei are presented at an incident proton energy of 200 MeV. The results obtained with different versions of chiral potentials at N4LO are compared. Conclusions: Our results indicate that convergence has been reached at N4LO. The agreement with the experimental data is comparable with the agreement obtained in our previous work. We confirm that building an optical potential within chiral perturbation theory is a promising approach for describing elastic proton-nucleus scattering.

A comprehensive analysis of elastic scattering of 14N projectile on 7Li, 9Be, 11B, 12C, 16O, 26Mg, 28Si, 40Ca, 56Fe, 59Co, 60,62Ni, 70,74Ge, 90Zr, 112Cd, 118Sn, 159Tb and 197Au at various incident energies

Elastic scattering data of 14N projectile on 7Li, 9Be, 11B, 12C, 16O, 26Mg, 28Si, 40Ca, 56Fe, 59Co, 60,62Ni, 70,74Ge, 90Zr, 112Cd, 118Sn, 159Tb and 197Au target nuclei are investigated at various incident energies. To obtain nuclear potential, two different approaches are applied. In first approach, the imaginary potential is assumed as the Woods-Saxon potential while the real potential is determined using the double folding model. In a second approach, both real and imaginary potentials are evaluated within the double folding model. The real and imaginary volume integrals and cross-sections of the systems investigated under different approaches are provided. Then, new equations which give the imaginary potential are obtained from the elastic scattering results. Finally, the effect of 10B + α and 13C + p cluster cases of 14N nucleus on the elastic scattering analysis is investigated by a simple approach.

Monte Carlo studies on neutron interactions in radiobiological experiments.

Monte Carlo method was used to study the characteristics of neutron interactions with cells underneath a water medium layer with varying thickness. The following results were obtained. (1) The fractions of neutron interaction with 1H, 12C, 14N and 16O nuclei in the cell layer were studied. The fraction with 1H increased with increasing medium thickness, while decreased for 12C, 14N and 16O nuclei. The bulges in the interaction fractions with 12C, 14N and 16O nuclei were explained by the resonance spikes in the interaction cross-section data. The interaction fraction decreased in the order: 1H > 16O > 12C > 14N. (2) In general, as the medium thickness increased, the number of “interacting neutrons” which exited the medium and then further interacted with the cell layer increased. (3) The area under the angular distributions for “interacting neutrons” decreased with increasing incident neutron energy. Such results would be useful for deciphering the reasons behind discrepancies among existing results in the literature.

Coherent fragmentation of 12C nuclei of momentum 4.5 GeV/c per nucleon through the 8Beg.s.+4He channel in a nuclear photoemulsion containing lead nuclei

A two-particle channel in which an unbound nucleus of 8Be in the ground state (8Beg.s.) was one of the fragments was selected among events where 12C nuclei of momentum 4.5 GeV/c per nucleon undergo coherent dissociation into three alpha particles. The events in question were detected in a track nuclear photoemulsion containing lead nuclei, which was irradiated at the synchrophasotron of the Laboratory of High Energies at the Joint Institute for Nuclear Research (JINR, Dubna). The average transverse momentum of alpha particles produced upon the decay of 8Beg.s. nuclei was 87±6 MeV/c, while that for “single” alpha (αs) particles was 123±15 MeV/c. The average value of the transverse-momentum transfer in the reaction being considered, Pt(12C), was 223 ± 20 MeV/c. The average value of the cross section for this channel involving Ag and Br target nuclei was 13 ± 4 mb, while the cross section for the reaction on the Pb nucleus was 40 ± 15 mb. The Coulomb dissociation contribution evaluated on the basis of the number of events where the momentum P t(12C) did not exceed 0.1 GeV/c saturated about 20%. In nine events, the measured total transverse energy of the fragments in the reference frame comoving with the decaying carbon nucleus did not exceed 0.45 MeV, which did not contradict the excitation of the participant 12C nucleus to the level at 7.65 MeV. The average value of the transverse momentum in those events was 234 ± 25 MeV/c.

Scaling of differential cross section ratios in inelastic (p, p′) reaction with nuclei at 1 GeV

The differential cross sections of the (p, p′) inelastic reaction on nuclei 12C, 28Si, 40Ca, and 56Fe at the initial proton energy of 1 GeV were measured over a wide range of the scattered proton momenta at a laboratory angle of Θ = 21°. Scattered protons were detected by means of the magnetic spectrometer equipped with a polarimeter based on multiwire proportional chambers. Momentum intervals were observed in which the ratios of the scattering cross sections off the nuclei do not depend on the scattered proton momentum (i.e., scaling).

Lateral variations of radiobiological properties of therapeutic fields of 1H, 4He, 12C and 16O ions studied with Geant4 and microdosimetric kinetic model

As known, in cancer therapy with ion beams the relative biological effectiveness (RBE) of ions changes in the course of their propagation in tissues. Such changes are caused not only by increasing the linear energy transfer (LET) of beam particles with the penetration depth towards the Bragg peak, but also by nuclear reactions induced by beam nuclei leading to the production of various secondary particles. Although the changes of RBE along the beam axis have been studied quite well, much less attention has been paid to the evolution of RBE in the transverse direction, perpendicular to the beam axis. In order to fill this gap, we simulated radiation fields of 1H, 4He, 12C and 16O nuclei of 20 mm in diameter by means of a Geant4-based Monte Carlo model for heavy-ion therapy connected with the modified microdosimetric kinetic model to describe the response of normal ( Gy) and early-responding ( Gy) tissues. Depth and radial distributions of saturation-corrected dose-mean lineal energy, RBE and RBE-weighted dose are investigated for passive beam shaping and active beam scanning. The field of 4He has a small lateral spread as compared with 1H field, and it is characterised by a modest lateral variation of RBE suggesting the use of fixed RBE values across the field transverse cross section at each depth. Reduced uncertainties of RBE on the boundary of a 4He treatment field can be advantageous in a specific case of an organ at risk located in lateral proximity to the target volume. It is found that the lateral distributions of RBE calculated for 12C and 16O fields demonstrate fast variations in the radial direction due to changes of dose and composition of secondary fragments in the field penumbra. Nevertheless, the radiation fields of all four projectiles at radii larger than 20 mm can be characterized by a common RBE value defined by tissue radiosensitivity. These findings can help, in particular, in accessing the transverse homogeneity of radiation fields of ions used in studies in vitro.

Search for the rare γ-decay mode in 12C

Excited states in 12C nuclei play a very important role in the nucleosynthesis in the universe. 12C nuclei are synthesized by the triple α reaction. Normally the triple α process proceeds via the state (Hoyle states) at Ex = 7.65 MeV in 12C. However, at high temperature T > 109, the highly excited 3α resonance states such as the state at Ex = 9.64 MeV might play a part of the triple α reaction. Unfortunately, the γ-decay probability of the state has not been determined, therefore we planned to measure 1H(12C, 12Cp) reaction without measuring γ-rays. The test experiment using the solid hydrogen target and GAGG(Gd3Al2Ga3O12) was recently carried out at the cyclotron facility in RCNP. The results of the test experiment are reported in this paper.

A novel visage of molecular resonances in 12C + 12C

Resonances observed in the 12C + 12C collisions are studied by the molecular model. Firstly, normal-modes analysis made around the equilibrium equator-equator touching configuration gives a basic insight into dynamics of the system. The quantum numbers of the states also indicate rotational motions of the constituent 12C nuclei, which relate the normal modes to the corresponding inelastic 12C + 12C channels. Next, low-lying 11 states are taken up as bases, and Coriolis coupling has been diagonalized. Many excited states are obtained with intermediate widths, which is just in accord with the experimental observation. For example, the second and third excited states have characteristic feature as low-lying mutual 2+ excitation with the spin vectors of 12C nuclei along the molecular z′-axis. Those states appear very close to the molecular ground state with the higher spin of ΔJ = 2, to form a bunch. Resultant excitation functions are surprisingly in good agreement with the experiments, which lights up a new physical picture of molecular structures of the high-spin 12C + 12C resonances.

Microscopic time-dependent description of alpha-cluster transfer and incomplete fusion in reactions with 12C and 16O near Coulomb barrier

The time-dependent Schrödinger equation has been numerically solved for the α-cluster wave function the in reaction 12C+51V at the energies near and above the Coulomb barrier. The α-target potential included an imaginary part as in the optical model. The α-cluster mean field of the shell model for 12C and 16O nuclei based on the results of Feynman’s integrals method is proposed. The evolution of the α-cluster probability density was calculated for the complete and incomplete fusion as well as transfer channels. The calculated cross sections show satisfactory agreement with the experimental data for (12C,α) and (12C,2α) transfer channels.

Quartet condensation in Fermi-systems. The Hoyle state in the 12C nucleus and life on earth

The possibility that a four component Fermi gas with attractive interaction can form a quartet condensate at low density is pointed out. It is discussed that for quartets only the Bose-Einstein Condensatio (BEC) phase exists and that the analogue to the weak coupling long coherence BCS phase of pairing is absent. Precurser phenomena in finite nuclei are presented. For instance, the present understanding of the structure of the Hoyle state in 12C being the gateway for Carbon production in the universe is reviewed. It is pointed out that a crucial test of any theory is the good reproduction of the experimental results for the inelastic form factor from ground to the Hoyle state. The performances of the so-called THSR wavwe function are outlined confirming the α particle condensation hypothesis proposed 15 years back in [1].

Structure effects in polarization and cross sections for A(p, p’)X inelastic reactions on 40Ca and 12C nuclei at 1 GeV

The polarization of the secondary protons in inelastic (p,p') reaction on the 40Ca and 12C nuclei at the initial proton energy 1 GeV was measured in the wide range of the scattered proton momenta at a laboratory angle 21 degree. The cross section of the reactions were measured as well. The outgoing protons from the reaction were detected using a magnetic spectrometer equipped with a multiwire-proportional chambers polarimeter. A structure in the polarization and cross section data, related probably to scattering of the nucleon correlation in the nuclei, was observed.

Microscopic Large Scale psd Shell Model with M3Y Residual Interaction to Calculate Electron Scattering Form Factors

The longitudinal and the transverse electron scattering form factors for 6Li, 9Be, 11B and 12C nuclei have been studied with and without core polarization effects using shell model calculations. The psdmwk is used as effective interaction for psd-shells. The core-polarization effects are calculated in the first-order perturbation theory including excitations up to 4ħω using the Michigan three-range Yakawa M3Y as a realistic interaction. The wave functions of radial single particle matrix elements have been calculated with harmonic oscillator potential. For all nuclei under studying, Comparison between experimental and theoretical calculations show that the form factors with core-polarization effect calculations give good consistency with experiment data. So we concluded that the large scale model space enhanced the results to become closed to the experimental data.