Total Reaction Cross Sections Research Articles

Successful Prediction of Total α-Induced Reaction Cross Sections at Astrophysically Relevant Sub-Coulomb Energies Using a Novel Approach.

The prediction of stellar (γ,α) reaction rates for heavy nuclei is based on the calculation of (α,γ) cross sections at sub-Coulomb energies. These rates are essential for modeling the nucleosynthesis of so-called p nuclei. The standard calculations in the statistical model show a dramatic sensitivity to the chosen α-nucleus potential. The present study explains the reason for this dramatic sensitivity which results from the tail of the imaginary α-nucleus potential in the underlying optical model calculation of the total reaction cross section. As an alternative to the optical model, a simple barrier transmission model is suggested. It is shown that this simple model in combination with a well-chosen α-nucleus potential is able to predict total α-induced reaction cross sections for a wide range of heavy target nuclei above A≳150 with uncertainties below a factor of 2. The new predictions from the simple model do not require any adjustment of parameters to experimental reaction cross sections whereas in previous statistical model calculations all predictions remained very uncertain because the parameters of the α-nucleus potential had to be adjusted to experimental data. The new model allows us to predict the reaction rate of the astrophysically important ^{176}W(α,γ)^{180}Os reaction with reduced uncertainties, leading to a significantly lower reaction rate at low temperatures. The new approach could also be validated for a broad range of target nuclei from A≈60 up to A≳200.

Radiation damage in particle accelerator complex for heavy ion inertial fusion

We investigated radiation damages induced by irradiating ions in a particle accelerator for a heavy-ion inertial fusion (HIF) system, because the radio-activation is an unavoidable issue to realize the future HIF power plant. In this study, we estimated the radio-activation at each part of the HIF accelerator. An evaluation using collisions due to Coulomb barrier gives the safer estimation in the radio-activation of the vacuum vessel wall. The estimation results of total cross sections of nuclear reactions between an incident ion and wall elements showed the potential radio-activation parts in the HIF accelerator. We indicated that schematic layouts of two types of HIF accelerators with the nuclear reaction cross section, and the activated area for the HIF accelerator was evaluated.

Semimicroscopic analysis of Li6 elastic scattering at 40 MeV/nucleon

Analysis of the differential cross sections for $^{6}\mathrm{Li}$ elastic scattering from $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, and $^{116}\mathrm{Sn}$ at 40 MeV/nucleon is performed within the framework of the optical double folding model. Simple phenomenological effective nucleon-nucleon interaction represented by a density-independent single Yukawa term is utilized to generate the real optical potential part. The derived potentials in conjunction with imaginary parts expressed in phenomenological volume Woods-Saxon forms have been successfully used to reproduce the seven sets of data. For the sake of comparison, the same measurements are reanalyzed using folded potentials based upon the density-independent M3Y effective interaction. Furthermore, reasonably successful reproduction of the data is obtained by Woods-Saxon-type optical model potentials. The radial sensitivity of the derived real potentials to the calculating elastic-scattering angular distributions has been investigated using the notch perturbation technique. The target mass dependence in real and imaginary volume integrals as well as total reaction cross sections are also investigated.

MULTI-2, a 4[formula omitted] spectrometer for total reaction cross section measurements

A detection setup for the direct measurement of the total reaction cross section with exotic nuclei is presented. The setup consists of a multi-detector telescope for beam-particle identification and a 4π gamma-ray spectrometer for the detection of prompt photons and neutrons accompanying the nuclear reactions. Measurements are based on the modified transmission method and gamma-ray tagging of nuclear reaction events. Registration efficiency and response characteristics of the gamma-ray spectrometer are investigated by Monte Carlo simulations and measurement with 60Co spectroscopic source. Results show strong a dependence of the registration efficiency on gamma-ray multiplicity, with minimum registration efficiency value of 70%. Evaluation of the registration efficiency for data measured in the total reaction cross section experiments is discussed.

Core swelling in spherical nuclei: An indication of the saturation of nuclear density

Background: Nuclear radius is one of the most important and basic properties of atomic nuclei and its evolution is closely related to the saturation of the nuclear density in the internal region but the systematics of the nuclear radii for the neutron-rich unstable nuclei is not well known. Purpose: Motivated by the recent interaction cross section measurement which indicates the 48Ca core swelling in the neutron-rich Ca isotopes, we explore the mechanism of the enhancement of the neutron and proton radii for spherical nuclei. Methods: Microscopic Hartree-Fock calculations with three sets of Skyrme-type effective interactions are performed for the neutron-rich Ca, Ni and Sn isotopes. The total reaction cross sections for the Ca isotopes are evaluated with the Glauber model to compare them with the recent cross section data. Results: We obtain good agreement with the measured cross sections and charge radii. The neutron and proton radii of the various "core" configurations are extracted from the full Hartree-Fock calculation and discuss the core swelling mechanism. Conclusions: The core swelling phenomena occur depending on the properties of the occupying valence single-neutron states to minimize the energy loss that comes from the saturation of the densities in the internal region, which appears to be prominent in light nuclei such as Ca isotopes.

Improved WKB Approximation for Nuclear Fusion Reactions

In this study, we have developed a mathematical approach to enhance the calculation of the probability of the WKB approximation in the semiclassical approach. This enhanced method was applied to study the total cross section of fusion reaction σfus , the barrier distribution of fusion Dfus and the probability of fusion Pfus for the light systems 6Li+64Zn, 13C+48Ti and 16O+46Ti. A quantum coupled-channel calculation is conducted using CC code with all order coupling to compare it with the calculations of the semiclassical method before and after improvement of the WKB probability. The improved approach used with WKB enhances the semiclassical calculations and more closer our theoretical results to the measured data to be in more agreement with the treatment of quantum mechanics which agrees with the measured data for the total reaction cross section σfus , the distribution of fusion barrier Dfus and the probability of fusion Pfus .

Two-neutron halo structure of F31 and a novel pairing antihalo effect

Background: A newly identified dripline nucleus $^{31}$F offers a unique opportunity to study the two-neutron ($2n$) correlation at the east shore of the island of inversion where the $N = 28$ shell closure is lost. Purpose: We aim to present the first three-body theoretical results for the radius and total reaction cross sections of $^{31}$F. This will further help to investigate how the pairing and breakdown of the $N = 28$ shell closure influence the formation of the $2n$-halo structure and the anti-halo effect in this mass region. Methods: A $^{29}$F$+n+n$ three-body system is described by the cluster orbital shell model, and its total reaction cross section is calculated by the Glauber theory. Results: Our three-body calculations predict 3.48-3.70 fm for the root-mean-square radius of $^{31}$F, which corresponds to the total reaction cross section of 1530 (1410)-1640 (1500) mb for a carbon target at 240 (900) MeV/nucleon. The binding mechanism and halo formation in $^{31}$F are discussed. Conclusions: The present study suggests a novel anti-halo effect in this mass region: When the pairing overcome the energy gap between the $p_{3/2}$ and $f_{7/2}$ orbits, the inversion of the occupation number of these orbits takes place, and it diminishes the $2n$-halo structure.

Neutron radii and neutron skin of neutron-rich nuclei deduced from proton-nucleus total reaction cross sections

A new method is proposed to deduce the neutron radii of neutron-rich nuclei. This method requires measuring the reaction cross sections of both the neutron-rich nucleus and its stable isotope at the same energy per nucleon on a proton target. Using this method and the available experimental data of 12,22C + p and 9,14Be + p at 40A MeV, the neutron radii of 22C and 14Be have been deduced.

Applicability of 9Be global optical potential to description of 8,10,11B elastic scattering * * Supported by the National Natural Science Foundation of China (11405099 and 11575291). This work is also a part of IAEA Coordinated Research Projects (CRPs) on Recommended Input Parameter Library (RIPL) for Fission Cross Section Calculations (20464)

We achieved a set of 9Be global phenomenological optical model potentials by fitting a large experimental dataset of the elastic scattering observable for target mass numbers from 24 to 209. The obtained 9Be global optical model potential was applied to predict elastic-scattering angular distributions and total reaction cross-sections of 8,10,11B projectiles. The predictions are made by performing a detailed analysis comparing with the available experimental data. Furthermore, these elastic scattering observables are also predicted for some lighter targets outside of the given mass number range, and reasonable results are obtained. Possible physical explanations for the observed differences are also discussed.

Angular momentum as a probe for the reaction mechanism: The [formula omitted] decay at three excitation energies

The angular momentum effects on the reaction mechanism in the decay of a hot system, formed in 48Ti + 40Ca → Mo⁎88 reaction at three excitation energies, have been studied using the dynamical cluster-decay model based on the quantum mechanical fragmentation theory. Angular momentum windows have been defined for the compound and non-compound nucleus processes (like deep inelastic collisions etc.) with respect to the angular momentum variation of the fission barriers of the incoming channel. First, the angular momentum distributions of the summed up preformation, penetration probabilities and the cross-sections for light particles, intermediate mass fragments and fission fragments have been calculated by considering the angular momentum up to the critical value. Then, the mass and charge distributions (with isotopic compositions) of the cross-sections have been calculated in accordance with the defined angular momentum windows. The cross-sections for fragments coming both from the compound nucleus decay and from other processes have been calculated and the total reaction cross-section is compared with the one presented in the work of Valdré and co-workers. The ratios of the observed fusion-evaporation and total fusion cross-sections to the total reaction cross-sections of (i) our calculation and (ii) presented in the work of Valdré and co-workers, are compared and found comparable. The change of the reaction mechanism has been analyzed as a function of the angular momentum variation of the cross-sections of the fission fragments. Finally, the effect of the incident energy on the compound nucleus formation and survival probabilities has been studied.

Study of α+32S scattering using different potentials at 386 MeV

Elastic and inelastic scattering of α-particles from 32S has been theoretically studied at Elab = 386 MeV using three different potentials. For this, the phenomenological Woods–Saxon parameterized potential, single folding cluster potential, and the high-energy approximation model have been used. The results of our calculations have been compared with the experimental differential cross sections obtained from previously measured angular distributions. Our method of calculations successfully reproduces the experimental data. The values of the total reaction cross-section σR as well as the deformation parameters have been calculated and compared with those available in the literature.

A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes

A dispersive optical model analysis of the alpha particles scattering by titanium element nucleus and its natural isotopes has been applied for a new scattering potential within the energy range (1-100) MeV which has contained the range of the Coulomb barrier, and for constant input values of the parameters of this potential. This potential is extent of the mean field potential and is called by (coulomb-nuclear) interference potential, that contains (spin-orbit) coulomb term. The results according to DOMACNIP program that has been designed for that purpose would contain: continuous energy variation of the depths of the real and imaginary parts of the mean field, which are connected by dispersion relations have been compared with these resulting from global parameterizations of the alpha particles scattering potential. In addition to continuous energy variation of the real radius parameter of the Wood-Saxon approximation to the mean field potential with its Hatree-Fock approximation of the nonlocal potential. Consequently, our results for the continuous energy variations of the predicted total reaction cross section within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), differential cross sections, Ratio of the differential elastic scattering cross section to Rutherford cross section and polarization resulted only from the Coulomb spin-orbit term that has been appeared characteristically for selected energy and for selected center-of-mass scattering angle within the energy range (1-100) MeV, showed the excellent agreement with available experimental data and better than these resulted from global parameterizations of the alpha particles scattering potential.

Fragmentation analysis of 88Mo* compound nucleus in view of different decay mechanisms

In reference to the experimental data, the decay mechanism of 88Mo* compound system formed in 48Ti+40Ca reaction is investigated at three beam energies (Ebeam = 300, 450, and 600 MeV) using the collective clusterization approach of Dynamical Cluster decay Model (DCM). The calculations are done for spherical choice of fragmentation and with the inclusion of quadrupole (β2) deformations having “optimum” orientations. According to the experimental evidence 88Mo* decays via Fusion-Evaporation (FE) and Fusion-Fission (FF) processes, thus the decay cross-sections of this hot and rotating compound system are calculated for both channels. In FF decay mode, the explicit contribution of Intermediate Mass Fragments (IMF), Heavy Mass Fragments (HMF) and fission fragments (symmetric/asymmetric) is detected within DCM framework. The calculated FE and FF decay cross-sections find nice agreement with the available experimental data. Experimentally, it has been observed that the total contribution of FE and FF decay cross-sections is less than the total reaction cross-sections possibly due to the presence of some nCN component such as deep inelastic collisions (DIC), which generally contributes above critical angular momentum (ℓcr). The possibility of DIC contribution can be addressed as a future assignment in view of diminishing pocket of interaction potential above ℓcr.

Exploring experimental conditions to reduce uncertainties in the optical potential

Background: Uncertainty quantification for nuclear theories has gained a more prominent role in the field, with more and more groups attempting to understand the uncertainties on their calculations. However, recent studies have shown that the uncertainties on the optical potentials are too large for the theory to be useful. Purpose: The purpose of this work is to explore possible experimental conditions that may reduced the uncertainties on elastic scattering and single-nucleon transfer cross sections that come from the fitting of the optical model parameters to experimental data. Method: Using Bayesian methods, we explore the effect of the uncertainties of optical model parameters on the angular grid of the differential cross section, including cross section data at nearby energies, and changes in the experimental error bars. We also study the effect on the resulting uncertainty when other observables are included in the fitting procedure, particularly the total (reaction) cross sections. Results: We study proton and neutron elastic scattering on 48Ca and 208Pb. We explore the parameter space with Markov- Chain Monte Carlo, produce posterior distributions for the optical model parameters, and construct the corresponding 95% confidence intervals on the elastic-scattering cross sections. We also propagate the uncertainties on the optical potentials to the 48Ca(d,p)49Ca(g.s.) and 208Pb(d,p)209Pb(g.s.) cross sections. Conclusions: We find little sensitivity to the angular grid and an improvement of up to a factor of 2 on the uncertainties by including data at a nearby energy. Although reducing the error bars on the data does reduce the uncertainty, the gain is often considerably smaller than one would naively expect.

Systematic analysis of elastic α scattering on [formula omitted] nuclei around the Coulomb barrier

Alpha elastic scattering angular distributions on target nuclei 118, 124Sn and 120-130Te at energies near the Coulomb barrier are analyzed. We used three versions of the nuclear optical model potentials (OMP) to analyze twenty-nine data sets. JLM and the density and energy-dependent DDM3Y1 with finite range exchange term effective interactions were used to generate these potentials. Two real folded potentials based on JLM and DDM3Y1 effective interactions supplied with the conventional Wood–Saxon (WS) imaginary potential are used in the cross sections calculations. These potentials are denoted as JLM-R and DDM3Y1-FR, respectively. In addition, we used the full complex folded OMP, denoted as JLM-RI, to analyze the same data. These potentials successfully predict the cross section of the systems under study. We found that the JLM-R and DDM3Y1-FR could reproduce the measured cross sections over the full angular range very well compared to microscopic JLM-RI potential. Our calculated potentials have a clear energy dependence and in addition a weak target mass dependence. The total reaction cross section and volume integral are investigated in comparison to previous studies. The derived potentials are very promising for the construction of a new global α-nucleus potential and provide new parameters of α–induced reactions and scattering at the energy range 17–27 MeV.

An analysis of cross-sections of 9Be+28Si interaction in the framework of the double-folding model

In this paper the experimental data on the differential cross sections for elastic scattering of 9 Be ions on 28 Si nucleus at the energies of the incident nucleus ranging from 12 to 201.6 MeV were analyzed in the framework of the double folding model using the Paris NN-potential CDM3Y. A good agreement with the experimental angular distributions of differential cross sections for elastic scattering was obtained and the values of the total reaction cross sections were calculated. When the double folding potential was used as real and imaginary parts, no manifestation of the threshold anomaly was detected. The reason for such a behavior of the potential can be explained by the presence of break up and/or transfer channels at low energies.

6Li+28Si reaction cross sections at sub-barrier energies

Total reaction cross sections at near barrier energies (9-13 MeV) were measured for the system 6Li+28Si adopting a new technique. The results will be discussed in terms of the threshold anomaly at barrier

Analysis of Elastic 16O + 40Ca Refractive Scattering at 214 MeV

The elastic scattering of 16O+40Ca system at the incident energy 214 MeV has been analyzed within the optical model (OM) potential using the phenomenological Woods-Saxon (WS) and the real optical potentials calculated in two different versions of the folded model based upon the α-α effective interaction and CDM3Y6 effective nucleon-nucleon (NN) interaction. The new cluster Fermi three-parameter (3PFC) density distribution has been extracted to calculate the DFC1 potential. The Airy oscillation observed recently in the elastic 16O+40Ca system at Elab = 214 MeV is well reproduced by using the DFC1 potential without renormalization factor. The observed minimum around θ ≈ 46° in the angular distribution with DFC1 approach was shown to be an Airy minimum, probably of the third order (A3), which is in agreement with the previous study. The predicted volume integrals and total reaction cross section are consistent with the previous analyses. This reflects the success of our DFC1 potential to reproduce a nice description of the Airy structure for HI elastic scattering.

Total reaction cross sections of neutron-rich light nuclei measured by the COMBAS fragment-separator

Preliminary results of measurements of the total reaction cross sections σR for nuclei 4He, 6He, 8He, 7Li, 8Li, 9Li, 1Li, 11Be, 9Be, 10Be, 11Be, 12Be, 8B, 10B, 11B and 12B nuclei at energy range (10-50) A MeV with 28Si target is presented. The secondary beams of light nuclei were produced by bombardment of the 15N (50 A MeV) primary beam on Be target and separated by COMBAS fragment-separator. In dispersive focal plane a horizontal slit defined the momentum acceptance as 1% and a wedge degrader of 600 μm Al was installed. The Bρ of the second section of the fragment-separator was adjusted for measurements in energy range (10-45) A MeV. The strong absorption model reproduces the A-dependence of ψR, but not the detailed structure. We are comparing our experimental data with predictions of microscopic (dashed line) and strong absorption model, Glauber multiple scattering theory and preliminary results are obtained.

Energy dependence of total reaction cross sections for 17Ne on a proton target

We measured the energy dependence of the total reaction cross sections (σR) for the proton drip-line nucleus of neon isotopes, 17Ne, with a solid hydrogen target. The σR on a proton target in the low- and intermediate-energy regions were provided, where only a few values are available for unstable nuclei. The new data were compared with theoretical calculations using the Glauber model. In the low-energy region (∼100A MeV), the theoretical cross sections overestimate the experimental ones, whereas the theoretical ones significantly underestimate the experimental data in the intermediate energy region (∼300-500A MeV). We discuss several possibilities for solving this discrepancy. This work suggests the necessity of more careful investigations of the energy dependence of σR for various nuclei on a proton target to determine the nuclear size properties precisely.