Total Reaction Cross Sections Research Articles

Estimation of optical model parameters and their correlation matrix using Unscented Transform Kalman Filter technique

In the present study, we have optimized the optical model parameters and also calculated their correlation matrix using the Unscented Transform Kalman Filter technique for the first time. We have used n+56Fe, n+45Sc and n+59Co reactions for this study in order to verify the application of this method. We have used the experimental differential cross section data for the elastically scattered neutrons from the EXFOR data library and DWBA calculations to determine the parameters. In this study we have assumed that the optical model provides correct results and the uncertainties come from the variation of fitting parameters only. We have used the TALYS nuclear reaction code for the DWBA calculations. The optical model parameters determined through this study, reproduce the calculations which are consistent with the experimental trends for the elastically scattered neutrons and total reaction cross sections. Also the correlations calculated in this work are consistent with the earlier study of n+56Fe reaction.

The role of the tightly bound core in the refractive scattering of 17F+12C

The refractive scattering of 17F+12C is analyzed systematically by using the optical model with the cluster folding potentials. First of all, the applicability of the cluster folding approach is validated by analyzing the elastic scattering data of 13C+12C and 12C+12C at 20 A MeV. To perform the optical model calculations of 17F+12C, the less ambiguous optical potentials of 16O+12C and the global optical potential of p+12C are used to give the cluster folding potentials. Apart from the reproduction of the experimental data of the elastic scattering of 17F+12C at 10 A MeV, the Airy patterns are noticeable from about 10 to 40 A MeV. For comparison, the optical model calculations of 17O+12C at the same energies per nucleon are also performed through the cluster folding approach, of which the results are very similar to those of 17F+12C. For both 17F+12C and 17O+12C, the energy dependence of the Airy minima is extracted and compared with that in the case of 16O+12C. It is found that the Airy minima characteristic of 17F+12C is nearly identical with that of 17O+12C and similar to that of 16O+12C, which indicates the strong contributions from the 16O core to the appearance of the nuclear rainbow effects in 17F scattering. At last, the calculated total reaction cross sections are compared with the strong absorption model, which verifies the reasonableness of the present optical model calculations.

Determination of the asymmetry term strength in the n–A elastic scattering process using a nonlocal optical model

In previous works, the imaginary surface and (or) the imaginary volume depths of the optical potential were parametrized as linear functions of the projectile’s incident energy and neutron-proton asymmetry (N – Z)/A of the target nucleus. However, the obtained asymmetry strength parameters were not robust nor unique. In this work, we determine values for the strength parameters by simultaneously fitting 38 angular distribution data sets corresponding to neutron elastic scattering off chains of isotopes. For each isotopic chain, we considered the data sets that are measured at the same energy. This minimises the effect of the known energy dependence of the optical model and projects the dependence on the asymmetry term, which in turn leads to more reliable values of the strength parameters. To demonstrate the significance of the obtained strength values, we use the model to predict elastic angular distributions for neutron scattering off nuclei not considered in the χ2 analysis. Our theoretical angular distributions are in good agreement with the measured data and are also comparable to the predictions of local global models. In addition, our predicted total elastic and total reaction cross sections are in fair overall agreement with experiment. An additional result of this work is the determination of a global set of nonlocal parameters that describe neutron elastic scattering off nuclei that fall in the mass range 24 ≤ A ≤ 208 corresponding to incident neutron energies between ≈10–30 MeV.

Nucleon stripping in deuteron-induced spallation reactions at hundreds MeV/nucleon * *Supported by the National Natural Science Foundation of China under (11875328)

A nucleon-nucleus dynamics model was developed to investigate the proton-, neutron-, and deuteron-induced reactions at hundreds of MeV/nucleon. In this model, the trajectory of incident nucleon is described by classical mechanics, and the probability of reaction between the nucleon and nucleus is calculated by exponential damping. It is shown that the total reaction cross sections calculated by the model agree in general with the predictions by the CDCC and the experimental data. The model was applied to investigate the nucleon stripping in deuteron-induced reactions and its symmetry energy dependence.

Study of 6,8He+p elastic scattering at 25–73 MeV/nucleon

In this work, p-6,8He elastic scattering differential cross sections in the energy range 25 ∼ 73 MeV/nucleon have been studied by applying the Coulomb modified Glauber scattering formalism. Three different density distribution models for proton and neutron densities have been used in calculating the differential cross sections. With the Bhagwat, Gambhir and Patil (BGP) nuclear density model, the calculated rms matter radius for 6He is found to be 2.49 fm which is larger than the experimental value 2.33 ± 0.04 fm while, for 8He it comes out to be 2.47 fm which is close to the experimental value 2.45 ± 0.07 fm. In general, the comparative analyses of the elastic scattering cross sections with different density models indicate that the calculation with BGP model density is qualitatively more successful to reproduce the p-6,8He experimental data. We emphasize that within the analyses no adjustable parameters are employed to fit the available experimental data. By varying the parameters of the spin-dependent amplitude, a very close agreement has been obtained in a simultaneous χ 2-fitting to the polarization data for p-6He elastic scattering measured at 71 MeV/nucleon. The total reaction cross sections for p-6,8He at these energies have also been compared with the corresponding cross sections obtained reported in earlier studies.

Electric dipole response of low-lying excitations in the two-neutron halo nucleus F29

The neutron-rich $^{28,29}$F isotopes have been recently studied via knockout and interaction cross-section measurements. The $2n$ halo in $^{29}$F has been linked to the occupancy of $pf$ intruder configurations. We investigate bound and continuum states in $^{29}$F, focusing on the $E1$ response of low-lying excitations and the effect of dipole couplings on nuclear reactions. $^{29}\text{F}$ ($^{27}\text{F}+n+n$) wave functions are built within the hyperspherical harmonics formalism, and reaction cross sections are calculated using the Glauber theory. Continuum states and $B(E1)$ transition probabilities are described in a pseudostate approach using the analytical THO basis. The corresponding structure form factors are used in CDCC calculations to describe low-energy scattering. Parity inversion in $^{28}$F leads to a $^{29}$F ground state characterized by 57.5% of $(p_{3/2})^2$ intruder components, a strong dineutron configuration, and an increase of the matter radius with respect to the core radius of $\Delta R=0.20$ fm. Glauber-model calculations for a carbon target at 240 MeV/nucleon provide a total reaction cross section of 1370 mb, in agreement with recent data. The model produces also a barely bound excited state corresponding to a quadrupole excitation. $B(E1)$ calculations into the continuum yield a total strength of 1.59 e$^2$fm$^2$ up to 6 MeV, and the $E1$ distribution exhibits a resonance at $\approx$ 0.85 MeV. Results using a standard shell-model order for $^{28}$F lead to a considerable reduction of the $B(E1)$ distribution. The four-body CDCC calculations for $^{29}\text{F}+^{120}\text{Sn}$ around the Coulomb barrier are dominated by dipole couplings, which totally cancel the Fresnel peak in the elastic cross section. These results are consistent with a two-neutron halo and may guide future experimental campaigns.

Global study of Be9 + p at 2.72A MeV

Background: In our recent experiment, $^9$Be+p at 5.67A MeV, the breakup decay rates to the 3 configurations, $\alpha$+$\alpha$+n, $^8$Be$^*$+n and $^5$He+$^4$He of $^9$Be, were observed and quantified, in a full kinematics approach. Unfolding step by step the accessibility to the above configurations, it will require similar studies at lower and higher energies as well as the interpretation of the data in a theoretical framework. Purpose: Investigate the breakup decay rate of $^9$Be+p at 2.72A MeV, where the $\alpha$+$\alpha$+n configuration is mainly accessible. Compare and interpret data at 2.72A MeV and 5.67A MeV into a 4-body CDCC formalism; Point out and discuss couplings to continuum. Methods: Our experimental method includes an exclusive breakup measurement in a full kinematic approach of $^9$Be incident on a proton target at 2.72A MeV, together with elastic scattering and other reaction channels measurements under the same experimental conditions. The interpretation of the data at 2.72A MeV and 5.67A MeV is considered in a 4-body CDCC approach, using the Transformed Harmonic Oscillator method for the 3-body projectile. Results: An elastic scattering angular distribution at 2.72A MeV is measured, which compares very well with CDCC calculations, indicating a strong coupling to continuum. At the same energy, the measured breakup and total reaction cross sections present good agreement with the calculated values. Further on, the elastic scattering and breakup cross section data at 5.67A MeV are found in very good agreement with the CDCC calculations. The present results support further our 3-body model for the structure of $^9$Be, validating relevant radiative reaction rates obtained previously.

Recent results on heavy-ion induced reactions of interest for neutrinoless double beta decay at INFN-LNS

The NUMEN project aims at accessing experimentally driven information on Nuclear Matrix Elements (NME) involved in the half-life of the neutrinoless double beta decay (0νββ). In this view measurements of Heavy Ion (HI) induced Double Charge Exchange (DCE) reaction cross sections are performed with high-accuracy. In particular, the (18O,18Ne) and (20Ne,20O) reactions are used as tools for β+β+ and β-β- decays, respectively. In the experiments, performed at INFN - Laboratory Nazionali del Sud (LNS) in Catania, the beams are accelerated by the Superconducting Cyclotron (CS) and the reaction ejectiles are detected the MAGNEX magnetic spectrometer. The measured cross sections are challengingly low (a few nb), being the total reaction cross section much larger (a few b), thus a high sensitivity and a large rejection capability are demanded to the experimental set-up. This limits the present exploration to few selected isotopes of interest in the context of typically low-yield experimental runs. A major upgrade of the LNS facility is under way in order to increase the experimental dataset of more than two orders of magnitude, still preserving the high sensitivity of the present set-up. When accomplished this effort will make the INFN-LNS as the state-of-the-art research infrastructure for the systematic study of all the cases of interest for 0νββ. In this view, frontiers technologies are going to be adopted for the accelerator and the detection systems. In parallel, advanced theoretical models are being developed in order to extract the nuclear structure information from the measured cross sections.

Measurements of total reaction cross sections for 17Ne using a solid hydrogen target

We measured the energy dependence of the total reaction cross sections (σR) for the proton-drip-line nucleus,17Ne, using a solid hydrogen target. We compared the experimental data with theoretical calculations using the Glauber model. We found that the theoretical cross sections overestimate the experimental ones in the low-energy region (∼100A MeV), whereas they significantly underestimate the experimental data in the intermediate-energy region (∼300-500A MeV). These trends are the same as those for σR for carbon-proton collisions, which were measured previously. We discuss several possibilities for resolving this discrepancy. This work demonstrates the necessity of additional careful investigations of the energy dependence of σR for various nuclei on proton targets in order to determine nuclear size properties precisely.

Total reaction cross section on a deuteron target and the eclipse effect of the constituent neutron and proton

Background: Eclipse effect of the neutron and proton in a deuteron target is essential to correctly describe high-energy deuteron scattering. The nucleus-deuteron scattering needs information not only on the nucleus-proton but also the nucleus-neutron interaction, for which no direct measurement of the nucleus-neutron cross sections is available for unstable nuclei. Purpose: We systematically evaluated the total reaction cross sections by a deuteron target to explore the feasibility of extracting the nucleus-neutron interaction from measurable cross sections. Methods: High-energy nucleus-deuteron collision is described by the Glauber model, in which the proton and neutron configuration of the deuteron is explicitly taken into account. Results: Our calculation reproduces available experimental total reaction cross section data on the nucleus-deuteron scattering. The possibility of extracting the nucleus-neutron total reaction cross section from nucleus-deuteron and nucleus-proton total reaction cross sections is explored. The total reaction cross sections of a nucleus by proton, neutron, and deuteron targets can be expressed, to good accuracy, in terms of the nuclear matter radius and neutron skin thickness. Incident-energy dependence of the total reaction cross sections is examined. Conclusions: The total reaction cross section on a deuteron target includes information on both the nucleus-neutron and nucleus-proton profile functions. Measuring the cross sections by deuteron and proton targets is a promising tool to extract the nuclear size properties.

The total reaction cross section of heavy-ion reactions induced by stable and unstable exotic beams: the low-energy regime

In this review paper we present a detailed account of the extraction and the calculation of the total reaction cross section of strongly bound and weakly bound, stable and unstable, exotic, nuclei. We discuss the optical model and the more general coupled channels model of direct reactions. The effect of long-range absorption due to the coupling to excited states in the target and to the breakup continuum in the projectile is also discussed. The generalized optical theorem for charged particle scattering and the resulting sum-of differences method is then discussed. The so-called "quarter-point recipe" is discussed next, and the quarter-point angle is introduced as a simple and rapid mean to obtain the total reaction cross section. The last topic discussed is the reduction of the total reaction cross section that would allow a large body of data to sit on a single universal function. Such a universal function exists in the case of the fusion data, and the aim of this last topic of the review is to extend the fusion case to the total reaction, by adding the direct reaction contribution. Also discussed is the inclusive breakup cross section and how it can be used to extract the total reaction cross section of the interacting fragment with the target. This method is also known as the Surrogate method and represents a case of hybrid reactions. The sum of the integrated inclusive breakup cross section with the complete fusion cross section supplies the total fusion cross section. The main experimental methods to determine the total reaction cross section are also discussed, with emphasis in recent techniques developed to deal with reactions induced by unstable beams.

Global optical model potential describing 12C-nucleus elastic scattering * *Supported by China National Natural Science Foundation (11405099, 11575291, 12065003), by Scientific and Technological Innovation Programs of Higher Education Institutions (STIP) in Shanxi of China (2019L0743) and by Science Foundation for General in Shanxi of China (201901D111317). This work is also a part of IAEA Coordinated Research Projects (CRPs) on Recommended

We construct a new global optical model potential to describe the elastic scattering of 12C. The experimental data of elastic-scattering angular distributions and total reaction cross sections for targets from 24Mg to 209Bi are considered below 200 MeV within the framework of the optical model. The results calculated using the derived global optical potential are then compared with the existing experimental data. The reliability of the global optical potential is further tested by predicting the elastic scattering data out of the mass and energy ranges, within which the global potential parameters are determined, and reasonable results are also obtained.

Fermi motion and medium effects on reaction cross sections of 13,14,15B + C, Al at intermediate and high energies

Analysis of reaction cross sections of [Formula: see text] are performed with Glauber model (GM) including medium modifications arising from Fermi motion and in-medium nucleon–nucleon (NN) total reaction cross section. The density distributions of Boron isotopes are described by a deformed-average Fermi shape, whose proton and neutron radii and deformation parameters are derived from relativistic mean field (RMF), harmonic oscillator (HO) and two-parameter Fermi (2pF). These densities can describe the reaction cross section of Boron isotopes except for [Formula: see text] which is better described by an HO core plus extended Gaussian (HOG) or HO plus a modified Yukawa (HOMY) tail, which depends on the 1n separation energy. It is found that Fermi motion effects dominated at intermediate energy, and they are important to describe the data in addition to in-medium effects. In-medium effects, which are incorporated locally, reduced the reaction cross section by about 3–5% at all energies. [Formula: see text] is confirmed as a one-neutron halo nucleus, where a large extended tail is observed in the extracted HOMY and HOG model densities as well as in the extracted radii, where the matter radius of [Formula: see text] is found to be about 2.92 fm, which is larger than that of [Formula: see text] (2.5 fm) and [Formula: see text] (2.82 fm) predicted using the GM model including Fermi motion and in-medium effects.

Nuclear reaction cross sections for hadron therapy

Treatment planning in hadron therapy uses Monte Carlo techniques that require total nuclear reaction cross sections for a variety of interacting systems and over a wide range of energies. Current empirical models are tuned to reproduce cross sections for stable isotopes, but in some cases, overestimate measured cross sections by 20%. Here we discuss an alternative approach: the optical limit of Glauber theory, which describes existing measurements better and offers more reliable predictions for the many systems where there is no experimental information. We also suggest how existing implementations of empirical models within GEANT4 could be improved. Ultimately, these calculations should contribute to improvements in planning of hadron therapy treatments.

Experimental Measurement Method of Beta Decay Strength of Unstable Nuclei

The β decays of atomic nuclei refer to the transformation that the nuclei emit a β particle or capture an electron. The accurate measurements of the β transition strength functions Sβ(E) are of great significance in exploring the structure of unstable nuclei, revealing the process of stellar nucleosynthesis and also verifying the β decay theories. Experimentally, one way to determine the β transition strength is to directly measure the beta decay product using β-γ coincidence technique and/or total absorption spectroscopy. This method can give the transition information within the Qβ window. Another method to obtain the β decay strength is via the charge exchange reactions performed at the intermediate energy region (100~400 MeV/u), such as (p, n) or (3He, t). This is done by a high-precision measurement of the differential cross section. This method allows to access the transition strength that beyond the Qβ window, however, it is restricted by the beam intensity, and as a consequence hard to perform a systematical study of unstable nucleus with low yields. In view of this, in this paper we proposes a systematic measurement of the total charge exchange reaction cross section of the unstable nuclei. Combined with the well developed nuclear reaction theory, this method may set a constrain to the summed strength of the Gamow-Teller transition of the unstable nuclei within the proton separation threshold. Moreover, we introduce briefly the relevant work that has been carried out and planned.

Utility of antiproton-nucleus scattering for probing nuclear surface density distributions

Antiproton-nucleon ($\bar{p}N$) total cross sections are typically 3-4 times larger than the $NN$ ones at incident energies from a few hundreds to thousands MeV. We investigate antiproton-nucleus scattering as it could work as a probe of the nuclear structure giving the sensitivity differently from a proton probe. High-energy antiproton-nucleus reactions are reasonably described by the Glauber model with a minimal profile function that reproduces the $\bar{p}N$ and $\bar{p}$-$^{12}$C cross section data. In contrast to the proton-nucleus scattering, we find that the complete absorption occurs even beyond the nuclear radius due to the large $\bar{p}N$ elementary cross sections, which shows stronger sensitivity to the nuclear density distribution in the tail region. This sensitivity is quantified in the total reaction cross sections with various density profiles for future measurement including neutron-rich unstable nuclei.

Ab Initio-Based Global Potential Energy Surface and Reaction Dynamics for H2S + C

Dynamics of the reaction of hydrogen sulfide, H2S(X1A1), with ground state atomic carbon, C(3Pj), was investigated over the interpolated ab initio based potential energy surface using the quasi-classical trajectory (QCT) simulation. The reaction probability and total reactive cross section were calculated at wide range of collision energies from 2.6 kJ mol-1 to 78.8 kJ mol-1. The total rate constant of the reaction was calculated using collision theory. The energy distribution for the formation of main products (HCS/HSC + H) were also investigated. At 44.6 kJ mol-1 collision energy approximately 39.5% and 12% of total available energy release to translational and rotational energy levels of the HCS + H products, respectively, while for HSC + H these values were found to be about 61.6% and 25.7% of total available energy. The rest of total energy deposited in the vibrational modes of the products.

Total Reaction Cross Sections for 6,8He and 9Li Nuclei on 28Si, 59Co, and 181Ta Targets

Experiments with 6,8He, 9Li + 28Si, 59Co, and 181Ta reactions in the energy range of 6,8He and 9Li beams 6–36 A MeV have been preformed. Prompt neutrons and gamma radiation were registered by a 12‑detector gamma spectrometer. The values of the total reaction cross sections and the multiplicity distributions for the emission of γ-quanta and neutrons were calculated taking into account the distributions over the number of triggered detectors.

A nonlocal optical potential with a Gaussian nonlocality for proton elastic scattering off light 1p-shell nuclei

In a recent work we used the nonlocal optical model of Perey and Buck (Nucl Phys A 32:353, 1962) to fit the angular distribution data corresponding to neutron elastic scattering off light nuclei from $$^6\hbox {Li}$$ to $$^{18}\hbox {O}$$ over the 9–35 MeV energy range. Although such nuclei posses diffuse edges that complicate the scattering process, the model resulted in improved angular distribution fits compared to those obtained using local optical models. In this work we extend the treatment to the case of proton elastic scattering off light 1p-shell nuclei, but consider the wider 10–70 MeV energy range. No single global set of nonlocal parameters adequately described the measured data across the entire energy range. Instead, we obtained two global sets of fixed nonlocal parameters; one corresponds to the 10–39 MeV range, the other is for the higher 40–70 MeV incident energies. Each set resulted in angular distribution fits which are in very good agreement with experimental data even in the large-angle scattering region, which is usually endowed by nonlocal effects. The fits were improved even further by expressing the imaginary volume and imaginary surface depths as linear functions of energy and the $$(N-Z)/A$$ asymmetry term. This indicates that there is still need for energy-dependent parameters even when nonlocality is explicitly included in the potential. We also used the model to predict elastic angular distributions for proton scattering off nuclei not included in the fitting procedure. The theoretical predictions showed very good agreement with experiment. As a further test of the nonlocal model, we calculated total reaction cross sections for proton scattering off light 1p-shell nuclei. Our predictions are in fair overall agreements with the experimental data.

Theoretical investigation of the CS + OH → Products reaction on an interpolated potential energy surface: reaction dynamic and chemical kinetic insights

An interpolated potential energy surface to describe the gas phase CS+OH reaction has been constructed by quantum chemical ab-initio data. Quasi-classical trajectory simulations are applied to calculate the probability of reaction. To obtain the physical observable parameters such as thermal rate constant and cross-section, the reaction probability is used. These calculations upon this interpolated surface illustrate that the total rate coefficient is close to that reported by Loison et al. The total reaction cross-section and corresponding reaction probability with respect to the relative translation energy of all species over a range of 2.63 to 170.66 kJ mol−1 are investigated as well. In addition, the effect of the impact parameter and relative translational energy of fragments on the reaction probability, average angular momentum, and scattering angle was studied. Depending on the orientation of reactant molecules, for the title reaction, two different channels were found. First, the OH radical comes close to the CS fragments and leads to formation of trans-HOCS with − 198.68 kJ mol−1 energy relative to the reactants’ total energy. Next, the C atom abstracts the oxygen of OH radical through a saddle point to generate the carbonyl sulfide with 45.31 kJ mol−1 barrier energy.