12C System Research Articles

Phenomenological and microscopic analysis for the 7Li + 12C system

We report the results of an analysis of the 7Li + 12C elastic scattering angular distributions measured at energies between 5.8 and 350 MeV. The analysis is based on various nuclear potentials and approaches. The objective of this study is to analyze the cluster character of the weakly bound 7Li nucleus in order to verify the associated breakup effects on the elastic scattering data and to examine the consistency of the acquired results across the various potentials used. The analysis shows the impact of strong coupling to the breakup channel. The fully microscopic continuum discretized coupled channel (CDCC) method is employed efficiently to elucidate the data under consideration.

Crystal structure of chalcogenides R'xR''yR'''zPbSi2S8 (R' – La, R'' – Tb, R''' – Er)

The chalcogenides LaxTbyErzPbSi2S8 were obtained by synthesizing the elementary components in vacuum quartz containers at 1320 K. The synthesized alloys were homogenized by annealing at 770 K during 500 hours. The cell parameters of synthesized sulfides are: a = 0,89576(3) nm, c = 2,65646(8) nm – La1,2Tb0,4Er0,4PbSi2S8; a = 0,89209(1) nm, c = 2,63466(5) nm – La0,9Tb0,2Er0,9PbSi2S8; a = 0,89002(3) nm, c = 2,62714(7) nm – La0,67Tb0,67Er0,67PbSi2S8; a = 0,88993(1) nm, c = 2,62973(4) nm – La0,6Tb1,2Er0,2PbSi2S8; a = 0,885161(7) nm, c = 2,60445(3) nm – La0,2Tb0,9Er0,9PbSi2S8 respectively. The atoms of statistical mixture (La,Tb,Er,Pb) occupy the site 18e (x y 1/4), and the atoms of Si occupy the site 12c (1/3 2/3 z) in the structure of the obtained chalcogenides. Coordinating polyhedra of atoms of the statistical mixture (La, Tb, Er, Pb) are trigonal prism with two additional atoms (CN = 8), and the atoms of Si occupying the crystallographic point system 12c describes with the tetrahedron. According to the results of the experiment, the synthesized chalcogenides crystallize in the structure type of La2PbSi2S8 (hR26,167). The structure of La2PbSi2S8 is described by using the theory of second anion coordination (SAC).

Study of fusion hindrance in the system 12C+24Mg

The phenomenon of fusion hindrance may have important consequences on the nuclear processes occurring in astrophysical scenarios, if it is a general behaviour of heavy-ion fusion at extreme sub-barrier energies, including reactions involving lighter systems, e.g. reactions in the carbon and oxygen burning stages of heavy stars. The hindrance is generally identified by the observation of a maximum of the S-factor vs. energy. Whether there is an S-factor maximum at very low energies for systems with a positive fusion Q-value is an experimentally challenging question. Our aim has been to search evidence for fusion hindrance in 12C + 24Mg which is a medium-light systems with positive Q-value for fusion, besides the heavier cases where hindrance is recognised to be a general phenomenon. The experiment has been performed at the XTU Tandem accelerator of LNL by directly detecting the fusion evaporation residues at very forward angles. The excitation function has been extended down to ≃10μb, i.e. 4 orders of magnitude lower than previous measurements and we observe that the S-factor develops a clear maximum vs. energy. Coupled-Channels calculations using a Woods-Saxon potential give a good account of the data near and above the barrier but over predict the cross sections at very low energies. Therefore the hindrance phenomenon is clearly recognised in 12 C + 24 Mg with an energy threshold that nicely fits the systematics in several medium-light systems. The fusion cross sections at the hindrance threshold show that the highest value (as=1.6mb) is indeed found for this system. It may be possible to extend the measurements further down in energy.

A theoretical analysis of the cross sections of 18,19,20O + 12C fusion reactions by using different density distributions

In this study, we examine the cross sections of 18,19,20O + 12C fusion reactions at energies near and below Coulomb barrier within the optical model. To propose alternative density distributions for theoretical studies of fusion reactions of oxygen isotopes (18,19,20O) and carbon target, we evaluate three different density distributions of 18,19,20O and 12C nuclei. Moreover, we apply two different theoretical approaches which consist of semi-microscopic and fully-microscopic in order to make a comparative study. The theoretical results are compared with each other as well as the experimental data. It is seen that the results are in good agreement with the data. The evaluated methods and density distributions are presented to be alternative ways in explaining the fusion cross sections of 18,19,20O + 12C systems. Finally, we show the effect of weak imaginary potential in fitting the experimental data.

Readjustment of the Bohr stopping force from energies of keV/n to a few tens of MeV/n ions in elemental targets

An analytical approach for the electronic stopping force for non-relativistic energies that has no adjustable parameters has been developed. The approach combines the Bohr model for the close collisions and the Firsov model for the distant collisions. In order to combine the two models, a probabilistic model was introduced. We have applied our model to 16O in 12C, 16O in 27Al, 84 Kr in 27Al, 5Li in 12C, 12C in 12C, and 132Xe in 12C systems and compared with SRIM/MSTAR software, the original Bohr model, the Firsov model and available experimental data. We have found that the calculated electronic stopping force values are in agreement with the general qualitative behaviour of the electronic stopping force as a function of particle velocity reported in the literature. The proposed analytical formula is expected to be valid for other projectile-target combinations but more experimental data are needed to verify this assumption.

Systematic investigation of “hindrance” in heavy-ion fusion reactions at deep sub-barrier energies

In order to explore the influence of adiabatic process on fusion reactions, we employ 13 different phenomenological nuclear potentials to make a systematic comparison of the experimental and calculated fusion cross sections. After two colliding nuclei contact, the adiabatic process is introduced to calculate the fusion cross sections at the above- and sub- barrier energies for 16 fusion reactions. At deep sub-barrier energy region, a detailed investigation is made to study the fusion hindrance by taking Krappe-Nix-Sierk, Bass (1980), and Akyüz-Winther nuclear potentials as examples. For newly observed fusion systems 12C + 198Pt, 11B + 197Au, and 40Ca + 90Zr, the calculated fusion cross sections are in good agreement with experimental data by considering the damping of coupled-channels effect. The results of astrophysical S factor and logarithmic derivative at deep sub-barrier energies show a close dependence on the behavior of potentials inside the Coulomb barrier. For newly observed light mass system 12C + 30Si, the corresponding improvement by considering the damping factor is small owing to the weak coupling effect.

Generating keV ion distributions for nuclear reactions at near solid-density using intense short-pulse lasers

Our understanding of a large range of astrophysical phenomena depends on a precise knowledge of charged particle nuclear reactions that occur at very low rates, which are difficult to measure under relevant plasma conditions. Here, we describe a method for generating dense plasmas at effective ion temperatures >20 keV, sufficient to induce measurable charged particle nuclear reactions. Our approach uses ultra-intense lasers to drive micron-sized, encapsulated nanofoam targets. Energetic electrons generated in the intense laser interaction pass through the foam, inducing a rapid expansion of the foam ions; this results in a hot, near-solid density plasma. We present the laser and target conditions necessary to achieve these conditions and illustrate the system performance using three-dimensional particle-in-cell simulations, outline potential applications and calculate expected nuclear reaction rates in the D(d,n) and 12C(p,γ) systems assuming CD, or CH aerogel foams.

Analysis of the fusion cross sections for 16,18,20O + 12C systems at low energies

Fusion cross section data for the 16,18,20O + 12C systems at energies near and below the Coulomb barrier are studied within the framework of the optical model. To examine these reactions, the microscopic nucleon–nucleon double folding potentials for real and imaginary parts are found. To make a comprehensive analysis of the effect of neutron-rich systems, we used three different reactions from stable to unstable systems. The microscopic nucleon–nucleon double folding potentials show very good agreement for 16,18,20O + 12C systems with a very weak imaginary potential. Also, we have obtained better agreement by using fully microscopic nucleon–nucleon double folding potentials with the 20O + 12C system’s experimental data than in previous works, but especially at low energies we still have some problems reproducing the 20O + 12C system’s fusion cross section data.

Asymptotic Normalization Coefficients in a Potential Model Involving Forbidden States

It is shown that values obtained for asymptotic normalization coefficients by means of a potential fitted to experimental data on elastic scattering depend substantially on the presence and the number n of possible forbidden states in the fitted potential. The present analysis was performed within exactly solvable potential models for various nuclear systems and various potentials without and with allowance for Coulomb interaction. Various methods for changing the number n that are based on the use of various versions of the change in the parameters of the potential model were studied. A compact analytic expression for the asymptotic normalization coefficients was derived for the case of the Hulthen potential. Specifically, the d + α and α + 12C systems, which are of importance for astrophysics, were examined. It was concluded that an incorrect choice of n could lead to a substantial errors in determining the asymptotic normalization coefficients. From the results of our calculations, it also follows that, for systems with a low binding energy and, as a consequence, with a large value of the Coulomb parameter, the inclusion of the Coulomb interaction may radically change the asymptotic normalization coefficients, increasing them sharply.

Study of the nuclear medium by 12C + 12C elastic scattering analysis at low energy region

The nuclear medium is investigated by studying the 12C + 12C elastic scattering at the low energies in the framework of optical model (OM) potential. Both frozen and adiabatic density approximations are used for the description of the nuclear medium during the colliding process. In the OM calculation, the double folding procedure using the realistic CDM3Y3 effective nucleon-nucleon (NN) interactions and the wave functions of colliding nuclei is employed to describe the nucleus-nucleus potential at low energy region below 10 MeV per nucleon. The obtained results from the elastic scattering analyses show that the adiabatic density approximation is more reasonable than the frozen density approximation to describe the overlapping density (the so-called nuclear medium) for the 12C + 12C system at low energy region.

A comparative analysis of the density distributions and the structure models of 9Li

In the present study, we have analysed the elastic scattering cross-section data of 9Li + 12C system at E lab = 540 MeV and 9Li + 208Pb system at E c.m. = 28.3 MeV for some cluster models and various density distributions of the 9Li nucleus. First, we have obtained five different density distributions of the 9Li nucleus to generate real potentials with the help of double-folding model. For these densities, we have calculated the elastic scattering angular distributions. Secondly, using a simple approach, we have investigated some cluster models of the 9Li nucleus consisting of 6He + 3H and 8Li + n systems. We have presented the comparison of elastic scattering angular distributions for each system with each other as well as with the experimental data. Finally, we have given the cross-section values obtained from the theoretical calculations for all the systems studied in this paper.

Measurement of multinucleon transfer cross-sections in 58Ni, 56Fe(12C, x); x: 13,11C, 11,10B, 10,9,7Be, 8Beg.s. and 7,6Li at E(12C) = 60 MeV

Cross-sections for one- and multinucleon transfer reactions, namely, 58Ni(12C, 13C), 58Ni(12C, 11C), 58Ni(12C, 11B), 58Ni(12C, 10B), 58Ni(12C, 10Be), 58Ni(12C, 9Be), 58Ni(12C, 8Be g.s.), 58Ni(12C, 7Be), 58Ni(12C, 7Li) and 58Ni(12C, 6Li) have been measured at an incident energy of 60 MeV. The reaction cross-section for the corresponding transfer channels in the system 12C+56Fe have also been measured under the same kinematical conditions. Angular distribution of the elastic scattering cross-section is measured at 60 MeV. The measured elastic scattering angular distributions for these two systems have been analysed using the optical model search code SFRESCO and the potential parameters are extracted. The multinucleon transfer data are analysed to obtain cross-section dependence on the number of nucleons transferred and on the ground state Q-values. The transfer probabilities for multinucleon stripping are extracted. A detailed comparison in the multiparticle stripping and elastic scattering cross-sections between these two systems are made to understand the mechanism of multinucleon transfer and possible role of two extra protons in 58Ni target nucleus as compared to the 56Fe core.

Evidence of a slight nuclear transparency in the alpha-nucleus systems

In earlier works, we proposed a model for the nuclear potential of the α + α and α + 12C systems. This theoretical model successfully described data related to the elastic and inelastic scattering processes as well as resonances that correspond to the capture reaction channel. In the present work, we extend the same model to obtain bare nuclear potentials for several α-nucleus systems. We adopt this interaction to analyze fusion, elastic, and inelastic scattering data within the context of the coupled-channel formalism. Our results indicate that, for these systems, the absorption of flux of the elastic channel at internal distances of interaction is not complete. In addition, we present new experimental angular distributions for the inelastic target excitation of α on Te.

A comprehensive study of 17F + 12C system at 60 MeV: cluster model, optical model and double

In the present study, we analyze the quasi-elastic scattering data of 17 F + 12 C reaction at 60 MeV using the cluster model, the optical model and the double folding model. We compare the theoretical results obtained for all the models with the experimental data. These comparison provide information about the similarities and differences of the models used in calculations.

The effect of nuclear structure in the emission of reaction products in heavy-ion reactions

Study of intermediate mass fragments (IMFs) and light charged particles (LCPs) emission has been carried out for a few reactions involving α-cluster and non- α-cluster systems to see how the emission processes are affected by nuclear clustering. Li, Be, B and α-particles have been studied from α-clustered system 16O + 12C for 117, 125, 145 and 160 MeV bombarding energies respectively. The enhanced yields of near-entrance channel fragment B and large quadrupole deformation of the produced composite 28Si∗ extracted from LCP spectra indicate the survival of orbiting-like process in 16O + 12C system at these energies. The same IMFs emitted from the α-cluster system 12C (77 MeV) + 28Si and nearby non- α cluster 11B (64 MeV) + 28Si and 12C (73 MeV) + 27Al (all having the same excitation energy of ∼67 MeV) have also been studied. The fully energy damped (fusion–fission) and the partially energy damped (deep inelastic) components of the fragment energy spectra have been extracted. It has been found that the yields of the fully energy damped fragments for all the above reactions are in conformity with the respective statistical model predictions. The time-scales of various deep inelastic fragment emissions have been extracted from the angular distribution data. The angular momentum dissipation in deep inelastic collisions has been estimated from the data and it has been found to be close to the corresponding sticking limit value.

Effect of the inelastic couplings on the scattering of alpha particles by 12C at low energies

We study the effects of the coupling to the first 2+ 12C excited state on the elastic scattering and capture reaction for the α + 12C system. The flux absorption from the elastic channel to the capture reaction is simulated by a tiny imaginary part included in the optical potential. Our analyses show that the effect of the coupling is quite significant even at energies below the threshold of the inelastic channel. We also study the behavior of the polarization potential as a function of the energy and angular momentum.

Study of the fusion reaction 12C + 12C at low beam energy

In this article we discuss two aspects related to the 12C + 12C fusion reaction at low energies for carbon burning in supermassive stars. First we present plausible arguments for the notion that the observed resonance structures at the lowest measured energies arise from the relatively large spacing and narrow width of 24Mg compound levels at the corresponding excitation energy region. We thus point out that the Incoming Wave Boundary Condition is inappropriate for calculating the fusion cross section under these situations. Secondly, we report on a particle-γ coincidence technique that has been used for the first time to measure the fusion cross section in the system 12C + 12C at low beam energies. Based on these results, it should be possible to measure this important fusion cross section down to the 10 pb level within a reasonable length of time.

Channel coupling and exchange of an alpha-particle cluster in deuteron scattering on 6Li nuclei

Existing experimental data on elastic and inelastic deuteron scattering on 6Li nuclei in the energy range from 8 to 50 MeV were analyzed within the approach of coupled reaction channels. The coupling of elastic scattering and inelastic scattering accompanied by the transition to the 3+ state at E x = 2.186 MeV and the mechanism involving the exchange of an alpha-particle cluster were taken into account in respective calculations. The phenomenological potentials obtained from the present analysis describe well experimental angular distributions at all energies and in full angular ranges. The depths of the real and imaginary parts of the potentials in question depend smoothly on energy at fixed values of the remaining parameters. The energy dependence of relevant volume integrals agrees well with similar data for the p + 6Li, α + 6Li, and 12C + 12C systems and with the predictions of a microscopic theory.

Measurements of fusion cross-sections in 12C+12C at low beam energies using a particle-[formula omitted] coincidence technique

A particle-γ coincidence technique has been used to measure the fusion cross-section in the system 12C+12C at low beam energies. Based on these results, it should be possible to measure this important fusion cross-section down to the 10pb level within a week-long run.

Causality principle and nuclear dispersion anomaly in the elastic scattering for α+ 12C system

The optical model analysis of the alpha particle elastic scattering on a carbon target was performed on the basis of the dispersion relation between the real and imaginary parts of the calculated volume integrals. A nuclear dispersion anomaly in an α+ 12C system was observed and interpreted clearly.