Total Reaction Cross Sections Research Articles

Measurements of Total Cross Sections for Reactions with Weakly Bound Nuclei Using a 4π Scintillation Spectrometer

Measurements of Total Cross Sections for Reactions with Weakly Bound Nuclei Using a 4π Scintillation Spectrometer

Modeling of Deuteron-Induced Reactions on Molybdenum at Low Energies

The activities of the EUROfusion consortium on the development of high quality nuclear data for fusion applications include evaluations of deuteron induced reactions and related data libraries for needs of the DEMO fusion power plant and IFMIF-DONES neutron-source nuclear analyses. Molybdenum is one of the major constituents of the reference stainless steels used in critical components of these projects. While the TENDL deuteron data library was the current reference used by EUROfusion, need of its further improvement has already been pointed out. The weak binding energy of the deuteron is responsible for the high complexity of its interaction with nuclei, involving also a variety of reactions initiated by the nucleons following the deuteron breakup. Their analysis completed that of the deuteron interactions with Mo and its stable isotopes, from elastic scattering to pre-equilibrium and compound–nucleus reactions, up to 50 MeV. A particular attention has been paid to the breakup, stripping, and pick-up direct interactions which amount to around half of the deuteron total–reaction cross section. The due account of most experimental data has validated the present approach, highlighted some prevalent features, and emphasized weak points and consequently the need for modeling/evaluation upgrade.

Investigation of breakup process in 9Be(α,n)12C reaction

Neutron energies and angular distributions were measured in 9Be(α,n)12C reaction for α energies of 5.5 and 6.5 MeV. Three major neutron groups were observed in the spectrum, which correspond to the ground and first two excited states of 12C. Measured data could only be explained by the TALYS calculation if reaction at more than one location within the target is considered for a given beam energy. The preferred locations are driven by the resonance energy levels existing in 13C. Neutron yield due to the 9Be breakup process was determined which is found to be 12.6 ± 0.2% and 18.4 ± 0.5% of the total reaction cross-section for 5.5 and 6.5 MeV respectively.

Comparative study of alpha scattering from various nuclei at 130 MeV: Microscopic potentials and coupled channel calculations

The angular distributions of the elastic and inelastic scattering cross sections of alpha projectiles on different heavy ion target nuclei including 12C, 16O, 24Mg, 28Si and 40Ca at energy of 130 MeV have been studied using two different microscopic real potentials generated by the energy density functional (EDF) theory, and single folding cluster model as well as phenomenological Woods-Saxon potentials. A new parameterization was considered for the first time by EDF and to make the normalization coefficient tend to unity, it is necessary to consider correction to the calculated real potential. Coupled channel calculations for various low-lying states were performed, and the best fit values for the deformation length with the above models were extracted by fitting the inelastic scattering cross section and compared to previous work values. The total reaction cross section, as well as the real and imaginary volume integrals, have been studied.

Nuclear radii from total reaction cross section measurements at intermediate energies with complex turning point corrections to the eikonal model

Nuclear radii from total reaction cross section measurements at intermediate energies with complex turning point corrections to the eikonal model

Construction of density-dependent α-nucleon interaction to describe α-nucleus scattering

We provide a global density-dependent α-nucleon (DD-αN) interaction to construct the α-nucleus optical potential in a wide range of incident energies. The α-nucleus potential based on the folding model with the present DD-αN interaction reproduces the experimental data up to backward angles using the point-nucleon density obtained by the mean-field model. The present DD-αN interaction is based on the phenomenological optical potential to reproduce the p + 4He elastic scattering at the incident energies at 12.04–1000 MeV. Namely, the α-nucleon system is considered an elementary process. The density dependence (medium effect) of the DD-αN interaction is phenomenologically added to reproduce the α elastic scatterings by the 16O, 40Ca, 58Ni, 90Zr and 208Pb targets at E/A = 10–342.5 MeV. The total reaction cross sections are also compared with the experimental data.

Breakup of 8B+natZr at the sub-barrier energy of 26.5 MeV

In our systematic research on reactions with weakly bound nuclei at suband nearbarrier energies, we have studied the system 8B+natZr at the sub-barrier energy of 26.5 MeV. Our measurements, performed at the TriSol radioactive beam facility of the University of Notre Dame, include angular distributions of both elastic scattering and breakup, for the determination of the total reaction and breakup cross sections as well as the direct-to-total reaction cross section ratio. Preliminary results of the breakup analysis will be presented, supported by Continuum Discretized Coupling Channel calculations.

Global density-dependent α–nucleon interaction for α–nucleus elastic scattering

Abstract We provide a global density-dependent 4He–nucleon (DD-αN) interaction to construct the α–nucleus optical model potential (OMP) across a wide range of incident energies. The global parametrization for the DD-αN interaction is obtained based on the proton–4He OMP, which reproduces the elastic scattering cross-section data very well in the incident energies of 12.04–500 MeV per nucleon. Using the present DD-αN interaction, we derive the α–nucleus potential by a folding procedure with the point-nucleon density obtained by a microscopic mean-field model. The density dependence of the DD-αN interaction is fixed phenomenologically to reproduce the α–nucleus elastic scattering cross-section data obtained from 16O, 40Ca, 58Ni, 90Zr, and 208Pb targets at E/A = 10–342.5 MeV. We also show the total reaction cross sections, which are helpful in fixing one free parameter, the renormalization factor for the imaginary part of the α–nucleus potential. Lastly, we show some examples, which clearly demonstrate the validity and power of the present DD-αN approach.

NUCLEAR STRUCTURE STUDY OF THE HALO NUCLEI

The existence of halo nuclei is one of the major important discoveries in the field of nuclear physics. These nuclei are treated as loosely bound system in which a core of normal nuclear density is surrounded by so-called neutron (or proton) halo of diluted nuclear matter. Many theoretical investigations have attempted to understand these nuclei, which exist at light to heavy masses. The phenomenon of nuclear halo is a quantum effect that occurs in nuclei due to the presence of valence nucleons with low separation energy and I = 0, 1 (low angular momentum), and is manifested by the extraordinarily large radii of these nuclei. The core plus halo model is commonly used to describe halo nuclei. This model recognizes the need to treat the core and the halo neutrons or protons separately. By considering different model spaces for the core and the halo nucleons, we can better explain the properties of halo nuclei. This separation is justified by the fact that the valence nucleons in a halo nucleus have different properties compared to the core. Halo nuclei at rest cannot be used as target due to their short-lived species and extraordinary ratio of neutrons and protons (either neutron-rich or proton-rich). Instead, they can be studied through direct reactions with a radioactive isotope beam, employing inverse kinematics where the role of the beam and target are exchanged. In order to investigate the charge and matter densities of these nuclei, total and differential reaction cross section analyses of proton scattering on halo nuclei have been carried out using various theoretical and phenomenological methods

Peripheral reactions and elastic scattering induced by strongly bound, weakly bound and exotic nuclei

A phenomenological study of peripheral reactions induced by strongly bound, weakly bound and exotic projectiles on different targets is presented. A large number of experimental elastic scattering differential cross sections at energies close to the Coulomb barrier is studied on the basis of a simple nuclear optical model potential that depends on a small number of parameters. The derived wave functions, together with the imaginary component of the optical potential, allow the analysis of the radial peripheral absorption density distributions for the different kind of projectiles. These distributions, when appropriately normalized, show a clear correlation with the type of projectile regardless of the involved target and indicate that projectiles more prone to break up show a more peripheral absorption density distribution. This manifests in their magnitude, location and width. The relationship of these variables in the strongly bound group and the weakly bound group are described with a simple exponential function, while the exotic projectiles show two distinct groups, namely the neutron-halo and the proton-halo. For the neutron-halo projectiles such as He6, Li11 and Be11 there is a notable increment of the radial peripheral absorption density peak and the total reaction cross section as the breakup separation energy decreases. The same relationship is established for the proton-halo projectiles B8 and F17 but their reduced effective dipole charge leads to a lower probability of dipole Coulomb breakup that results in a substantial reduction in the extent of their peripheral absorption.

Elastic scattering and total reaction cross sections of 6Li examined via a microscopic continuum discretized coupled-channels model* *Supported by the National Natural Science Foundation of China (U2067205)

We present a systematic study of 6Li elastic scattering and total reaction cross sections at incident energies around the Coulomb barrier within the continuum discretized coupled-channels (CDCC) framework, where 6Li is treated in an α+d two-body model. Collisions with 27Al, 64Zn, 138Ba, and 208Pa are analyzed. The microscopic optical potentials (MOP) based on Skyrme nucleon-nucleon interaction for α and d are adopted in CDCC calculations and satisfactory agreement with the experimental data is obtained without any adjustment on MOPs. For comparison, α and d global phenomenological optical potentials (GOP) are also used in CDCC analysis and a reduction of no less than 50% on the surface imaginary part of deuteron GOP is required for describing the data. In all cases, the 6Li breakup effect is significant and provides repulsive correction to the folding model potential. The reduction on the surface imaginary part of GOP of deuteron reveals a strong suppression of the reaction probability of deuteron as a component of 6Li when compared with that of a free deuteron. Further investigation is performed by considering the d breakup process equivalently within the dynamic polarization potential approach, and the results show that d behaves in a manner similar to a tightly bound nucleus in 6Li induced reactions.

Vibrational, non-adiabatic and isotopic effects in the dynamics of the H2 + H2 + → H3 + + H reaction: application to plasma modelling

The title reaction is studied using a quasi-classical trajectory method for collision energies between 0.1 meV and 10 eV, considering the vibrational excitation of H 2 + reactant. A new potential energy surface is developed based on a Neural Network many body correction of a triatomics-in-molecules potential, which significantly improves the accuracy of the potential up to energies of 17 eV, higher than in other previous fits. The effect of the fit accuracy and the non-adiabatic transitions on the dynamics are analysed in detail. The reaction cross section for collision energies above 1 eV increases significantly with the increasing of the vibrational excitation of H 2 + ( v ′ ), for values up to v ′ =6. The total reaction cross section (including the double fragmentation channel) obtained for v ′ =6 matches the new experimental results obtained by Savic, Schlemmer and Gerlich [Chem. Phys. Chem. 21 (13), 1429.1435 (2020). doi:10.1002/cphc.v21.13]. The differences among several experimental setups, for collision energies above 1 eV, showing cross sections scattered/dispersed over a rather wide interval, can be explained by the differences in the vibrational excitations obtained in the formation of H 2 + reactants. On the contrary, for collision energies below 1 eV, the cross section is determined by the long range behaviour of the potential and do not depend strongly on the vibrational state of H 2 + . In addition in this study, the calculated reaction cross sections are used in a plasma model and compared with previous results. We conclude that the efficiency of the formation of H 3 + in the plasma is affected by the potential energy surface used.

First near-threshold measurements of the C13(α,n1)O16 reaction for low-background-environment characterization

The modeling of background sources in large volume detection systems requires accurate nuclear cross sections for a variety of reactions. Among the most important are $(\ensuremath{\alpha},n)$ on light nuclei, where $\ensuremath{\alpha}$ particles, up to $\ensuremath{\approx}9$ MeV, are produced from the decay of actinides present in trace amounts in detection and structural material. In order to model the neutron energy spectra and production of other secondary particles, the partial cross sections are needed. Yet very little experimental data exists for these partial cross sections because past measurements, hampered by the experimental challenges of neutron detection, have focused mostly on total reaction cross section measurements. Here the partial cross section of the $^{13}\mathrm{C}(\ensuremath{\alpha},{n}_{1})^{16}\mathrm{O}$ reaction is reported for the first time. The measurements were made near the reaction threshold using a high energy resolution helium spectrometer. The measurements show a rapidly increasing cross section, which quickly becomes a significant fraction of the total reaction cross section. Measurements are compared with previous theory estimates and differences of more than an order of magnitude are found. A comparison is made with new total cross section measurements and the current level of consistency is demonstrated.

Nuclear charge radii of Cr46–62 isotopes and reaction cross sections for p−Cr

The nuclear charge radii and density distributions for $^{46--62}\mathrm{Cr}$ have been calculated in the frameworks of both relativistic and nonrelativistic self-consistent mean-field models. The relativistic Hartree-Bogoliubov model with density-dependent meson-exchange functional DD-ME2 and the nonrelativistic Hartree-Fock-Bogoliubov model with the Gogny D1S interaction, hereafter referred to as DIRHB and HFB, respectively, are used to compute ground-state properties of even $^{46--62}\mathrm{Cr}$ isotopes. Both calculations for the root-mean-squared charge radii reveal the characteristic kink at the $N$ = 28 shell closure in accordance with the corresponding experimental radii. The point proton and neutron density distributions calculated from both DIRHB and HFB are used to obtain the optical potentials for $p$-Cr at an incident proton energy of 65 MeV. The elastic scattering differential and total reaction cross sections, computed from the semimicroscopic proton optical potentials, have been derived by folding each of the target matter densities with the Jeukenne-Lejeune-Mahaux-Bruye\ifmmode \acute{r}\else \'{r}\fi{}es (JLMB) energy- and density-dependent internucleon interaction. The calculated elastic scattering differential cross sections for stable even isotopes, $^{50,52,54}\mathrm{Cr}$, using the respective DIRHB and HFB densities in the folding model reproduce the corresponding cross-section data well. The correlation between root-mean-squared charge radii and nuclear reaction observables obtained from the DIRHB and HFB calculations have been used in the folding model approach to predict the reaction cross sections for $p\text{\ensuremath{-}}^{46--62}\mathrm{Cr}$ at an incident proton energy of 65 MeV.

Role of neutron transfer in the reaction mechanism of 9Be+169Tm, 181Ta, 187Re and 197Au systems

The contribution of one neutron stripping cross section to the total reaction cross section has been studied for 9Be projectile incident on 169Tm, 181Ta, 187Re and 197Au targets around Coulomb barrier energy. The measured one neutron stripping cross sections for these systems have been compared with the coupled channel calculations. The recently developed global set of optical model potential parameters for 9Be projectile has been used in the present calculations. The cumulative of measured complete fusion (CF), incomplete fusion (ICF), one neutron stripping and calculated non-capture breakup (NCBU) cross sections is found to explain almost the reaction cross sections for all the targets. A very small contribution from target inelastic states and elastic breakup may contribute to the remaining part. The percentage fraction of cross section for CF, ICF, one neutron stripping, and NCBU over reaction cross section show the dominance of neutron transfer and NCBU at below barrier energies while CF and ICF processes have the major contribution at above barrier energies.

Quasielastic scattering of light radioactive and stable projectiles on Be9

Quasielastic scattering angular distributions of radioactive $(^{8}\mathrm{Li},$ $^{7,10}\mathrm{Be}, \mathrm{and} ^{8,12}\mathrm{B})$ and stable $(^{6,7}\mathrm{Li},$ $^{9}\mathrm{Be}, \mathrm{and} ^{11}\mathrm{B})$ projectiles on a $^{9}\mathrm{Be}$ target are presented. The angular distributions have been analyzed by the optical model using Woods-Saxon form factor and S\~ao Paulo potential. Total reaction cross sections have been obtained from the optical model analysis and a comparison between different systems is presented. Coupled channels (CC), coupled reaction channels (CRC), and continuum-discretized coupled channels (CDCC) calculations have been performed to investigate the effect of the cluster configuration in the projectile inelastic excitation, breakup, and stripping reactions on the quasielastic angular distributions.

Density profiles near the nuclear surface of Ti44,52 : An indication of α clustering

We investigate the degree of $\alpha$ ($^4$He nucleus) clustering in the ground-state density profiles of $^{44}$Ti and $^{52}$Ti. Two types of density distributions, shell- and cluster-model configurations, are generated fully microscopically with the antisymmetrized quasi-cluster model, which can describe both the j-j coupling shell and $\alpha$-cluster configurations in a single scheme. Despite both the models reproducing measured charge radius data, we found that the $\alpha$ clustering significantly diffuses the density profiles near the nuclear surface compared to the ideal j-j coupling shell model configuration. The effect is most significant for $^{44}$Ti, while it is less for $^{52}$Ti due to the occupation of the $0f_{7/2}$ orbits in the $^{48}$Ca core. This difference can be detected by measuring proton-nucleus elastic scattering or the total reaction cross section on a carbon target at intermediate energies.

The calculation of light element impurity ([formula omitted], n) yield curves in a PuO[formula omitted] matrix and associated specific yield coefficients: Influence of the reaction cross sections

Most of the Pu separated from irradiated commercial nuclear fuel is stored as PuO 2. The primary quantitative nondestructive measurement technique used to verify the amount of Pu in storage containers is passive neutron correlation counting. An important physical property of the oxide material is the ratio, α, of the rate of (α, n) neutrons produced inside the item to the rate of neutrons produced by spontaneous fission. This ratio influences the precision of the correlated counting method and affects the interpretation of the data because of how it changes both the primary total neutron production rate and the rate of induced fission events taking place inside the item. In addition to the main O(α, n) contribution, additional contributions come from α-particle interactions with light element impurities that are inevitably present. In this work, we calculate specific (α, n) yield coefficients, expressed in units of neutrons per second per gram of α-emitting nuclide per part per million by mass of the specified impurity element distributed in a pure PuO 2 matrix, for some key α-emitting actinides commonly present in reprocessed Pu (238–242Pu+241Am). These coefficients are directly applicable to nuclear safeguards verification work in which the α ratio is often calculated from the Pu-isotopic composition and chemical information obtained by other means. They also provide a convenient up-to-date reference set against which values generated by other methods can be compared. Results are presented for impurities with atomic number from 3 to 17 inclusive, plus K and Fe. In most cases, these coefficients are not expected to change by more than 5%–10% at any time in the future. However, as new data become available, changes as large as 20% may be needed for some targets (e.g., F). The present yield calculations are limited by the general shortage of quality experimental total (α, n) reaction cross section data, which, together with unexplained variation between determinations, means that an objective and coherent evaluation is not possible. The situation is even less satisfactory for the partial differential cross section needed to calculate neutron spectra.

Analysis of 4,6,8He+208Pb elastic scattering at E=22 MeV using various potentials

Using phenomenological and microscopic potentials, the experimental angular distributions for the 4,6,8He nuclei elastically scattered from a 208Pb target at are investigated. Both the modified version of CDM3Y6 interaction based on the inclusion of the rearrangement term (RT) and those obtained from the Sao Paulo Potentials are used for the microscopic potentials. The cluster folding potential for 6He+208Pb is calculated using the triton + triton cluster structure for 6He. This analysis revealed that the real cluster folding potential strength must be reduced by about 90%. Using the extracted potentials, the total reaction cross sections were successfully reproduced.

Study of elastic and inelastic scattering of 7Be + 12C at 35 MeV

The elastic and inelastic scattering of 7Be from 12C have been measured at an incident energy of 35 MeV. The inelastic scattering leading to the 4.439 MeV excited state of 12C has been measured for the first time. The experimental data cover an angular range of θcm = 15∘-120∘. Optical model analyses were carried out with Woods-Saxon and double-folding potential using the density dependent M3Y (DDM3Y) effective interaction. The microscopic analysis of the elastic data indicates breakup channel coupling effect. A coupled-channel analysis of the inelastic scattering, based on collective form factors, shows that mutual excitation of both 7Be and 12C is significantly smaller than the single excitation of 12C. The larger deformation length obtained from the DWBA analysis could be explained by including the excitation of 7Be in a coupled-channel analysis. The breakup cross section of 7Be is estimated to be less than 10% of the reaction cross section. The intrinsic deformation length obtained for the 12C⁎ (4.439 MeV) state is δ2 = 1.37 fm. The total reaction cross section deduced from the analysis agrees very well with Wong's calculations for similar weakly bound light nuclei on 12C target.